Applied Science, Faculty of
Engineering, School of (Okanagan)
DSpace
UBCO
Saif, Mohammed
Doctor of Philosophy - PhD
University of British Columbia
Cooperation is a key enabler for delivering popular contents to users in today's centralized wireless communication networks where the cloud-computing base station (CBS) is connected with low power base-stations, also named as remote radio heads (RRHs), via fronthaul links. The performance of today's wireless communication networks is constrained by the scarcity of radio resources and limited-capacity of fronhaul links. Edge caching (EC) is a powerful networking technique, where popular contents are cached in the edge nodes, that reduces the burden on fronthaul links. State-of-the-art literature on content delivery focuses on allocating a single user to each radio resource-block (RRB). However, this needs a large numbers of RRBs to satisfy the tremendous increase in the number of users. Consequently, network coding (NC) is employed to mix users' contents and simultaneously allocate different users to the same RRB. This dissertation designs innovative NC schemes for effective resource allocation in cache-enabled 5G networks, where the goal is to optimize different metrics, such as throughput, CBS offloading, and completion time. We first study the cross-layer throughput maximization problem in cloud-radio access network (C-RAN). For this problem, we develop novel cross-layer NC (CLNC) frameworks that propose to optimize RRHs' transmit powers and users' rates in making the coding decisions. Subsequently, we study CBS offloading and users' quality of service (QoS)-guarantee trade-off for fog-RAN system subject to the cached contents, the required minimum rate, power control, and NC constraints. Next, we focus on developing NC schemes for device-to-device (D2D)-aided F-RAN system. The developed NC schemes exploit the aforementioned F-RAN's optimization factors and potential D2D communications to minimize the completion time of users. Finally, to circumvent the necessity for CBSs in the above-mentioned centralized systems, we develop a distributed and decentralized game-theoretical NC framework for partially connected D2D networks such that the number of required D2D transmissions until all users receive all their requested contents is minimized. Simulation results are provided to attest the effectiveness of the proposed frameworks against baseline schemes for each of the above systems.
Network Codes for Effective ResourceAllocation in Cache-Enabled 5GMobile NetworksbyMohammed SaifB.Sc. Faculty of Engineering, Taiz University, 2010M.Sc., King Fahd University of Petroleum and Minerals, 2017A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Electrical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)August 2020© Mohammed Saif, 2020The following individuals certify that they have read, and recommendto the College of Graduate Studies for acceptance, a thesis/dissertation en-titled:Network Codes for Effective Resource Allocation in Cache-Enabled 5G Mobile Networkssubmitted by Mohammed Saif in partial fulfilment of the requirements ofthe degree of Doctor of PhilosophyDr. Md. Jahangir Hossain, School of EngineeringSupervisorDr. Stephen OâLeary, School of EngineeringSupervisory Committee MemberDr. Anas Chaaban, School of EngineeringSupervisory Committee MemberDr. Shawn Wang, Irving K. Barber School of Arts and SciencesUniversity ExaminerDr. Lin Cai, Electrical and Computer Engineering, University of Victoria (UVIC), CanadaExternal ExamineriiAbstractCooperation is a key enabler for delivering popular contents to usersin todayâs centralized wireless communication networks where the cloud-computing base station (CBS) is connected with low power base-stations,also named as remote radio heads (RRHs), via fronthaul links. The perfor-mance of todayâs wireless communication networks is constrained by thescarcity of radio resources and limited-capacity of fronhaul links. Edgecaching (EC) is a powerful networking technique, where popular contentsare cached in the edge nodes, that reduces the burden on fronthaul links.State-of-the-art literature on content delivery focuses on allocating a singleuser to each radio resource-block (RRB). However, this needs a large num-bers of RRBs to satisfy the tremendous increase in the number of users.Consequently, network coding (NC) is employed to mix usersâ contents andsimultaneously allocate different users to the same RRB. This dissertationdesigns innovative NC schemes for effective resource allocation in cache-enabled 5G networks, where the goal is to optimize different metrics, suchas throughput, CBS offloading, and completion time. We first study thecross-layer throughput maximization problem in cloud-radio access network(C-RAN). For this problem, we develop novel cross-layer NC (CLNC) frame-works that propose to optimize RRHsâ transmit powers and usersâ rates inmaking the coding decisions. Subsequently, we study CBS offloading andusersâ quality of service (QoS)-guarantee trade-off for fog-RAN system sub-ject to the cached contents, the required minimum rate, power control, andNC constraints. Next, we focus on developing NC schemes for device-to-device (D2D)-aided F-RAN system. The developed NC schemes exploit theaforementioned F-RANâs optimization factors and potential D2D commu-nications to minimize the completion time of users. Finally, to circumventiiiAbstractthe necessity for CBSs in the above-mentioned centralized systems, we de-velop a distributed and decentralized game-theoretical NC framework forpartially connected D2D networks such that the number of required D2Dtransmissions until all users receive all their requested contents is minimized.Simulation results are provided to attest the effectiveness of the proposedframeworks against baseline schemes for each of the above systems.ivLay SummaryImagine that a group of users are located in a hotspot, e.g., playground,and request popular-contents that represent popular-videos. Streaming suchusersâ requests with minimum possible delay while reducing the burdenon the core-network is a key requirement for todayâs cellular networks.Proactive-caching is inevitable for offloading the core-network, where thepopular contents, that are frequently requested by users, are cached in edge-servers and streamed to users with low intervention from the core-network.To efficiently utilize the radio-resources and stream popular contents to alarge set of users with a minimum delay, network coding is a communica-tion paradigm that was proposed to ensure instantaneous streaming of con-tents and simultaneous transmissions. We aim to stream popular contentswith the goal of optimizing throughput and delay. Towards this objective,we develop network coding schemes for several cache-enabled 5G-systems.Through extensive simulations, we demonstrate the efficiency of the pro-posed schemes against baseline methods.vPrefaceThis thesis is based on the research conducted under the supervisionof Prof. Md. Jahangir Hossain. For all the chapters, I conducted the re-quired literature review and developed the research ideas. I carried out therequired mathematical analysis and prepared simulations. Moreover, I pre-pared the related manuscripts. My supervisor provided feedback on systemmodels, problemsâ solutions and their corresponding computational com-plexities, and improved the presentation of all articles for scholarly publica-tion. Some collaborations on part of this thesis is conducted with Dr. SamehSorour and Dr. Ahmed Douik. Both helped me to discuss system modelsand developed ideas, and improve the presentation of some manuscripts.Following is the list of the journal and conference publications relatedto the chapters of the thesis. Both published and submitted journal articlesare provided in this list.Published and Submitted Journal PapersJ1. M.-S. Al-Abiad, A. Douik, S. Sorour, and Md. J. Hossain, âThrough-put maximization in cloud-radio access networks using cross-layer networkcoding,â IEEE Trans. on Mobile Computing, Early Access, Aug. 2020(Chapter 2).J2. M.-S. Al-Abiad, Md. J. Hossain, and S. Sorour âCross-layer cloudoffloading with quality of service guarantees in Fog-RANs,â IEEE Trans.on Commun., vol. 67, no. 12, pp. 8435-8449, Jun. 2019 (Chapter 3).J3. M.-S. Al-Abiad and Md. J. Hossain, âCompletion time minimizationviPrefacein Fog-RANs using D2D communications and rate-aware network coding,âsubmitted for publication at IEEE Trans. Wireless Commun. (Chapter 4).J4. M.-S. Al-Abiad, A. Douik, and Md. J. Hossain, âCoalition forma-tion game for cooperative content delivery in network coding assisted D2Dcommunications,â IEEE Access, Early Access, Sep. 2020 (Chapter 5).Referred Conference PublicationsC1. M.-S. Al-Abiad, A. Douik, S. Sorour, and Md. J. Hossain, âThroughputmaximization in cloud radio access networks using network codes,â EEE In-ternational Conference on Communications (ICCâ 2018) Kansas, USA, May,2018, pp. 1-6 (part of Chapter 2).C2. M.-S. Al-Abiad, S. Sorour, and Md. J. Hossain, âCloud offloading withQoS provisioning using cross-layer network coding,â IEEE Globecomâ18,Abu Dhabi, UAE, 2018, pp. 1-6 (part of Chapter 3).The following papers are also prepared during my PhD study; however,the materials of these papers are not included in the thesis.1. A. Douik, M.-S. Al-Abiad, and Md. J. Hossain, âAn improved weightdesign for unwanted packets in multicast instantly decodable network Cod-ing,â IEEE Commun. Lett., vol. 23, no. 11, pp. 2122-2125, Nov. 2019.2. M.-S. Al-Abiad, Md. Z. Hassan, A. Douik, and Md. J. Hossain, âLow-complexity power allocation for network-coded scheduling in cloud-RANs,ârevision pending at IEEE Commun. Lett.3- M.-S. Al-Abiad, Md. Z. Hassan, and Md. J. Hossain, âRate-aware net-work codes for distributed content sharing in cache-enabled D2D network,âto be submitted for publication at IEEE Internet of Things Journal.viiPreface4- M.-S. Al-Abiad, Md. Z. Hassan, and Md. J. Hossain, âCross-layer net-work codes for content delivery in cache-enabled D2D networks,â to be sub-mitted for publication at IEEE Commun. Lett.viiiTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . ixList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xivList of Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . .xviiList of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . xixAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . .xxiiDedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xxiiiChapter 1: Introduction and Background . . . . . . . . . . . . 11.1 An Overview of Cache-Enabled 5G Networks . . . . . . . . . 11.2 Network Coding . . . . . . . . . . . . . . . . . . . . . . . . . 51.2.1 Introduction to Network Coding . . . . . . . . . . . . 51.2.2 IDNC Graph . . . . . . . . . . . . . . . . . . . . . . . 91.2.3 IDNC and Rate-Aware IDNC . . . . . . . . . . . . . . 121.2.4 Game Theory . . . . . . . . . . . . . . . . . . . . . . . 141.3 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . 15ixTABLE OF CONTENTS1.3.1 Throughput Maximization in C-RAN System . . . . . 151.3.2 CBS Offloading in F-RAN System . . . . . . . . . . . 181.3.3 Cooperative F-RAN and D2D Communications . . . . 201.3.4 Content Delivery in D2D Networks . . . . . . . . . . . 231.4 Thesis Objective . . . . . . . . . . . . . . . . . . . . . . . . . 271.5 Thesis Contributions . . . . . . . . . . . . . . . . . . . . . . . 281.6 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . 32Chapter 2: Throughput Maximization in C-RAN using Cross-Layer Network Coding . . . . . . . . . . . . . . . . 362.1 Accomplished Works and Research Contributions . . . . . . . 372.2 System Model and Problem Formulation . . . . . . . . . . . . 372.2.1 C-RAN Model . . . . . . . . . . . . . . . . . . . . . . 372.2.2 Cross-Layer Network Coding (CLNC) Model . . . . . 402.2.3 Problem Formulation . . . . . . . . . . . . . . . . . . 432.3 Joint Scheduling and Power Adaptation Solution using CLNC 442.3.1 CLNC Graph Design . . . . . . . . . . . . . . . . . . . 452.3.2 Joint Scheduling and Power Allocation Solution . . . . 482.3.3 Complexity Analysis of Joint Solution . . . . . . . . . 502.4 Iterative Optimization for Coordinated Scheduling and PowerAdaptation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532.4.1 Coordinated Scheduling: Solution to Problem (2.9) . . 542.4.2 Power Allocation: Solution to Problem (2.10) . . . . . 562.5 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 622.6 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . 69Chapter 3: Cross-Layer Cloud Offloading with Quality of Ser-vice Guarantees in F-RANs . . . . . . . . . . . . . 703.1 Accomplished Works and Research Contributions . . . . . . . 713.2 System Model and Assumptions . . . . . . . . . . . . . . . . . 723.3 Modeling and Problem Formulation . . . . . . . . . . . . . . 743.3.1 Physical-Layer . . . . . . . . . . . . . . . . . . . . . . 743.3.2 Opportunistic Network Coding in the Network-Layer . 76xTABLE OF CONTENTS3.3.3 Problem Formulation . . . . . . . . . . . . . . . . . . 783.4 CBS Offloading and QoS Guarantee: Joint Approach . . . . . 813.4.1 FRAN-Cross-Layer NC Graph . . . . . . . . . . . . . 813.4.2 Greedy Algorithm . . . . . . . . . . . . . . . . . . . . 853.4.3 Computational Complexity of Joint Approach . . . . . 873.5 CBS Offloading and QoS Guarantee: Iterative Approach . . . 893.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 923.7 Chapter Summery . . . . . . . . . . . . . . . . . . . . . . . . 96Chapter 4: Completion Time Minimization in F-RANs usingD2D Communications and Rate-Aware NC . . . . 984.1 Accomplished Works and Research Contributions . . . . . . . 994.2 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 994.3 Completion Time Minimization for D2D-aided F-RAN Systems1024.3.1 Network Coding in the Network-Layer . . . . . . . . . 1024.3.2 Transmission Time Analysis and Expression of theCompletion Time . . . . . . . . . . . . . . . . . . . . . 1034.4 Problem Formulation and Problem Decomposition . . . . . . 1084.5 Joint Solution for Completion Time Minimization Problem . 1104.5.1 Solution to Sub-problem P2 . . . . . . . . . . . . . . . 1114.5.2 Solution to Sub-problem P3 . . . . . . . . . . . . . . . 1154.6 Coordinated Scheduling Solution for Completion Time Mini-mization Problem . . . . . . . . . . . . . . . . . . . . . . . . . 1204.7 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 1244.8 Chapter Summary . . . . . . . . . . . . . . . . . . . . . . . . 129Chapter 5: Coalition Formation Game for Cooperative Con-tent Delivery in Network Coding Assisted D2DCommunications . . . . . . . . . . . . . . . . . . . . 1305.1 Accomplished Works and Research Contributions . . . . . . . 1315.2 System Overview and Problem Formulation . . . . . . . . . . 1325.2.1 System Overview . . . . . . . . . . . . . . . . . . . . . 1325.2.2 Instantly Decodable Network Coding Model . . . . . . 134xiTABLE OF CONTENTS5.2.3 Completion Time Minimization Problem Formulation 1355.3 Distributed Completion Time Minimization as a CoalitionGame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1395.4 Proposed Fully Distributed Solution . . . . . . . . . . . . . . 1435.4.1 Coalition Formation Constraints . . . . . . . . . . . . 1435.4.2 A Distributed Coalition Formation Algorithm . . . . . 1455.5 Theoretical Analysis of the Proposed Game . . . . . . . . . . 1505.6 Numerical Results . . . . . . . . . . . . . . . . . . . . . . . . 1555.6.1 Completion Time Performance Analysis . . . . . . . . 1565.6.2 Proposed CFG Performance Analysis . . . . . . . . . . 1615.7 Chapter Summery . . . . . . . . . . . . . . . . . . . . . . . . 164Chapter 6: Conclusions . . . . . . . . . . . . . . . . . . . . . . . 1656.1 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . 1656.2 Suggested Future Work . . . . . . . . . . . . . . . . . . . . . 168Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192Appendix A: Proof of Theorem 2.1 . . . . . . . . . . . . . . . . . . 192Appendix B: Illustration of Algorithm 1 . . . . . . . . . . . . . . . 195Appendix C: Illustration of Algorithm 4 . . . . . . . . . . . . . . . 198xiiList of TablesTable 2.1 Numerical parameters . . . . . . . . . . . . . . . . . . 62Table 5.1 The influence of changing Ï on the completion timeperformance of the proposed scheme . . . . . . . . . . 163Table 5.2 Average Running Times of the different schemes . . . 163Table 5.3 Average Number of Coalitions and Split/merge rulesof the proposed scheme in the first iteration . . . . . . 163Table B.1 All possible IDNC combinations SIDNC . . . . . . . . 195Table B.2 All feasible schedules Sz1,fs . . . . . . . . . . . . . . . . 196Table B.3 The generated vertices and their corresponding weights 197Table C.1 All Possible File Combinations SIDNC,b1 and SIDNC,b2 . 199Table C.2 All feasible Schedules Sfs . . . . . . . . . . . . . . . . . 199Table C.3 The represented vertices and their corresponding weights201xiiiList of FiguresFigure 1.1 A simple model containing 4 users, 4 packets, and 1RRH. The RRH cached the whole set of packets. . . . 12Figure 1.2 Illustration of the IDNC graph. . . . . . . . . . . . . 13Figure 2.1 A cloud radio access network composed of a centralCBS, 6 users, and 3 RRHs. The CBS communicateswith the RRHs through low-rate fronthaul links. . . . 38Figure 2.2 Frame structure of the RRHs. Each RRH possessesZ orthogonal RRBs synchronized with the RRBs ofthe remaining RRHs. . . . . . . . . . . . . . . . . . . 38Figure 2.3 A simple C-RAN system composed of 3 users, 3 files,2 RRHs, and 1 RRB in each RRHâs transmit frame. . 42Figure 2.4 The coordinated scheduling graph of the network pre-sented in Figure 2.3 using Algorithm 2. . . . . . . . . 56Figure 2.5 Average sum throughput in bits/Hz. vs the numberof users U . . . . . . . . . . . . . . . . . . . . . . . . . 63Figure 2.6 Average sum throughput in bits/Hz. vs a large num-ber of users U . . . . . . . . . . . . . . . . . . . . . . . 64Figure 2.7 Average sum throughput in bits/Hz. vs. the numberof radio resource blocks Z. . . . . . . . . . . . . . . . 66Figure 2.8 Average sum throughput in bits/Hz. vs maximumpower Pmax. . . . . . . . . . . . . . . . . . . . . . . . 66Figure 2.9 Average sum throughput in bits/Hz. vs cell size D inKm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67xivLIST OF FIGURESFigure 2.10 Average sum throughput in bits/Hz. vs the numberof iterations. . . . . . . . . . . . . . . . . . . . . . . . 67Figure 2.11 Average number of scheduled users vs the total num-ber of users U . . . . . . . . . . . . . . . . . . . . . . . 68Figure 3.1 A fog radio access network composed of CBS, 11 users,and 3 eRRHs. Only low-rate fronthaul links are re-quired to connect the CBS with the eRRHs. . . . . . 74Figure 3.2 Illustration of the transmission frames of the eRRHsand CBSâs resources, i.e., time in seconds of the CBSâsorthogonal channels. . . . . . . . . . . . . . . . . . . . 75Figure 3.3 An illustration of the ONC and color graphs for asimple system containing 5 users, in which each userrequests one file. . . . . . . . . . . . . . . . . . . . . . 79Figure 3.4 Total CBS consumed time and average throughput inbits/second versus number of users U . . . . . . . . . . 94Figure 3.5 Total CBS consumed time and average throughput inbits/second versus number of files F . . . . . . . . . . 95Figure 3.6 Total CBS consumed time and average throughput inbits/second versus number of RRBs Z. . . . . . . . . 96Figure 4.1 Illustration of the D2D-aided F-RAN model with 13users, 3 eRRHs and 1 CBS. . . . . . . . . . . . . . . . 100Figure 4.2 Transmission time structure for eRRHs and potentialD2D transmitters for one time slot. . . . . . . . . . . 104Figure 4.3 D2D-aided F-RAN system containing 2 users and theircorresponding requested/received files and rates. . . . 108Figure 4.4 Illustration of both IA-IDNC and D2D conflict graphsof the example presented in Figure 4.3. . . . . . . . . 120Figure 4.5 Average completion time versus the number of users U .125Figure 4.6 Average completion time versus the number of files F . 127Figure 4.7 Average completion time versus file size N . . . . . . . 128xvLIST OF FIGURESFigure 5.1 Illustration of a partially connected D2D network with13 UDs. For simplicity, only the coverage zones ofthe possibly transmitting UDs u2, u6, u8, and u11 aredrawn. . . . . . . . . . . . . . . . . . . . . . . . . . . 132Figure 5.2 A partially connected D2D network containing 6 UDsand 4 packets. . . . . . . . . . . . . . . . . . . . . . . 137Figure 5.3 A resulting coalition structure Ψfin = {S1,S2} fromAlgorithm 8 for a partially connected D2D networkthat is presented in Figure 5.2. . . . . . . . . . . . . . 153Figure 5.4 Average completion time versus the number of playersU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157Figure 5.5 Average completion time versus the number of pack-ets M . . . . . . . . . . . . . . . . . . . . . . . . . . . 158Figure 5.6 Average completion time versus the average player-player erasure probability Ï. . . . . . . . . . . . . . . 160Figure 5.7 Average completion time versus the connectivity in-dex C. . . . . . . . . . . . . . . . . . . . . . . . . . . 161Figure 5.8 Average number of coalitions versus the number ofplayers U . . . . . . . . . . . . . . . . . . . . . . . . . 161Figure B.1 CRAN-CLNC graph of Example 1 that presented inFigure 2.3 based on Algorithm 1. . . . . . . . . . . . 197Figure C.1 F-RAN system containing 5 users, 2 eRRHs, 1 RRBin each eRRHâs frame, and their side information isgiven on the left part of the figure. This figure alsoshows the ONC, FRAN-CLNC, and color graphs ofexample 3, respectively. . . . . . . . . . . . . . . . . . 199xviList of AcronymsAcronyms Definitions5G Fifth GenerationEC Edge CachingRRB Radio Resource BlockNC Network CodingC-RAN Cloud Radio Access NetworkCLNC Cross Layer Network CodingRRH Remote Radio HeadF-RAN Fog Radio Access NetworkD2D Device-to-DeviceIoT Internet-of-thingsBS Base StationCBS Cloud Base StationEN Edge NodeeRRH Enhanced Remote Radio HeadLTE Long Term EvolutionRNC Random Network CodingONC Opportunistic Network CodingGF Galois FieldRLNC Random Linear Network CodingIDNC Instantly Decodable Network CodingNP Nondeterministic PolynomialRA-IDNC Rate-Aware IDNCPMP Point to MultipointRSNC Rate Selection and Network CodingUD User DevicexviiList of AcronymsCFG Coalition Formation GamePL Power LevelSUI Stanford University InterimSINR Signal-to-Interference-Plus-Noise-RatioAWGN Additive White Gaussian Noisebps Bits-per-secondMHz Meaga HertzLC Local ConditionCC Conflict ConditionKKT Karush-Kuhn-TuckerMb Meaga-byteRC Rate ConditionTC Transmission ConditionIA-IDNC Interference-Aware IDNCIS Independent SetNTU Non Transfer UtilityACK AcknowledgmentMC Merge ConditionSC Split ConditionONC One Coalition FormationxviiiList of SymbolsSymbols DefinitionsB Set of B RRHsU Set of U UsersF Set of F FilesP(F) Power set of the set F|F| Cardinality of the set FZ Set of Z RRHshuibnzm Channel gain from zm-th RRB in bn-th RRH to ui-th userÏ2 Additive white Gaussian noise (AWGN) powerPbnzm Power level (PL) of zm-th RRB in bn-th RRHPmaxbnzm Maximum PL of zm RRB in bn-th RRHP Matrix containing the PLs of RRBsN Size of fileR Set of all achievable capacitiesWui Set of requested files by ui-th userHui Set of received files at ui-th userRbnzm Transmission rate of zm-th RRB in bn-th RRHκbnzm The encoded file of zm-th RRB in bn-th RRHÏbnzm Set of scheduled users to zm-th RRB in bn-th RRHs Association schemeSIDNC Set of all possible IDNC file combinationsA Set of all possible associations between RRHs, RRBs, files, and ratesAzm All associations in A that are indexed by zm-th RRBS Feasible scheduleAfs Set of all feasible schedulesG(V, E) Graph and its vertices V and edges ExixList of Symbolsw(v) Weight of vertex vC Maximum weight cliqueO Complexity operatorD Cell sizeµ Caching ratioHbn Set of cached files at bn-th eRRHP Transmitted power of the CBShui Channel gain from the CBS to the ui-th userI Independent setRth Rate thresholdÏ Mapping functionI Maximum weight independent setnPr Permutation operator(nk)Combination operatorCui Coverage zone of ui-th userR Coverage zone radiushd2dukui D2D channel gain between uk-th and ui-th usersR Capacity status matrix (CSM)Utra Set of transmitting userst Time indexκd2duk XOR file to be sent by uk-th D2D transmitterÏ(Îºd2duk ) Scheduled users to uk-th transmitterT cbn Transmission duration of the bn-th eRRHT d2duk Transmission duration of the uk-th D2D transmitterTmax Maximum transmission durationDul Accumulated time delay of ul-th userTul Completion time of ul-th userTo Overall completion timeP Set of P packetspuk XOR packet to be sent by uk-th UDT Transmission scheduleÏukul Packet erasure probability from uk-th UD to ul-th UDn Binary vector of the transmitting UDsxxList of SymbolsD Decoding delay experienced by all UDsI UDs hearing more than one transmissionO Out of transmission range UDsE[Ïuk ] Expected erasure probability of uk-th UDδukum Kronecker symbol between uk and um UDsÏ(Ss) Payoff of coalition SsÏuk(Ss) Payoff of uk-th UD in a coalition SsΨ Coalition structureÏ(Î¨) Payoff of coalition structure Ψ. Preference operatorΨini Initial coalition structureΨfin Final converged coalition structureDhp Stable coalition structureC Connectivity index CBS-to-UD erasure probabilityxxiAcknowledgementsI would like to express my sincere and unlimited gratitude to my advisorDr. Md. Jahangir Hossain for the continuous support of my Ph.D research,and for his constant encouragement and motivation. He spent a lot of hisprecious time helping me at each step of discussing system models, improvingthe manuscripts and revising them for submission. Besides his academichelp, I am also extremely grateful to Dr. Hossain for advising me in non-academic aspects.Besides my advisor, I would like to thank Dr. Sameh Sorour and Dr.Ahmed Douik for their insightful comments, valuable feedback, and for theirstimulating discussions. Also, I would like to thank my thesis committeemembers Dr. Stephen Oâleary, Dr. Anas Chaaban, Dr. Shawn Wang and,Dr. Lin Cai, for their willingness to serve on my supervisory committee. I amvery thankful to Dr. Stephen Oâleary and Dr. Anas Chaaban for providingme their sincere feedback, critical comments, and suggestions during myqualification exam.Throughout my PhD journey, I have met with different people fromUBCO. I would like to thank my fellow labmates and friends from UBCOfor the stimulating discussions and for all the fun we have had in this journey.Finally, I would like to thank my family members for keeping their faithin me. I would like to pay my humble respect and the deepest thanks frommy heart to my parents, my brothers, and my sisters for their patience,understanding, and encouragement. I would also like to sincerely thank mywife, the beautiful smile in my life, for her unconditional love and encour-agement in all these years. She constantly motivated me during my goodtime and bad time. My achievements would not have been possible withoutthe continuous support of my wife.xxiiTo my parents, my wife, and my kidsxxiiiChapter 1Introduction andBackground1.1 An Overview of Cache-Enabled 5G NetworksCommunication networks are a predominant component of our currentlife. Everywhere around us, people and devices exchange information amongeach other at different scales, speeds, and throughput. The ever-increasingnumber of devices combined with their explosive demand for bandwidth-hungry data services constrain todayâs wireless communication networks,specially cellular networks. A recent data-flow report, prepared by CiscoInc., shows that by 2023 the number of users will increase seven folds com-pared to the number of users of todayâs network [1]. In addition, with theevolution of so-called Internet-of-things (IoT), the number of connected-devices will dramatically increase and reach around up to 30 billions by2021 [2]. This high growth of data-flow demand and network size has driventhe research and industrial communities to explore a new wireless networkarchitecture, commonly referred as fifth generation (5G) wireless communi-cation network. One of the most key potentials of 5G technology is networkdensification through planning a massive deployment of small-cells and im-plementing their corresponding low-power base-stations (BSs) [3]. However,deploying a massive number of small cells and managing the BSs are chal-lenging [3]. Cloud radio access network (C-RAN), proposed by China MobileInc., is an innovative and practical platform for 5G that efficiently accom-modates network densification. In C-RAN, low-power BSs, also named asremote radio heads (RRHs), are connected to a cloud-computing base sta-11.1. An Overview of Cache-Enabled 5G Networkstion (CBS) through fronthaul links. Thus, RRH in C-RAN is designed toonly perform radio functionality and all other baseband signal processingfunctionalities and computations are centrally performed at the CBS. Con-sequently, compared to the traditional BSs, the power consumption andcomplexity of the RRHs are substantially reduced. Essentially, decreasingthe prices of RRHs and increasing the density of RRHs in network is fi-nancially affordable. Due to its centralized coordination, C-RAN offers apractical technology that provides effective resource optimization throughcloud computing, reliable interference mitigation mechanism through col-laborative signal processing, and enhanced energy efficiency [4]. Besidesits centralized coordination, heterogeneity through the deployment of var-ious sizes of RRHs and their different transmission powers and ranges isan another important feature key of C-RAN. In C-RAN, the CBS coordi-nates the different transmit frames of the connected RRHs and shares usersâcontents among all (or a subset of) these RRHs (depends on the level ofcoordination, i.e., signal-level or scheduling-level). In signal-level coordi-nation [5], [6], [7], usersâ contents are shared among various RRHs, whichrequires high-capacity, low-latency fronthaul links. On the other hand, inscheduling-level coordination [8], [9], the CBS allocates users to the radioresources of the different RRHs, under the system constraint that each usercan be connected to at most a single RRH. This system constraint not onlyovercomes sharing usersâ contents among multiple RRHs, but also managesinterference in C-RAN. As a result, scheduling-level coordination in C-RANoffers simplified, yet efficient, resource coordination frameworks.The unprecedented increase of wireless systems radically reshaped ourcurrent daily lives and led to the proliferation of mobile devices and thepopularity of mobile multimedia applications among them. Yet, despite thisgrowth in demand for wireless data, it is observed that users tend to requestmultiple copies of a particular widespread audio, photo, or video within ashort period of time [10]. The plethora of frequent contents streamed fromthe C-RAN core network (e.g., the CBS) to the RRHs introduce an unnec-essary load on the fronthaul links. However, the C-RAN architecture is,in fact, restricted to the practical limitations of fronthaul links, especially21.1. An Overview of Cache-Enabled 5G Networksin ultra-dense wireless networks. In order to satisfy the fronthaul demandof C-RAN in such ultra-dense networking scenario, a powerful wireless net-working technology, known as edge-caching (EC), has emerged [11]. EC isbeing widely used and motivated due to the fact that a large portion ofmobile multimedia traffic is generated by many duplicate downloads of par-ticular popular contents [10], [11]. Apart from its essential goal of reducingthe traffic fronthaul congestion of 5G networks, EC can also provide oppor-tunities for cooperative transmission if there are common contents across thecaches of multiple edge-nodes. Further, EC is shown to be an effective wayof reducing the delivery time [12], [13]. By pre-fetching popular contentsto the local storage of RRHs at off-peak times, RRHs can efficiently streamsuch contents to requesting users with low or no intervention from the CBS.As such, the traffic can be efficiently delivered while offloading the C-RANâsfronthaul links. These high-capability RRHs are henceforth referred to asenhanced RRHs (eRRHs). With EC, the wireless networks design experi-ences a paradigm shift from focusing solely on eRRH-user association to theconsideration of the content dissemination at the eRRHs. This shift intro-duces a novel wireless architecture referred as Fog-RAN (F-RAN) [14], [15],[16]. Therefore, F-RAN can exploit the advantages of both centralized pro-cessing of C-RAN and fast access of EC [17]. Harvesting these advantagesneeds careful design of the content distribution among eRRHs and contentdelivery. The former needs to consider many factors, such as the cacheplacement (where is it best to put caches?), request-to-cache routing (howare cached content copies to be found?), and the cache capacity (how manycontents to cache in each node?). The latter focuses on improving networkresource utilization and efficiently delivering contents to their intended users[18]. In this thesis, we focus only on contents delivery problem which drawsits importance from the required usersâ quality of service (QoS).Long range communications through wireless links between eRRHs andusers are subject to fading, shadowing, and so on. This results in linkfailures to deliver usersâ content(s). Motivated by this fact and evolution ofIoT, device-to-device (D2D) communication technology is proposed as a keyenabler of 5G networks [19], [20], [21], [22]. Due to its short range commu-31.1. An Overview of Cache-Enabled 5G Networksnication, cooperation, and data exchange between connected devices, D2Dcommunication technology offloads the traffic from the eRRHs and CBSsand can thus free up some spectrum for them to boost data rates and serveother users [3, 23]. Thus, the performance of F-RANs can be further im-proved by implementing D2D communications, where caching at the eRRHsand usersâ cooperation via D2D communications are exploited. This inte-grated system is referred as D2D-aided F-RAN [24]. The performance of ECat the eRRHs can be further improved by pushing some popular contents tothe devices near to the eRRHs. In the over congested network of beyond-5Gera, the size of the popular contents will be significantly large and it will notbe possible to cache the overall set of the popular contents in the eRRHsowing to their equipment costs and sizes issues. To circumvent this prob-lem, caching at devices are employed [25], [26]. With distributed caching ateRRHs/devices and D2D-aided F-RAN system, not only the eRRHs trans-mit their cached contents to requested devices, but devices can also deliverthe contents they cache to other devices via D2D communications. Besidesits integration with F-RANs for contents delivery, D2D communication isalso a core component in many mobile cloud/fog computing systems thatdistribute heavy processing tasks, e.g., distributed optimization and compu-tation, over a computationally limited CBS.Several advancements aimed to develop schemes that efficiently utilizeradio resources to speed up contents delivery in the aforementioned cache-enabled 5G systems, i.e., C-RAN, F-RAN, D2D communications, and D2D-aided F-RAN. One trend is to assign a single user to each radio resourceblock (RRB), and thus transmit only one content from that RRB. However,with the tremendous increase of number of users nowdays, it is highly chal-lenging to serve them by assigning a single user to each RRB. As previouslyexplained, it has been observed that users tend to have a common interestin downloading popular contents, especially videos, within a small intervalof time. The prior downloads of these popular contents by different usersand the erasures of different contents create a pool of side information in thenetwork, which is widely found in the current wireless networks. By com-bining this side information (i.e., downloaded/cached and erased contents)41.2. Network Codingusing network coding, multiple users can be served simultaneously on thesame RRB. Thus, significant improvements can be achieved in transmissionefficiency, contents recovery, throughput and delay, and CBS offloading, inmany sorts of wireless networks including the aforementioned cache-enabled5G mobile systems. In accordance with the aforementioned overview, themain theme of this dissertation is to investigate effective resource allocationschemes using network coding for delivering usersâ contents and ensuring therequired QoS in cache-enabled 5G networks.1.2 Network Coding1.2.1 Introduction to Network CodingFrom its inception in 2000 to now, network coding (NC) has built astrong reputation in improving content1 recovery process and achieving max-imum information flow in both wired and wireless communication systems[27], [28], [29], [30]. Imagine a group of geographically close individuals areusing their smartphones to stream popular videos, exchange information onsocial media, while others are meeting online through teleconferencing ap-plications, and so on. To ensure this simultaneous demand, multicast andbroadcast services have become key enablers in the design of wireless sys-tems and networking protocols, e.g., long term evolution (LTE) [31]. Theseapplications, especially video streaming, not only consumes huge amount ofnetwork resources, but also they are delay-sensitive. This means packetsthat are not instantly useful at their reception at users may cause interrup-tion to the stream. Few years ago people would tolerate some delays for avideo to be streamed before watching. This is almost unacceptable for anyindividual nowadays with the advancements of wireless communication anddiversity of social media. Therefore, the design of wireless communicationprotocols should efficiently consider high-rate demand, maximum informa-tion flow, and immediate packet decoding to meet the delay requirementsand ensure good streaming quality. To this end, NC can achieve maximum1In the context of this thesis, popular content represents a frame of files/packets.51.2. Network Codinginformation flow by combining packets at the source and intermediate nodesin the network.NC, initiated by Ahlswede et al. [27], performs on the network layerand relies on a simple idea; it enables intermediate nodes in the network tosend a combination of the source packets they obtained instead of the simplereceive-and-forward technique (i.e., uncoded). To attest this fact, let us con-sider a simple network that contains 1 BS, 2 users, and suppose that thereare 2 packets need to be transmitted to the users over erasure-free channels.Assume that user 1 already received packet 2 and user 2 received packet1. Traditionally, the BS needs two transmissions to complete the receptionof all packets at both users. However, NC reduces the number to a singletransmission by combining both packets at the BS. Generally, for a systemof various users and source packets, the key potential of NC is to ensure apartial (or hopefully full) reception of these source packets at the multipleusers by sending network coded packets. With such leverage of NC, dif-ferent network metrics can be optimized, e.g., maximizing the throughput,minimizing the delay, or the number of transmissions. In the literature, twoNC design methods are categorized into random (or full) network coding(RNC) and opportunistic network coding (ONC). In the former trend, thetransmitter first combines all source packets using random and independentcoefficients from a given Galois Field (GF), and then broadcasts this com-bined packet to all users. In the latter trend, the sender exploits the diversityof requested and received packets at each user in the selection process of thecombined packets. As such, a particular optimization aim is achieved. Itis worth mentioning that in wireless networks, channel impairments, suchas fading and shadowing result in packet loss. Such a packet loss is seen,at the application layer, as an erasure [32], [33] that affects the deliveryof information flow and the ability of users to decode the combined packets[34]. Consequently, a higher information flow in the network achieved by NCdoes not always mean a lower delay at the users [35], [36]. This is becausethe combined packets have to be retrieved (if they successfully received atusers) first before using them at the application layer. Thus, optimizing onemetric (e.g., throughput) degrades the other (e.g., delay), i.e., indeed there61.2. Network Codingis a throughput-delay trade-off.The most remarkable example that shows the above-mentioned interplayof throughput and delay is Random Linear NC (RLNC) [37], [38], [39], [40],[41] in broadcast scenarios. To show this interplay, consider that a frame ofMtotal packets need to be transmitted to all users. Using RLNC, the trans-mitter combines these Mtotal packets and performs fountain property suchthat each single user successfully receives Mtotal of these independent com-binations [42], [43]. From throughput perspective, RLNC achieves optimalthroughput, and from delay perspective, each user is able to start decodingonly after it has successfully received Mtotal combinations. Clearly, RLNCprovides high information flow in the network and optimally in minimizingthe number of packet transmissions in broadcast scenarios. Further, it doesnot require feedback from users for recovery. However, due to its high delay,RLNC is only suitable for delay tolerant applications as it does not provideinstant packet decoding. From a complexity point of view, the computa-tional complexity for decoding the packets at users increases cubically withthe number of packets [42]. Such high complexity is not affordable on thebattery-constrained devices. In addition, RLNC is not sufficient in multi-cast transmissions where different groups of users are interested in differentsubsets of packets.In contrast, ONC is a potential candidate to overcome the aforemen-tioned problems of RLNC. However, ONC has high encoding computationalcomplexity and scalability issues in optimally solving many ONC problemsin real time. This is because the optimal solution of online optimization (i.e.,real time optimization) requires knowing all future channel realizations andthe number of possibilities of usersâ side information. This is clearly in-tractable [44]. Fortunately, significant advancements in the analysis andalgorithm designs for different optimization metrics have been achieved fora particular ONC, namely instantly decodable NC (IDNC). Lately, Sorouret al. [44], [46], [47], [48], [49], [50] studied deeply the instantaneously de-codable codes and introduced the term IDNC. The key potential of IDNCis that it allows that the received coded packets are either immediately de-coded at their delivery time or discarded. As a result, IDNC facilitates fast71.2. Network Codingand simple coding/decoding processes which are essential for future wire-less networks. These fast and progressive packet reception features of IDNCbalances between throughput-delay interplay with negligible decoding com-plexity, which ensures a better QoS for users. These simple and powerfulfeatures of IDNC attracted much attention in the last few years thanks tothe following benefits:1. The immediate decodability feature of received packets makes themuseful at the reception time, which meets the streaming applicationsrequirements [51].2. Encoding at the transmitter is performed using a simple binary XORoperation, which reduces the coefficient reporting overhead as com-pared to RLNC. Likewise, decoding at the users is performed usinga simple binary XOR operation, which overcomes the high computa-tional complexity of RLNC.3. Any received packets that are not instantly decodable will be dis-carded, thus IDNC overcomes the need for buffers to store these non-instantly decodable packets for possible future decoding. This featurenot only overcomes the buffer requirements, but it also allows the de-sign of cost and energy efficient devices.Owing to its aforementioned benefits, IDNC has received a considerableattention in the research community, e.g., relay-aided networks [52], [53],[54], video-on-demand and multimedia streaming [55], [56], [57], [58], [59],[60], and D2D-enabled systems [61], [62], [63], [64], [65], [66], [67], [69], [70].A survey of different techniques and applications of IDNC in centralizedand decentralized networks can be found in [68]. The reason, besides itsaforementioned features, of such tremendous investigations in the analysisand the development of simple algorithms for IDNC is its representation asa simple graph model as given below.81.2. Network Coding1.2.2 IDNC GraphIn order to represent all packet combinations that are instantly decodableby a subset (possibly all) users, the authors in [47] proposed a graph model,known as the IDNC graph. This graph model is first designed in [71], [72]as a heuristic algorithm to solve the index coding problem.Before constructing the IDNC graph, we first introduce the two followingsets for each user uk in the network:â The Has set: Denoted by Huk and defined as the set of packets suc-cessfully received at uk-th user.â The Wants set: Denoted by Wuk and defined as the set of requestedpackets by uk-th user. Intuitively, in the broadcast context, these twosets are complementary.These two sets are referred as the side information of the users and sum-marized in a binary U Ã M state matrix S = [suk,pl ] wherein the entrysuk,pl = 0 represents that the pl-th packet is successfully received at uk-thuser and 1 otherwise, U is the number of users, and M is the number ofpackets. Therefore, the transmitter constructs the IDNC graph solely basedon the side information of users.The key idea of constructing the IDNC graph is that two packets arerequested by two users are combinable (coded) if these two users can bothbenefit from the combination. In other words, two packets can be combinedinto one combination if these packets are instantly decodable to the corre-sponding associated users. This scenario occurs if and only if (i) the twousers are requesting the same packet, or (ii) the packet requested by eachuser is already received by the other user. These two constraints for theencoding process at the transmitter can be represented by edges (lines) inthe IDNC graph. Likewise, the requested packets and their correspondingrequesting users can be represented by vertices (circles) in the IDNC graph.The IDNC graph is an undirected graph, in which its edges have no ori-entation. Consequently, to construct the IDNC graph, denoted by G(V, E)where V represents set of vertices and E represents set of edges, a vertex91.2. Network Codingvukpl â V is generated for each requested packet pl â Wuk by every user uk.Two distinct vertices vukpl and vukâ²plâ² in V are connected with an edge in Eif one of the two following conditions is satisfied:â pl = plâ² : This represents that the same packet pl is requested by bothusers uk and ukâ² .â pl â Hukâ² and plâ² â Huk : This represents that the XOR combinationpl â plâ² is decodable by both users uk and ukâ² .The aforementioned conditions emphasize that a feasible packet combinationis a combination that helps at least a single user receiving one of its requestedpackets. Finding the optimal packet combination that provides the highestobjective function to a given networkâs metric requires an exhaustive searchover all possible file combinations, which is clearly non-feasible for largenetwork sizes [68].From the IDNC graph construction, each clique2 in the graph representsa feasible packet combination that can be decoded by all users having ver-tices in that clique. Cliques usually show the tangible properties of graphs.For instance, one can consider that vertices in the graph represent peopleand edges represent friendâs relationships. So, a clique in this case is a set ofindividuals who are all friends with each other. In fact, the term âcliqueâ,borrowed from French and used in a 1949âs study of the above social networkmodel [73], refers to a group of individuals with a common interest. A max-imal clique in a graph is a clique that cannot be expanded to include moreadjacent vertices without violating its connectivity conditions, i.e., it is nota part of a larger clique. Likewise, a maximal clique with the highest num-ber of vertices in a graph is called the maximum clique. Unlike clique thatprovides local properties of the graph, the maximum clique reveals globaltrends of the graph.As previously explained, each feasible packet combination can be rep-resented by a clique in the IDNC graph. Therefore, finding the combina-tion that provides the highest objective function is equivalent to finding the2Clique is a set of vertices that are pairwise connected to each other.101.2. Network Codingmaximum clique [68]. Without loss of generality, solving the IDNC relatedproblems (e.g., completion time, decoding delay, so on) is equivalent to solv-ing the maximum clique problem [68], where the maximum clique problemis a problem that finds the largest set of vertices in a graph. Althoughlooks easy to solve, maximum clique problems are NP-hard problems [74],[75], [76]. A detail analysis of the developed algorithms, complexity, andapplications of maximum clique problems can be found in [77]. The maxi-mum weight clique problem is similar to the maximum clique problem, butit is applied on weighted graphs. In weighted graphs, every vertex has aparticular weight that reflects the contribution of that vertex to optimize agiven metric in a network. Throughout this thesis, we consider a weightedIDNC graph, where the weight of a vertex vukpl â V is denoted by w(vukpl).Consequently, we consider maximum weight clique problems.To illustrate the construction of the IDNC graph and its correspondingmaximum clique, let us consider a simple example in Figure 1.1. We consideran arbitrary usersâ side information as shown in the feedback matrix on theleft side of Figure 1.2. Assume error free transmissions. Based on usersâ sideinformation and RRHâs cached files, the corresponding IDNC graph is shownon the right side of Figure 1.2. For example, packet p3 that is requested byuser u1 is represented by a vertex (1, 3) in the graph. In order to maximizethe number of targeted users for this example, many possible solutions canbe found. One possible solution is that RRH combines packets p1, p3 andtransmits the combination p1 â p3 to the set of targeted users u1, u2, u3,and u4. The corresponding vertices of this combination are drawn by yellowcolor in the figure. Under this scenario, the decoding process at the usersare as follows.â The u1-th user already has p1, so it can XOR the combination (p1âp3)with p1 (i.e., (p1âp3)âp1) to retrieve p3. In this case, the transmissionis instantly decodable for u1.â The u2-th user already has p3, so it can XOR the combination (p1âp3)with p3 (i.e., (p1âp3)âp3) to retrieve p1. In this case, the transmissionis instantly decodable for u2.111.2. Network Codingp1 p2 p3 p4u1u2u3u4Cachep1 p2 p4p2 p3 p4p2 p3p1 p4Wants={p3}Wants={p1}Wants={p1, p4}Wants={p2, p3}C = p1 XOR p3Figure 1.1: A simple model containing 4 users, 4 packets, and 1 RRH. TheRRH cached the whole set of packets. The side information of users is alsoshown, where each user has received some packets and wants some otherpackets. For example, user u1 already received packets p1, p2, and p4 andrequests p3.â The u3-th user already has p3, so it can XOR the combination (p1âp3)with p3 (i.e., (p1âp3)âp3) to retrieve p1. In this case, the transmissionis instantly decodable for u3.â The u4-th user already has p1, so it can XOR the combination (p1âp3)with p1 (i.e., (p1âp3)âp1) to retrieve p3. In this case, the transmissionis instantly decodable for u4.1.2.3 IDNC and Rate-Aware IDNCThe previously explained IDNC technique is solely performed at the net-work layer and depends on usersâ side information in the network. Thus,the coding decision at the transmitter solely depends on the requested andcached packets at the users. Essentially, IDNC aims at finding a packetcombination that hopefully satisfies all users in a network as shown in theprevious example and in Figure 1.2. To satisfy all users, the transmissionrate of the transmitter is adopted to the minimum achievable capacity ofthe assigned users. This results in serving a large number of users but alsoleads to physical layer throughput degradation. Therefore, IDNC maximizes121.2. Network Coding3, 12, 11, 34, 3 3, 44, 2p1 p2 p3 p4u1u2u3u40 0 1 01 0 0 01 0 0 10 1 1 0maxmium cliqueFeedback matrix giving the requestedand received packets for all users. â0âmeans that a packet is received and â1âmeans that it is requestedIDNC graph and its correspondingFigure 1.2: Illustration of the IDNC graph. Each vertex represents a re-quested packet by one user, i.e., vertex (2, 1) represents the indices of useru2 and packet p1. Each clique in the IDNC graph represents a feasible IDNCcombination. For example, one possible clique is: {(1, 3), (2, 1), (3, 1), (4, 3)}that corresponds to transmitting the combination p1 â p3 to the targetedusers u1, u2, u3, and u4.the information flow in the network layer, but it degrades the physical-layerperformance. In fact, wireless channels are dynamic with heterogeneouscapacities, which requires the transmitters to judiciously adopt the trans-mission rates. For instance, a packet transmission with a high rate will takea shorter time but will be only successfully received by the users with highchannel capacities. In contrast, a packet transmission with a lower rate willbe received by more users but will take a longer time. In order to improvethe physical layer performance and usersâ QoS, the channel capacity shouldbe included as another factor in the network coding decisions. As a result,the coding decision depends on both the requested and cached packets atthe users and their channel capacities. This is called rate-aware IDNC (RA-IDNC) [78]. Thus, RA-IDNC scheme has the potential to serve significantset of users with relatively fair transmission rate. Thanks to this potentialfeature, RA-IDNC scheme has been recommended in a number of works, forexample [70], [78], [79], [80], [81], [82].131.2. Network Coding1.2.4 Game TheoryIn the centralized scenarios (e.g., C-RAN), the CBS performs the wholeprocess of constructing the IDNC graph, planning IDNC packet combina-tions, and coordinating transmissions. However, the aim of the distributedsystems, i.e., D2D communications, is to offload the CBS. In this regard,game theory is an amazing tool to model distributed systems without acentral CBS. In game theory, users, known as game players, interact withother game players to achieve the desired global objective [83]. Two typesof game theory are usually used, namely non-cooperative games and coali-tion games, also known as cooperative games. In non-cooperative games,each player makes its decisions individually and selfishly. In coalition games,players interact with each other to make cooperative and altruistic decisionsto achieve further the delay for delivering the contents [83]. In order to im-prove the distributed solutions using game theory, studying and optimizingthe different type of equilibrium, such that the Nash equilibrium and thePareto optimal [84], is crucial. Game theory has been well investigated tosolve NC problems in different D2D models, see the survey paper [68]. Ingeneral, the considered games in those works were complete and perfect. Thecomplete information assumption means that the utility function and thestrategy that each player can take are known by all other players involved inthe game. Likely, the perfect information assumption means that all playersknow the history of the game perfectly. In this thesis, we are interested inincomplete information game that draws its importance from the fact thatlimited-coverage zone players are distributed in an area, where players knowthe information about their neighbors, not all players in the game course.An elegant subclass of coalition games to model NC problems is the coali-tion formation game (CFG). The game is called CFG because it involves theformation of independent and disjoint coalitions. The key idea of formingcoalitions is to study the cooperative behavior of players in coalitions. In-deed, UDs are formed coalitions so that they maximize/minimize the utility(e.g., minimize completion time, minimize delay, maximize throughput, andso on) compared to when they do not form coalitions.141.3. Literature Review1.3 Literature Review1.3.1 Throughput Maximization in C-RAN SystemC-RANs are promising solutions to satisfy the growing traffic demandin 5G mobile networks. In the C-RANs literature, two common strategieshave been proposed, namely data-sharing strategy and compression-basedstrategy, to efficiently use the fronthaul links [85]. In the data-sharing strat-egy, the CBS splits and shares userâs message with only a subset of RRHs,which encode these messages and send them over wireless channels to theusers [86], [87]. The RRHs in the compression-based strategy transmit onlycompressed versions of the encoded messages to the users [7]. Different cod-ing schemes [88], [89], [90] have been studied in the literature as a meansto maximize the achievable rates. For example, in [89], the authors pro-posed two lattice-based coding schemes that maximize the achievable sum-rate in uplink multi-cell networks. In [91], the authors built on the codeproposed in [90] to further improve the sum rate. Cross-layer design thatuses NC has also been proposed to optimize different parameters in differ-ent network settings [92], [96]. In [92], the authors used NC to maximizethe sum-rate in C-RANs. The authors of [93], [94] proposed a cross-layerdesign for network planning in Ad-Hoc wireless networks. In [95], [96],the authors considered a cross-layer optimization and NC to optimize thethroughput in wireless queuing tandem and wireless multi-hop networks,respectively. However, the aforementioned existing works require optimiza-tion over different factors, such as RRHs beamforming vectors, user-RRHassociation, and message traffic over the fronthaul links. This makes the C-RANâs design complex. Therefore, we consider in this section the downlinkof C-RANs and its existing works from a different perspective. Particularly,works considered the joint target of users-RRHs scheduling policy, usersâ sideinformation, and power control at the CBS, and relay them to the RRHsthrough low-rate fronthaul links. In general, the existing works addressedthe throughput maximization problem and its related factors individually.Particularly, works discussed in [7], [97], [98], [99], [100], [101], [102], [103],[104], [105], [106], [107], [108], [109], [110] considered only the physical-layer151.3. Literature Reviewfactors, such as resource scheduling and power adaptation. This results inassigning a single user to each RRB. On the contrary, works presented in[44], [48], [68], [111], [112], [113], [114], [115], [116] considered only upper-layer factors, such as usersâ side information. This allocates many users toeach RRB. However, in order to serve all assigned users, each RRB in eachRRH adopts its transmission rate to the minimum rate of all its assignedusers.The throughput maximization problem in C-RAN, also known as jointuser scheduling and power allocation problem, is shown to be challenging[97], [98], [99]. Indeed, besides its joint combinatorial nature, the mathe-matical formulation reveals that the power adaptation itself in this settingcan be non-convex. A large body of literature, see for examples, [97], [98],[99], [103], [104] tackled the problem by solving it iteratively. The authors of[97], [99] solved the problem via an integer relaxation method in single andmulti-cell configurations, respectively, to maximize throughput. In [7], [105],the authors considered inter-cell level coordination in which only low-ratefronthaul link is used. The studies are extended in [106], [107], [108] to op-timize the power level of each RRB through a power optimization step. Tothis end, the authors of [109], [110] considered a scheduling-level coordinatedC-RAN to solve the joint user scheduling and power optimization problemusing graph theory techniques. As previously stated, all studies mentionedabove viewed the network solely from the physical-layer perspective withouttaking into consideration upper-layer facts. This results in assigning a singleuser to each RRB. However, it has been observed that users tend to havea common interest in downloading popular files, especially videos, within asmall interval of time. This creates a pool of side information in the network.This side information is widely found in the current wireless networks. Forexample, the channel imperfections, e.g., interference, fading, etc. alwayscause fileâs erasures. The diversity in prior downloads of the popular files bydifferent users generates side information for their new requests by others.Also, the rate-based service optimization protocols with usersâ achievablecapacities play a significant role in generating side information. For clarifi-cation, let us consider a scenario of two groups of users where both groups161.3. Literature Revieware interested in popular files. The achievable capacities of the first groupare much lower than the second one. The modern LTE broadcast will targetthe first group of users with very low rates. If we use NC, users in the firstgroup would not be served in the current transmissionâs frame and left to beserved on a later transmissionâs frame when their rates become higher. Thisresults in generating side information, which can be clearly exploited usingNC to maximize throughput. In NC, such side information is employed tomix usersâ requests and aid the coding decision at the CBS. Hence, it leadsto serving these users simultaneously on the same RRB.A large body of literature, see for example, [44], [48], [68], [111], [112],[113], [114], [115], [116] optimized throughput, i.e., maximized the informa-tion flow in the network, by taking advantage of usersâ side information. Forexample, the authors of [44], [48] reduced the total completion time and thedecoding delay in point-to multipoint system (PMP), respectively. In [115],a delay-based analysis is provided to reduce the completion time. However,they ignored the physical-layer factors in the coding decisions. If we incor-porate some physical-layer factors in the NC decisions, we can optimize thecross-layer throughput. In the recent literature, RA-IDNC scheme has beenrecommended in a number of works, see for example [78], [79], [80], [81], [82].In the RA-IDNC scheme, both the side information and rate heterogeneityof different users to different RRHs are used for making NC decisions. Thus,RA-IDNC scheme has the potential to maximize the systemâs throughput.The authors of [81] proposed a novel joint rate selection and network coding(RSNC) scheme for increasing the systemâs benefit in PMP. In [80], [82],the authors proposed RA-IDNC scheme to minimize the actual completiontime in PMP and C-RAN systems, respectively. However, in [82], the au-thors assumed that each RRH maintains at a fixed power. Moreover, thetransmission rate of all RRHs is the same and will be limited by the weakestRRH, i.e., the RRH who can support the lowest transmission rate. Thismay violate the QoS rate guarantee.From the above discussions, we observe it is crucial to consider boththe NC at the network layer and the aforementioned physical layer fac-tors, to improve throughput. However, NC and C-RANâs resources can be171.3. Literature Reviewcontradicting as their combined effect, if not jointly optimized, can resultin a performance degradation. Indeed, by combining usersâ side informa-tion and scheduling multiple users to the same RRB, the total number oftargeted users in each RRB increases. For successful transmission for thescheduled users, the transmission rate in each RRB will be dictated by theworst userâs rate. Consequently, if such user-RRB associations and ratesare not carefully chosen when deciding on file combinations, the throughputof each RRB may decrease compared to serving a single user in it. Thisresults in worse throughput performance. Further, power level employed ineach RRB plays a significant role in this trade-off due to the interference onthe users served by the same RRB in different RRHs. Therefore, it is im-portant to investigate these trade-offs between usersâ side information, theirassociations to RRBs, power adaptation, and rate heterogeneity in C-RANresource setting. In this context, in Chapter 2, we introduce a fully cross-layer optimization framework for capturing the above-mentioned interplays.We investigate the following two scenarios. In the first scenario, we solve thethroughput maximization problem by jointly considering the network-codeduser scheduling and power optimization. In the second scenario, we over-come the high implementation complexity of the joint solution by solvingthe problem iteratively.1.3.2 CBS Offloading in F-RAN SystemCBS offloading is an important performance metric that has to be op-timized to compensate the limited capacity of C-RANâs fronthaul links. Inorder to optimize the offloading of CBSâs resources, i.e., time and frequency,RRHs need to pre-store and transmit usersâ side information at the networkedge (i.e., close to the end users). By pre-fetching most usersâ side informa-tion to their local storages at off-peak times, eRRHs can efficiently deliversuch files to requesting users with low or no intervention from the CBS.As such, CBSâs resources are significantly offloaded. Therefore, F-RAN canexploit the advantages of both centralized processing of C-RAN and fastaccess of edge caching [17]. Harvesting these advantages needs careful op-181.3. Literature Reviewtimization of the filesâ distribution among eRRHs as well as the immediateand fast delivery of requested files to users to satisfy their QoS. Thus, ad-dressing the scheduling of immediate file delivery problem is important tomeet the required QoS. If all popular files are cached in eRRHs, the imme-diate file delivery to users may necessitate the involvement of the CBS inserving the users that cannot be immediately served by the eRRHs. Thus,an efficient scheduling of file delivery from the eRRHs and (possibly) theCBS is required not only to maximize the CBS offloading (i.e., minimize theamount of CBS resources consumed in serving unserved users by the eR-RHs), but also to guarantee the required QoS. The joint CBS offloading andQoS guarantee problem in F-RANs involves many factors, such as the dif-ferent subsets of the files cached in each eRRHs, the usersâ requested files,their rates, need to be jointly considered. Existing works considered theabove factors and their corresponding problems separately. In particular,works presented in [7], [109], [119], [120] considered optimizing user-eRRHassociations and power in F-RANs, without any upper-layer considerations.Moreover, these works did not attempt to reduce CBS involvement in de-livering popular files. Other works [121], [122], [123], [124], [125] addresseda simplified version of the problem, in which the CBS offloading problem issolved irrespective of usersâ QoS in F-RAN.In the recent literature, a fronthaul-upper layer offloading design withone-to-one and one-to-many user-cache connections has been investigated ina number of works, e.g., [121], [122], [123], for small network settings. Thefocus of these works was mostly on cached files optimization and user ser-vice delay, without any immediate request of such service nor exploitationthe potentials of the IDNC to maximize fronthaul offloading. IDNC [124]suits most of the critical-time applications that need an immediate deliveryof usersâ requested files. The authors of [125] developed a framework forIDNC download time optimization from multiple CBS storage servers. Onestep further, the authors of [126] built on that model to employ NC in CBSoffloading given the immediate file delivery constraint. The main limitationof the work in [126] is its network-layer view of the problem. It employed NCon both the eRRHs (therein called femto-caches) and CBS (therein called191.3. Literature Reviewmacro base-station) to minimize the number of CBS channels required toserve the users that are not instantaneously served by the eRRHs. However,this work did not consider the heterogeneity in the rates of these users leftto be served by the CBS. The study in [126] is extended one step further byusing RA-IDNC to achieve better physical CBS offloading, i.e., reduces theconsumed frequency and time resources of the CBS [127]. To the best of ourknowledge, [127] was the first attempt to achieve CBS offloading maximiza-tion while considering some physical-layer aspects using RA-IDNC. How-ever, the work in [127] did not consider the standard F-RAN physical-layerresource structures that can be possibly allocated to different sets of users.More importantly, it did not consider to optimize rates through power selec-tion in each RRB. Furthermore, no attention was given to the usersâ achievedQoS. Unlike the RA-IDNC scheme that uses the rates as passive inputs, theproposed cross-layer NC controls these rate-aware codes by deciding on theset of power levels of the RRBs and their corresponding transmission ratesin F-RAN setting. Motivated by the above limitations of the existing works,it is crucial to propose an efficient cross-layer resource scheduling of file de-livery from the eRRHs and (possibly) the CBS. As such, the CBS offloadingis maximized while guaranteeing the required QoS. Clearly, maintaining theaforementioned two objectives in F-RAN settings can be contradicting. Forexample, by coding more (or judiciously selected) usersâ requests to each ofthe RRBs, the number of users left to be served by the CBS (if any) canbe reduced. As mentioned before, the transmission rate in each RRB willbe limited by the weakest user. This may violate the QoS rate guarantee.On the contrary, pre-setting a minimum rate in each RRB usually resultsin assigning less users to it. Thus, it increases the burden on the CBS toserve the remaining users. Consequently, in Chapter 3, we study such hightrade-off between throughput maximization and CBS offloading.1.3.3 Cooperative F-RAN and D2D CommunicationsAs mentioned before, F-RAN has been introduced to exploit both ECand C-RAN for carrying out file delivery effectively. In order to further201.3. Literature Reviewimprove the performance of F-RANs, implementing D2D communicationsin F-RAN is shown to be a potential technology in 5G and beyond. Thisintegrated system is referred as D2D-aided F-RAN [24]. D2D-aided F-RANsystem draws a remarkable benefit for reducing both usersâ files deliverytime and burden on fronthaul links. Thanks to the EC at the eRRHs andusersâ cooperation via D2D communications, we focus on files delivery prob-lem in D2D-aided F-RAN system. The files delivery problem of interest ismotivated by immediate delivery of common popular files for real-time ap-plications, i.e., live video streaming. In particular, we study the schedulingof files delivery problem from both the eRRHs and potential transmittingusers in D2D-aided F-RAN system using NC. The problem of delivering aframe of delay-sensitive files to a set of users with minimum possible delayhas been a topic of research for a quite some time. This problem is referredas completion time minimization problem. Based on layer functionalities,existing NC solutions for this problem can be classified into upper-layer NC[44], [48], [60], [67], [71] and RA-IDNC [78], [79], [80], [81], [82] methods.As their names indicate, upper layer NC algorithms focused only on NCat the network layer to minimize the number of transmissions. RA-IDNCapproaches incorporate both upper and physical layers to minimize the com-pletion time (in second) required to deliver requested files to all requestingusers. The latter is more practically relevant as it involves the dynamicnature of wireless channels in the completion time optimization.The completion time minimization problem in IDNC-based networks wasconsidered in different network settings, e.g., PMP [44], [48], D2D networks[61], D2D F-RAN [67]. In particular, the authors of [44], [48] proposedschemes to deliver the requested files by users with a minimum possible num-ber of transmissions. Recently, in [67], a centralized D2D F-RAN schemewas proposed for completion time reduction. However, the aforementionedworks considered IDNC from the perspective of network-layer. The maindrawback is that the transmission rate of each RRB is selected based on theuser with the weakest channel quality. This results in prolonged file receptiontime and thus, consumes the time resources of network. Therefore, consid-ering both network layer coding and physical layer factors for the RA-IDNC211.3. Literature Reviewis crucial [80]. With RA-IDNC, the completion time minimization problemneeds a careful optimization of selecting the IDNC file and transmissionrate of each RRB, see for example [78], [79], [80], [81], [82]. The authorsof [82] used RA-IDNC in C-RANs for completion time reduction. However,the authors assumed that all RRHs maintain a fixed transmit power level.Moreover, for synchronization purposes, the same transmission rate (i.e., thelowest transmission rate of all RRHs) is selected. This may violate the QoSrate guarantee and lead to a longer time for file transmission. Importantly,the proposed solution did not exploit the high capabilities of D2D communi-cations. Recently, a cross-layer IDNC scheme was proposed for throughputmaximization in C-RAN and CBS offloading in F-RAN [117], [118], [128],[129] respectively. Inspired by our preliminary works [118], [129], in Chap-ter 4, we address the completion time minimization problem in D2D-aidedF-RAN system using RA-IDNC and D2D communications. The consid-ered completion time minimization problem in D2D-aided F-RAN involvesmany factors, such as cached files at the eRRHs, usersâ limited coveragezones, their requested and previously received files, and their heterogeneousphysical-layer capacities. To the best of the our knowledge, the literaturedoes not solve the completion time minimization problem while consideringall above factors. Therefore, a balance among the conflicting effects of theaforementioned factors, such as IDNC codes, scheduled users, and trans-mission rates of eRRHs and users in D2D-aided F-RAN system is crucialto minimize the total frame delivery time. In Chapter 4, we investigatetwo scenarios as follows. In the first scenario, we solve the completion timeproblem by first minimizing the transmission time from the eRRHs. Giventhe obtained transmission time from the eRRHs, we maximize the numberof unscheduled users to eRRHs by implementing D2D communications. Inthe second scenario, we first schedule users via D2D communications andobtain the possible transmission time. Then, the unscheduled users via D2Dcommunications are scheduled to eRRHs over cellular channels during theobtained transmission time from the D2D communications.221.3. Literature Review1.3.4 Content Delivery in D2D NetworksThe use of smartphones and data-hungry applications in radio accessnetworks are increasing dramatically worldwide. This growth impacts theability of traditional wireless networks to meet the required QoS for its userdevices (UDs). As explained earlier, D2D communication, as one of thecandidate technology for 5G and beyond [3], supports a massive number ofconnected UDs and possibly improves the data-rate without fixed infras-tructure for content delivery [19], [20], [21], [22]. The decentralized natureof D2D networks allows UDs to communicate with other nearby UDs viaD2D links, which is suitable for numerous applications in mobile networks.For example, in wireless cellular networks, a D2D system enables cellularoffloading by UD cooperations for content downloading and sharing. Basedon [1], most wireless data contents are mainly distributed in hotspot areas,such as a playground, public transport, a conference hall. In such hotspots,there is a tremendous high UD density that requests high volumes of datatraffic, which causes network congestion and interruption at UDs. Actually,it is noticed that some UDs tend to have a common interest in download-ing the same content, known as popular content. This frequently happenswhere UDs download a popular application, an electronic map, or stream-ing multimedia contents, such as videos. This consumes a huge amount ofresources of cellular systems [11]. Therefore, D2D communication techniquecan be exploited to distribute the popular content as such to offload theCBS and reduce network congestion in the cellular networks. For instance,consider that a content consists of 3 packets p1, p2, and p3 is requested by3 UDs u1, u2, and u3. Suppose that the CBS transmitted the requestedcontents to the UDs and due to channel impairments UD ui did not receivepacket pi for 1 â¤ i â¤ 3. Traditionally, the missing packets are retransmittedrepeatedly from the CBS to each UD. As a result, the CBS needs at least3 uncoded transmissions for packets delivery, which degrades system per-formance [130]. However, UDs can be either packet holders providing theirreceived packets to other UDs or packet requesters receiving the requestedpackets from other UDs. For example, u1-th UD holds p2, p3, and accord-231.3. Literature Reviewingly, transmits binary XOR combination p2 â p3 to the u2-th and u3-thUDs. Then, u2-th UD holds p1 and can provide it to u1-th UD. As a result,2 transmissions are required for packets delivery. Therefore, D2D techniquescan be used with binary XOR combination to combine contents and trans-mit them to interested UDs via D2D links. Thus, minimizing the number oftransmission slots and offloading the CBSâs resources. The completion timeminimization problem was solved centrally in different network settings forvarious applications. For example, Raptor codes [131], and RLNC [39] ad-dressed the problem and achieved maximum network throughput. However,they are not attractive techniques for delivering delay-sensitive contents forreal-time applications, such as online gaming, and teleconferencing. On theother hand, IDNC improves throughput while allowing progressive decodingof the received contents, e.g., [68] and its references. It has been applied inseveral real-time broadcast applications wherein received contents need tobe used at the application layer immediately to maintain a high QoS, e.g.,relay-aided networks [52], [53], [54].The aforementioned IDNC works that are listed in the survey paper [68],for both fixed infrastructures and D2D networks, are centralized in the sensethat they require a central CBS to plan packet combinations and coordinatetransmissions. For example, the authors of [67] considered the completiontime minimization problem in a partially connected D2D fog network. Theproblem was solved by optimization under the assumption that the fog iswithin the transmission range of all UDs and has perfect knowledge of thenetwork topology. Accordingly, the fog selects transmitting UDs and theirpacket combinations and conveys the information to the UDs for execution.The above mentioned centralized approaches provide good performance forthe decentralized system, but they bring large challenges to the system.First, they require high computation cost at the fog units and high powerconsumption at each UD. Indeed, UDs need to send the status of all D2Dchannels to the fog after each transmission slot. Second, the fog requires toknow the downloading history of UDs for content delivery. Recently, in [132],[133], a non-cooperative game was used to reduce the communication timefor content reception. Still, the authors just considered a fully connected241.3. Literature Reviewscenario that only one player transmits the contents in each transmissionslot. The fully connected model is ideal in the sense that all players areconnected, and each player makes its decisions individually and selfishly.Thus, it ignored the cooperative and altruistic decisions of players to mini-mize further the delay for delivering the contents [83]. The cooperative andaltruistic decisions of players have shown the potential of coalition games inoptimizing different parameters in different models [134], [135], [136], [137],[138], [139]. For example, the tutorial in [134] classified the coalition gamesand demonstrated the applications of coalition games in communication net-works. The authors of [135] proposed a distributed game-theoretic schemefor playersâ cooperation in wireless networks to maximize the sum-rate. In[139], the authors recommend that UDs can cooperatively obtain the samecontent through multi-hop D2D communications. However, the aforemen-tioned works are agnostic to the available side information at the networklayer, i.e., requested and previously received contents by different UDs. Asa result, each UD sends uncoded (i.e., without NC) content that servesa single UD. Such side information can be exploited to efficiently select acombination of contents that can benefit a subset of interested UDs.In addition to their investigations in uncoded existing works, coalitiongames for network coding-enabled networks have been extensively exploredfrom various perspectives [140], [141], [142]. Prior network coding workswith coalition games aimed to maximize sum rate, e.g., [140], [141]. In par-ticular, the authors in [141] showed the potential of network coding in max-imizing the sum rate in network coding-aided D2D communication. More-over, some prior works analyzed content dissemination when network codingis enabled, e.g., [143], [144]. The authors in [143] presented efficient non-cooperative game theoretic scheme for content dissemination using RLNC.However the above related works [143], [144] used RLNC for content dis-semination. As previously mentioned, RLNC is not attractive technique fordelivering delay-sensitive contents for real-time applications of interest inthis work. Recently, the authors of [145] proposed a coalition game frame-work for packet recovery reduction in a partially connected D2D networkusing IDNC. However, the authors assumed that the cluster head selection251.3. Literature Reviewis predetermined. Moreover, all clusters are formed once at the beginningof recovery phase. This does not give flexibility to UDs to choose their owngroups in the next transfer. Importantly, if no available packets in any clus-ter, UDs in that cluster have to stop their intra-cluster recovery phase andwait for their cluster head to perform the inter-cluster recovery phase. Thisresults in prolonged packets delivery time. To this end, we consider a moregeneral setting in which a decentralized and distributed framework is devel-oped to: i) derive the rules for optimizing the selection of the transmittingUD in each formed coalition, and ii) give flexibility to UDs to choose theirown alliances at each transmission. As such, all packets are delivered to allUDs in only intra-coalition delivery phase with minimum completion time.Motivated by the above limitations of the existing works, in Chapter 5,we consider a partially connected D2D networks comprising several single-antenna UDs distributed in a hotspot, and each UD is partially connectedto other UDs. The completion time minimization problem is motivated byreal-time applications that tolerate only low delays. In such applications,the contents, represented by a frame of packets, need to be delivered toUDs via D2D links with few numbers of D2D transmissions. Our proposedmodel appears in different applications. For example, UDs at the edge of theservice area or in dense urban areas often experience packet losses from CBSsdue to channel impairments. Our proposed distributed scheme would servethese UDs via D2D links. Moreover, in cell centers with low erasures, ourproposed scheme would offload the CBSâs resources, e.g., time, bandwidth,and the ability to serve more UDs. To this end, our main goal in Chapter 5is to develop a distributed framework that models the collaborations amongthe UDs of an IDNC-based D2D network. In order to do that, we use gametheory because it involves a set of players that interact with each other toform a coalition without any coordination from the CBS. Further, as therequested packets are transmitted simultaneously from multiple UDs, wecan formulate the content delivery problem as a coalition game, and eachgroup of UDs constitutes a coalition. Thus, each UD acts as a game playerto be either packets holder providing its acquired packets to other playersor packets requester. Meanwhile, each game player has its own decision to261.4. Thesis Objectivejoin or leave the coalition based on its preference as well as other playersâpreferences in that coalition. Therefore, the interactions among players andtheir cooperative decisions motivate us to model and solve the completiontime problem in a distributed manner using game theory.1.4 Thesis ObjectiveIn accordance with the aforementioned introduction and background, themain theme of this dissertation is to investigate NC schemes for throughputmaximization and completion time minimization in cache-enabled 5G sys-tems. In particular, we consider instantaneous NC schemes for the followingcache-enabled 5G networks: (i) C-RAN downlink communication system;(ii) F-RAN downlink communication system; (iii) D2D-aided F-RAN sys-tem; and (iv) partially connected D2D networks. To this end, this thesis isbuilt on the following four research objectives.1. Develop cross-layer NC schemes for C-RAN downlink communicationsystem to efficiently stream a set of popular files to users with themaximum throughput.2. Investigate joint cross-layer CBS offloading and usersâ QoS guaranteeoptimization in F-RAN system by considering cross-layer NC, poweroptimization, and distributed caching strategy at the eRRHs.3. Develop joint and iterative rate-aware NC schemes for completion timeminimization (in second) in F-RAN architecture with D2D communi-cations.4. Develop a distributed and decentralized game-theoretical NC frame-work for partially connected D2D networks to minimize the completiontime in terms of number of D2D transmissions.271.5. Thesis Contributions1.5 Thesis ContributionsThe key contribution of this thesis is to design innovative NC schemes foreffective resource allocation in cache-enabled 5G networks, where the goalis to optimize different metrics, such as throughput, CBS offloading, andcompletion time. Specifically, in this thesis, we make the following four-foldcontributions.â Development of cross-layer NC schemes for C-RAN system: The mainnovelty of this contribution is the development of cross-layer NC schemesfor C-RAN resource setting. The developed joint and iterative cross-layer NC schemes maximize the cross-layer throughput of C-RAN sys-tem by performing user scheduling, file encoding, and power alloca-tion. The main contributions of this part as follows. First, we intro-duce a new graph, known as CRAN-CLNC graph, to formulate thecross-layer throughput maximization problem as a maximum weightclique problem. Second, using this graph, we develop a joint solutionthat greedily selects the maximum weight clique. For the high im-plementation complexity of the joint scheme, we develop an efficientiterative scheme that has relatively low-complexity. Numerical resultsreveal that the proposed joint and iterative schemes offer improvedthroughput performances as compared to the existing algorithms inthe literature. Compared to our proposed joint scheme, the iterativescheme has a certain degradation, roughly in the range of 9%-14%.This small degradation in the throughput performance of the itera-tive scheme comes at the achieved low computational complexity ascompared to the complexity of the joint scheme.â CBS offloading, QoS trade-off in F-RAN system: The main novelty ofthis contribution is to propose smart scheduling of file delivery schemesfor maximizing the CBS offloading while ensuring the required QoS inF-RAN system. In particular, for F-RAN system, we develop frame-work(s) where eRRHs and CBS judiciously collaborate to immediatelydeliver a set of requested popular files to users. As such, CBS offload-281.5. Thesis Contributionsing maximization and required QoS guarantee trade-off is investigated.The main contributions of this part are as follows. First, we use theONC graph to formulate the joint cross-layer CBS offloading and QoSguarantee optimization problem, and we show its NP-hardness. Totackle the problem, we design a graph, known as FRAN-CLNC graph,that considers both aforementioned C-RANâs optimization factors, thedifferent subsets of the files cached in each eRRHs, the required QoS. Inthis FRAN-CLNC graph, cross-layer vertex weight is designed, whereone vertex weight corresponds to CBS offloading while the other corre-sponds to QoS guarantee (i.e., rate maximization). The joint problemis, then, formulated on the FRAN-CLNC graph and shown to be equiv-alent to maximum-weight independent set and maximum weight col-oring problems. Afterward, a greedy vertex search and vertex coloringschemes are developed to efficiently solve the joint problem. Second,we proposed a simpler and efficient solution that mainly performs onsolving the joint cross-layer CBS offloading and QoS guarantee opti-mization problem iteratively. Presented numerical results reveal thatboth proposed schemes achieve significant gains in usersâ throughputcompared to the existing solutions. Compared to the QoS un-awarealgorithm, our proposed schemes have a certain degradation in CBSoffloading.â Development of RA-IDNC schemes for completion time minimizationin D2D-aided F-RAN system: The main novelty is to introduce noveloptimization framework(s) taking network coding, rate adaptation,potential D2D communications, and usersâ limited coverage zones intoaccount. As such, we minimize the completion time for sending allrequested files to all users in D2D-aided F-RAN system. Given theintractability of solving the completion time minimization problemover all possible future NC decisions, we reformulate the problem ateach transmission with the constraints on user scheduling, their lim-ited coverage zones, transmission rates, and QoS rate guarantee. Then,through transmission time analysis, we decompose the problem into291.5. Thesis Contributionstwo subproblems, namely transmission time minimization subproblemand number of served users maximization subproblem. The first partin this contribution aims at proposing a joint approach that developsnetwork-coded transmissions from both eRRHs and potential users forthe aforementioned subproblems. The second part aims at proposingan efficient and effective coordinated scheduling solution from bothD2D transmitters and eRRHs. Simulation results have shown thatour proposed schemes can effectively minimize the frame delivery timeas compared to conventional schemes.The main observations of the above three-fold contributions are asfollows.1. It is advantageous to serve many (possibly all) users with NC filesas in the classical IDNC algorithm, but selecting the minimumtransmission rate of all scheduled users degrades its performance,e.g., throughput, CBS offloading, completion time, and so on.Thus, this scheme is impractical from physical-layer perspective.2. It is advantageous to allocate users experiencing high rates to theRRBs as in the uncoded (i.e., without NC) scheme. However,with the increase of number of users, it is highly challenging toserve them by assigning a single user to each RRB. For a systemconsists of Ztotal RRBs, the maximum number of scheduled usersis Ztotal, which limits the overall gain in the average throughput ofthe uncoded scheme. Further, at each transmission, the numberof transmitted uncoded-files from all RRBs is limited to onlyZtotal files. As a result, a large number of transmissions is requiredfor transmitting a frame of files. Consequently, employing thisscheme in practical is highly challenging as it consumes networkresources.3. Our developed solutions strike a balance between the aforemen-tioned aspects by judiciously scheduling a significant set of usergiven their requested files are combined using NC, adopting thetransmission rates of each RRB and optimizing the transmission301.5. Thesis Contributionspower of each RRB. Such novel solutions offer improved perfor-mance in terms of throughput, CBS offloading and QoS improve-ment, and completion time in different resource settings, such asC-RAN, F-RAN, and D2D-aided F-RAN.â Game-theoretical development for contents delivery in D2D networks:Our main novelty in this part is the development of a distributed anddecentralized game-theoretical framework for contents delivery mini-mization in partially connected D2D networks. As such, we overcomethe need for the CBSs while minimizing the completion time. Themain contributions of this part are given as follows. First, we de-velop a decentralized IDNC-assisted D2D game theoretical frameworkto minimize the completion time while offloading the CBSs. In par-ticular, the completion time minimization problem is formulated andmodeled as a coalition game. Given the difficulty of expressing theproblem as a coalition game with non-transfer utility (NTU), we re-lax it to a coalition formation game (CFG). Second, in the relaxedCFG, the completion time metric is written as the utility function,which is transferred to each playerâs payoff in each coalition. We de-rive the rules for associating players, selecting the transmitting player,and finding its packet combination that is beneficial for a set of inter-ested UDs in each disjoint altruistic coalition. Afterward, we developa coalition formation distributed algorithm in each transmission slotbased on merge-and-split rules. Finally, the proposed coalition for-mation algorithm is proved to converge to a Nash-stable equilibrium,and its complexity and communication overhead are analyzed theoret-ically. We validate our theoretical finding using comprehensive numer-ical simulations, which reveal that our distributed scheme can signifi-cantly outperform existing centralized and fully distributed methods.For the presented network setups, our proposed decentralized schemeoffers almost the same performance as the centralized F-RAN D2Dscheme.311.6. Thesis Organization1.6 Thesis OrganizationThis thesis is organized into six chapters. In what follows, we summarizethe material of each chapter.Chapter 1 is divided into two main parts, introduction and backgroundand literature review. In the first part, we presented a brief background onthe development of cache-enabled 5G networks along with the competenceof EC technology for 5G fronthaul network offloading. We, then, provideda comprehensive introduction to network coding and its sub-classes. Wefurther showed how to construct the IDNC graph and find its correspondingmaximum clique. A brief description of both RA-IDNC and game theoryis also provided. In the second part, we comprehensively discussed andpresented existing related works on throughput, CBS offloading, and com-pletion time optimizations. The research objectives of this thesis are alsopresented. Finally, the contributions of the overall thesis are summarized.In Chapter 2, we present the C-RAN system model and provide the re-quired RA-IDNC materials for formulating the cross-layer throughput max-imization problem. Then, we introduce a new graph, called the CRAN-CLNC graph that transforms the cross-layer throughput maximization prob-lem into a maximum weigh clique problem. Given this designed graph, wedevelop a joint solution and analyze its computational complexity. After-ward, we develop an iterative scheme that solves cross-layer throughputmaximization problem efficiently and overcomes the high complexity of thejoint scheme. Numerical results demonstrate that our proposed joint anditerative schemes significantly outperform the conventional coded and un-coded schemes. Compared to the proposed joint solution, our proposediterative scheme has a certain degradation in the range of 9%-14%. Thissmall degradation in the performance of the iterative scheme comes at theachieved low computational complexity as compared to the high complexityof the joint solution. This chapter has been included in published conferenceand submitted journal articles [117], [118] respectively.In Chapter 3, we investigate the trade-off between throughput maxi-mization and CBS offloading in F-RAN setting. First, we overview the321.6. Thesis OrganizationF-RAN model and its assumptions. Then, we formulate the joint CBS of-floading and QoS guarantee optimization problem in the downlink F-RAN,given its cross-layer architecture (i.e., physical and network layers) and thewell-known ONC graph. Then, we propose a joint approach to solve the for-mulated optimization problem of joint cross-layer CBS offloading and QoSguarantee. This graph-based approach designs cross-layer weight for eachvertex in the FRAN-CLNC graph that reflects both maximizing CBS offload-ing and ensuring the required QoS for users. In addition, we propose a lowcomplexity iterative approach. Extensive simulations are finally performedto illustrate the potential CBS offloading and user throughput trade-offs ofthe proposed approaches. Presented numerical results revealed that bothproposed schemes achieve significant gains in usersâ throughput comparedto the existing solutions. Compared to the QoS un-aware algorithm, ourproposed schemes have a certain degradation in CBS consumed time. Thischapter has been included in two published conference and journal articles[128], [129], respectively.In Chapter 4, we study the completion time minimization (in seconds)problem in D2D-aided F-RAN system. First, we develop a framework whereeRRHs and users collaborate to minimize the completion time. In partic-ular, given the intractability of solving the completion time minimizationproblem over all possible future NC decisions, we reformulate the problemat each transmission with the constraints on user scheduling, their limitedcoverage zones, transmission rates, and QoS rate guarantee. By analyzingthe problem, we decompose it into two subproblems. Given the decomposedsubproblems, we develop two graph-based approaches that efficiently min-imize the completion time in D2D-aided F-RAN system. Using simulationresults, we compare our proposed schemes with existing coded and uncoded(without NC) schemes. Selected numerical results demonstrate that the pro-posed schemes can effectively improve completion time performance. Thematerials presented in this chapter have been included in a submitted jour-nal article [146].In Chapter 5, we develop a distributed game-theoretical framework fora partially connected D2D network using coalition game and IDNC opti-331.6. Thesis Organizationmization. Our proposed model is formulated as a coalition formation gamewith non-transferable utility, and a fully distributed coalition formation al-gorithm is proposed. We show that the proposed distributed algorithm isconverged to a Nash-stable coalition structure using split-and-merge ruleswhile accounting for the altruistic playersâ preferences. We comprehensivelyevaluate the completion time and game performances of the proposed dis-tributed solution, which demonstrate that the proposed distributed solutionoffers almost the same completion time performance similar to the central-ized F-RAN D2D network. Several advantageous of our proposed schemecompared to the one in F-RAN D2D are given as follows. First, our dis-tributed and decentralized scheme has roughly same performance of theF-RAN D2D centralized model while offloading the CBS. Such offloadingpolicy will allow the CBS to serve more UDs. Second, our scheme alleviatesthe required high power at UDs to deliver their channelsâ status to the CBSby using reliable and short D2D links. Third, if some UDs move from oneCBS to another, their lost/received content status have to be transferred tothe new CBS. This requires implementing handover procedure at the CBSswhich is not an issue in our distributed scheme as each UD receives its re-quested packets from other nearby UDs. The materials presented in thischapter have been included in a submitted journal article [147].Finally, Chapter 6 summarizes concluding remarks on the accomplishedworks of the entire thesis. In addition, potential future research topics re-lated to this thesis are also discussed in this chapter.Remark 1: In all chapters, we use the term âuserâ, but in Chapter 5 thatconsiders D2D networks, we use the term âuser devices (UDs)â. This iswell-known notation for D2D communications. Furthermore, in the contextof game theory in Chapter 5, each UD acts as a game player, and thus, UDsand players are used interchangeably.Remark 2: In Chapter 2, Chapter 3, and Chapter 4, usersâ side informa-tion refers to the cached and requested files by the users. In these chapters,we consider networkâs and physicalâs layers factors. In Chapter 5, since theD2D network is viewed only from the network layer, we consider a frame ofpackets where the aim is to deliver these packets to UDs within minimum341.6. Thesis Organizationpossible delay. This is well-known in NC at network-layer for packet recov-ery and packet delivery problems [68]. Therefore, in Chapter 5, UDsâ sideinformation refers to the cached and requested packets by the UDs.Remark 3: In Chapter 2, we consider C-RAN setting and thus low-powerBSs are represented by RRHs. This is standard in C-RAN system model.However, in Chapter 3 and Chapter 4, we consider F-RAN and D2D-aided F-RAN models, respectively, and thus these RRHs are implemented by cachingcapabilities and called eRRHs.35Chapter 2Throughput Maximization inC-RAN using Cross-LayerNetwork CodingIn this chapter, we study throughput maximization for C-RAN setting,in which a set of users already have asymmetric side information due to priordownloads of some popular files (constituting a finite frame of files). Thisframe of files is already cached at the different RRHs during off-peak times.Therefore, when each of the users requests one of these files (that it does nothave) to be streamed to it at a given time instant, these streaming requestsare time-critical (as is usually the case of caching), and must be done with themaximum possible throughput (unlike pre-loads that can be done at muchlower rates or at off-peak times). Such workâs setup is practically relevantin current and future 5G wireless networks. This chapterâs organization isgiven as follows. The accomplished works and research contributions aresummarized in Section 2.1. The C-RAN and cross-layer NC models arediscussed in Section 2.2. In this section, we also formulate the throughputmaximization problem. In Section 2.3 and Section 2.4, we develop joint anditerative scheduling and power adaptation approaches. In Section 2.5, wepresent some selected numerical results, and in Section 2.6, we provide someconcluding remarks.362.1. Accomplished Works and Research Contributions2.1 Accomplished Works and ResearchContributionsThe contributions of this chapter are summarized as follows. We addressthe cross-layer throughput maximization problem in C-RAN downlink sys-tems by jointly considering the problemâs related factors, such as resourcescheduling and power adaptation at the physical layer and usersâ side in-formation at the network layer. Two different cross-layer NC schemes aredeveloped, namely, the joint cross-layer NC scheme and iterative cross-layerNC scheme. In the joint scheme, we jointly consider network-coded userscheduling and rate/power adaptations of each RRB in each RRHâs frame.On the other hand, in the iterative scheme, network-coded scheduling andpower allocation are considered individually. New graphs are designed forthe above two techniques, namely, CRAN-CLNC and coordinated schedul-ing graphs such as we transform the throughput maximization problem intomaximum weight clique problems. Selected numerical results reveal the ef-fectiveness of the proposed schemes in improving throughput performancesas compared to the existing schemes.2.2 System Model and Problem Formulation2.2.1 C-RAN ModelWe consider the downlink communication in C-RAN in which a CBSis connected to B RRHs, denoted by the set B = {b1, b2, · · · , bB}. TheseRRHs are distributed in different geographic locations within a cell andcooperated in serving U users, denoted by the set U = {u1, u2, · · · , uU}.The B RRHs are under the CBS coordination and communicate with theCBS through low-rate fronthaul links. Similar to [109], each user and eachRRH is assumed to be equipped with one single-antenna. Figure 2.1 showsa C-RAN with 3 RRHs cooperating to serve 6 users simultaneously. Thetransmit frame of each RRH consists of Z orthogonal time/frequency RRBsthat are denoted by the set Z = {z1, z2, · · · , zZ}, as shown in Figure 2.2.372.2. System Model and Problem FormulationFronthaulRRH2RRH1RRH3CPUserFigure 2.1: A cloud radio access network composed of a central CBS, 6users, and 3 RRHs. The CBS communicates with the RRHs through low-rate fronthaul links.Pb2z1PbBz1 PbBzZPb2zZPb1zZPb1z1RRB z1 RRB zZPower Level ofRRB z1 in RRHb1 and b2RRH transmis-sion framesFigure 2.2: Frame structure of the RRHs. Each RRH possesses Z orthog-onal RRBs synchronized with the RRBs of the remaining RRHs.382.2. System Model and Problem FormulationTherefore, the total number of RRBs in the system is Ztot = Z. Let Pbnzmbe the power allocation level (PL) of the zm-th RRB in the bn-th RRH. LetP = [Pbnzm ] be a B Ã Z matrix containing the PLs of the RRBs/RRHs inthe considered system. From practical constraints, the power level of eachRRB is bounded by Pbnzm 6 Pmax, where Pmaxbnzm is the maximum power levelof the RRBs in the system. Let huibnzm be the complex channel gain from thezm-th RRB in the bn-th RRH to the ui-th user. The channel is assumed tobe constant during the transmission time of a single uncoded/coded file andto change from one transmission to another. In our simulation setup, weused the SUI model in which the channel information {huibnzm}bnâB,zmâZ,uiâUis affected by multiple factors, e.g., fading, shadowing, but the location ofthe user within the service area is the dominant factor. Such channel modelleads to heterogeneous physical-layer rates from different RBBs/RRHs todifferent users. The achievable rate of the ui-th user assigned to the zm-thRRB in the bn-th RRH can be expressed asRuibnzm = log2(1 + SINRuibnzl(P)), (2.1)where SINRuibnzm(P) is the corresponding signal-to-interference plus noise-ratio experienced by the ui-th user when it is assigned with the zm-th RRBof the bn-th RRH, and can be expressed asSINRuibnzm(P) =Pbnzm |huibnzm |2Ï2 +âbnâ²âB,bnâ² 6=bn, Pbnâ²zm |huibnâ²zm|2, (2.2)where Ï2 is the additive white Gaussian noise (AWGN) power. As statedearlier, the transmit frame of each RRH consists of Z orthogonal RRBs.Therefore, interference at the zm-th RRB is seen only from the same zm-thRRB in the other RRHs. In other words, SINRuibnzm(P) depends solely onthe scheduled users in zm-th RRB across the remaining bnâ² 6= bn RRHs andthe corresponding power level Pbnâ²zm . We consider that the reception of anuncoded/encoded file sent in the zm-th RRB of the bn-th RRH is successfulat the ui-th user if Rbnzm 6 Ruibnzm , where Rbnzm is the transmission rateof that RRB. The set of achievable rates of all users in all RRBs across all392.2. System Model and Problem FormulationRRHs can be represented by the setR =â(bn,zm,ui)â BÃZÃURuibnzm , (2.3)where the symbolârepresents the product of the set of the achievablecapacities.2.2.2 Cross-Layer Network Coding (CLNC) ModelWe assume that all users are interested in streaming one file or moreout of a set F = {f1, f2, · · · , fF } containing a finite window of F files.These files are deemed popular due to their previous multiple downloads bydifferent subsets of the users over a short period of time. Popular files inthis work represent frames from video-on-demand streaming. A user canstart playing the video after some (short) time for buffering in zm-th RRB,while download goes on in other zm 6= zmâ² RRBs in the same RRH. If usersrequest more than one file simultaneously, they can get them from the sameRRH by listening to multiple RRBs, each delivering one of its required files.All files in F are assumed to be stored in the CBS with the same size ofN bits. The size of any XOR encoded file (binary encoding operation) isalso N bits. It is assumed that each RRH holds/caches the whole set offiles F that they receive from the CBS and updates the CBS of the indicesof the downloaded files by users after each transmission. Furthermore, theCBS, which is a high computational device, keeps a log file to temporarilystore all the requested and downloaded popular files by the users under itscoverage. Then, it can track the downloaded files by users and use them todo instantly decodable NC (IDNC) combinations. Finally, the log entriesof users of the current popular files are transferred as part of this userâshandover procedure if this user moves from one CBS to another. RRHs andusers use the previously mentioned asymmetric usersâ downloaded/cachedfiles to perform XOR encoding and decoding operations, respectively, whennew files requested by users. In particular, users need the cached files toextract the wanted files immediately. The entire process of receiving and402.2. System Model and Problem Formulationdecoding these requested files takes a small duration of time. Thus, in anyarbitrary scheduling epoch, the files of F can be classified for ui-th user asfollows.â The Has set Hui containing files previously cached by the ui-th user.â The Lacks set Lui = FHui containing the non-cached files.â The Wants set Wui â Lui containing files requested by the ui-th userin the current scheduling frame.The CBS exploits the diversity of side information to transmit encoded filesin order to maximize the number of successfully received bits, i.e., through-put, in each scheduling frame. Let Ïbnzm denotes the targeted set of usersbenefiting from the encoded file κbnzm that transmitted over the zm-th RRBof the bn-th RRH, where κbnzm is an element of the power set P(F) rep-resenting a coded combination of a set of files. An instantly decodablecombination κbnzm is used to retrieve a new wanted file by ui-th user if andonly if1. Rbnzm 6 Ruibnzm : The ui-th user can properly receive the combinationwith a rate below its achievable capacity on the zm-th RRB of thebn-th RRH.2. |Wuiâ©Îºbnzm | = 1: The ui-th user can re-XOR κbnzm with its previouslycached files to retrieve a new file. In particular, user ui can re-XORκbnzm with its previously received packets that are in the combinationκbnzm .Therefore, the set of targeted users when the zm-th RRB in bn-th RRHtransmits the IDNC combination κbnzm isÏbnzm ={ui â Uâ£â£â£â£|Wui â© κbnzm | = 1 & Rbnzm 6 Ruibnzm} (2.4)The above-mentioned concepts can be illustrated in the following exam-ple.412.2. System Model and Problem Formulationf1f2 f3f3f3u1u2u3RRH b1Side-information and achievabel capacities CLNC solutionâf2 f3Classical IDNCf3RRH b2u1u2u3Ruib1z10.522211f2f2f2f1f1f1f1 âf2 f3Rb1z1 = 2Rb2z1 = 2f1âRb1z1 = 0.5Ruib2z1RRH b1RRH b2 RRH b1Figure 2.3: A simple C-RAN system composed of 3 users, 3 files, 2 RRHs,and 1 RRB in each RRHâs transmit frame.Example 1: This example considers a simple model in Figure 2.3 that con-sists of 2 RRHs, 1 RRB in each RRHâs transmit frame, 3 users, usersâ sideinformation and their rates. Each user ui possesses 2 files and wants 1 file.For example, u1 possesses f2, f3, and wants f1. The whole set of files iscached by each RRH. Given a certain power level to each of the RRHs,assume that usersâ rates in bits/s are provided in a table on the middle ofFigure 2.3. In order to maximize throughput for this example, many possiblesolutions can be found as follows.â CLNC solution: The b1-th RRH XORes f2 and f3 into κb1z1 =f2 â f3 and transmits κb1z1 with a rate of 2 bits/s to the set of usersÏb1z1 = (u2, u3). The b2-th transmits κb2z1 = f1 with a rate of 2bits/s to the set Ïb2z1 = u1 by sending. Thus, κb1z1 in b1-th RRH isinstantly decodable for all served users Ïb1z1 , and κb2z1 in b2-th RRHis instantly decodable only for u1 in Ïb2z1 . Given this, we have thefollowing decoding process at the users. User u2 gets f2 by XORingκb1z1 with f3 and user u3 gets f3 by XORing κb1z1 with f2. Therefore,the best achievable overall throughput in this scenario is 6 bits/s aseach served user will simultaneously receive 2 bits/s.â Uncoded solution: The b1-th and b2-th RRHs transmits f2 and f1with an equal rate of 2 bits/s, respectively, to u2 and u1. This resultsin 4 bits/s throughput achievable.â Classical IDNC solution: The b1-th XORes f1, f2, and f3 intoκb1zz = f1 â f2 â f3 and transmits κb1zz to to the set of users Ïb1z1 =422.2. System Model and Problem Formulation{u1, u2, u3}. This can be done from the network coding viewpoint butwould degrade the throughput than the uncoded and CLNC solutions.Indeed, to serve all users given their files are combined using NC,this solution will limit the rate sent to 0.5 bit/s, resulting in totalthroughput of 1.5 bits/s.From the completion time viewpoint, CLNC needs a total of N seconds,the uncoded solution consumes 1.5N seconds, and classical IDNC requires2N seconds. This clearly shows that CLNC is more efficient in maximizingthe throughput and minimizing the completion time. These results can befurther improved by optimizing the power allocation for each RRB in eachRRH.2.2.3 Problem FormulationThe joint user scheduling and power optimization problem considered inthis paper is equivalent to assigning users to the RRBs of the RRHs andadapt the power levels under the following network connectivity constraints(CC).â CC1: Each user can connect to at most one RRH, but possibly tomany RRBs in that RRH.â CC2: Each power level PL is bounded by a value.Let Xuibnzm be a binary variable that is equal to 1 if ui-th user is assignedto zm-th RRB of bn-th RRH, and zero otherwise. Typically, Xuibnzmwill be0 if bn-th RRH does not store the requested file by ui-th user. Let Yuibnbea binary variable that is set to 1 if ui-th user is assigned to bn-th RRH,and zero otherwise. The joint coordinated scheduling and power allocation432.3. Joint Scheduling and Power Adaptation Solution using CLNCproblem can be formulated as followsmaxâbnâBâzmâZâuiâUXuibnzm minuiâ²âÏbnâ²zmâ²log2(1 + SINRuiâ²bnâ²zmâ²(P)) (2.5a)s.t. Y uibn = min(âzmXuibnzm , 1), (bn, ui) â B Ã U , (2.5b)âbnY uibn 6 1, ui â U , (2.5c)0 â¤ Pbnzm â¤ Pmax, (bn, zm) â B Ã Z, (2.5d)Xuibnzm , Yuibnâ {0, 1}, κbnzm â P(F), (ui, bn, zm) â U Ã B Ã Z, (2.5e)where the optimization is carried over the variables Xuibnzm , Yuibn, κbnzm ,Rbnzm , and Pbnzm . The variables Xuibnzmand Y uibn are discrete optimizationparameters that represent the user-RRH and user-RRB associations, respec-tively. On the other hand, the variables κbnzm , Rbz and Pbnzm account for thefile combination, the transmission rate, and the PLs for the zm-th RRB ofthe bn-th RRH, respectively. Constraints (2.5b) and (2.5c) translate CC1.Constraint (2.5d) corresponds to constraint CC2. The problem in (2.5) isNP-hard. To show its hardness, we consider a simpler case when all usershave the same rates to all RRBs/RRHs. This makes the objective functionconstant. In this case, the problem in (2.5) is reduced to be an NC problem,which is shown to be NP-hard [116]. Therefore, the problem in (2.5) hasthe worst case exponential solution but can be solved using the branch andbound algorithm whose performance depends on the quality of lower andupper bounds. To reach a tractable solution to (2.5), one can discretize thecontinuous power Pbnzm into a set of discrete PLs P while constructing theCRAN-CLNC graph simultaneously.2.3 Joint Scheduling and Power AdaptationSolution using CLNCIn this section, we first design the CRAN-CLNC graph to reformulatethe throughput maximization problem as a maximum-weight clique problem.442.3. Joint Scheduling and Power Adaptation Solution using CLNCThen, using the deigned graph, we propose an efficient greedy joint approach.2.3.1 CLNC Graph DesignIn this subsection, we first generate all possible IDNC file combinationsfor configuring the power control subgraph for each zm-th RRB in the net-work. Afterward, we design the CRAN-CLNC graph from all power controlsubgraphs.Let S be the set of all possible associations between users and files (pairsof users and their requested files), which is defined by S = UÃF , and s is anelement in S. For example, the set of all possible associations between usersand their requested files in Example 1 is S = {(u1, f1), (u2, f2), (u3, f3)},s = (u1, f1) represents the association of u1-th user and its f1-th requestedfile. For simplicity, ui(s) represents the ui-th user in the s-th association.The generation of the set of the possible IDNC file combinations, denotedby SIDNC, relies on the fact that the corresponding users in the combinedassociations in S can be instantly served by one IDNC file. Therefore, anytwo distinct associations s â S and sâ² â S are combined if one of thefollowing conditions is satisfied.â C1: ui(s) 6= ui(sâ²) and fk(s) = fk(sâ²). The two associations s, sâ² areinduced by the same file fk that is requested by two distinct users.â C2: ui(s) 6= ui(sâ²) and fk(s) â Hui(sâ²) and fk(sâ²) â Hui(s). Thisrepresents that two different files are wanted by two different users.Meanwhile, each wanted file in each association is in the Has set ofthe user that induced the other association.These conditions ensure that any IDNC file combination in SIDNC is al-ways decodable for the users represented by the corresponding combinedassociations. Therefore, SIDNC consists of all possible IDNC file combina-tions resulted from the associations in S, and s = (κ, Ï) is an element inSIDNC, where κ and Ï are defined in Section 2.2.2. For example, associationss = (u1, f1) â S and sâ² = (u2, f2) â S satisfy C1 and C2, and accordingly,we can combine them into s = (κ, Ï) = {(f1 â f2), (u1, u2)}. Let A be the452.3. Joint Scheduling and Power Adaptation Solution using CLNCset of all possible associations between RRHs, RRBs, IDNC file combina-tions, and achievable capacities, i.e., A = BÃZ ÃSIDNCÃR. For example,one possible association in A is (bn, zm, s, R) which represents the RRH bn,RRB zm, IDNC combination s, and rate R. Basically, each element in Acontains combined associations of s â S representing an IDNC combina-tion s that is transmitted from RRH bn on RRB zm with its correspondingrate R. Let Azm â A represent the associations relative to the zm-th RRBacross all RRHs. In other words, Azm represents all associations in A thatare indexed by zm.Now let the power control subgraph of the zm-th RRB in the network bedenoted by Gzm(Vzm , Ezm) wherein Vzm and Ezm refer to the set of verticesand edges of this subgraph, respectively. The set of vertices in the Gzm-th subgraph is generated by merging all possible associations in Azm forthe different RRHs under the system condition CC1. Any possible mergedassociations inAzm is referred to as feasible schedule and denoted by S. In S,the same associated user is not scheduled to different RRHs as stated in thecondition CC1. The set of all possible feasible schedules S correspondingto the zm-th RRB is represented by Szm,fs. Therefore, a vertex v â Vzmassociated with S â Szm,fs satisfies bn(s) 6= bn(sâ²) and ui(s) 6= ui(sâ²) for alls 6= sâ² â S. As a result, each vertex v â Vzm represents the partial scheduleof users to the zm-th RRB across all RRHs.As mentioned above, the set of all vertices Ezm represents the set ofall merged associations. Therefore, each v â Vzm representing the feasibleschedule S â Szm,fs satisfies the following local conditions (LC).â LC1: For all (s, sâ²) â S such that bn(s) = bn(sâ²), we have R(s) = R(sâ²).This condition guarantees that all associations in the same RRB zmand RRH bn have the same transmission rate.â LC2: For all (s, sâ²) â S such that bn(s) 6= bn(sâ²), we have Ï â© Ï â² = â .This condition guarantees that each user is scheduled to at most asingle RRH.Suppose that the power distribution P will be computed later, then a vertexv representing the schedule S has a weight that reflects the total contribution462.3. Joint Scheduling and Power Adaptation Solution using CLNCof the vertex to the network. This weight can be expressed asw(v) =âsâSminui(s)âÏbn(s)zm(s)log2(1 + SINRui(s)bn(s)zm(s)(P)). (2.6)We design the CRAN-CLNC graph G(V, E) by generating the Z power con-trol subgraphs. Without loss of generality, the set of all schedules in thenetwork is the union of schedules of all RRBs, i.e., Sfs =âzmâZSzm,fs. There-fore, the vertex set of the CRAN-CLNC graph is simply the union of verticesof all the power control subgraphs, i.e., V = âzmâZVzm . Since we already de-scribed the edges between vertices within each subgraph Gzm in the previoussubsection, the rest of this section describes remaining edges correspondingto different subgraphs. Following similar philosophy as before, two differentvertices belonging to two different subgraphs are adjacent if their combina-tion results in a feasible schedule. In particular, two vertices are connectedif no user is scheduled to different RRHs. To mathematically formulate this,let vertex v â Gzm be corresponding to the schedule S â Szm,fs and ver-tex vâ² â Gzmâ² corresponding to the schedule Sâ² â Szmâ² ,fs. Vertices v and vâ²are adjacent if the associations they represent satisfy the following generalcondition (GC).â GC: For all (s, sâ²) â SÃSâ² such that Ïâ©Ï â² 6= â , we have bn(s) = bn(sâ²).The condition guarantees that the same user can be associated onlyto a unique RRH.The design of the CRAN-CLNC graph G makes any maximal cliquesatisfies the following criterion.â All targeted users can retrieve a new file(s) from the transmissionschedule of all RRBs and RRHs.â Each user is scheduled to a single RRH.â Each RRB identified by the vertices in a maximal clique adopts thetransmission rate identified by the vertex. This rate supports thesmallest channel capacity of all scheduled users to that RRB.472.3. Joint Scheduling and Power Adaptation Solution using CLNCGiven the optimal power allocation P, the following theorem reformu-lates the problem (2.5).Theorem 2.1. The CRAN joint coordinated scheduling and power alloca-tion problem (2.5) is equivalent to a maximum-weight clique problem overthe CRAN-CLNC graph, and can be written asarg maxCâCâvâCw(v), (2.7)where C is a maximal clique in the CRAN-CLNC graph, C is the set of allpossible maximal cliques, and w(v) is defined in (2.6). The vertices in Crepresents the targeted users and the file combinations in each RRB acrossall RRHs.For proof, please refer to Appendix A.The maximum-weight clique problem in Theorem 2.1 is NP-hard. How-ever, we use one of the existing algorithms in the literature, e.g., [148], [149],[150] to solve problem (2.5) heuristically for one particular transmission. Theproposed algorithm selects a number of vertices with the maximum weights,wherein each vertexâs weight represents the sum of transmission rates of thezm-th RRB across all RRHs that suitable for only a subset of associatedusers.2.3.2 Joint Scheduling and Power Allocation SolutionThis subsection presents the joint CRAN-CLNC solution to (2.5). Theidea is to solve the power control problem for each vertex of the powercontrol subgraph. This would allow the design of the CRAN-CLNC graph.Afterward, we heuristically solve the reformulated problem in Theorem 2.1using greedy graph algorithm.We discretize a set of power levels to solve (2.5) efficiently. More specif-ically, we show that by simultaneously computing the optimal power al-locations P while designing the CRAN-CLNC graph, we can achieve atractable solution to (2.5). Consider the zm-th power control subgraph482.3. Joint Scheduling and Power Adaptation Solution using CLNCand a vertex v â Vzm in that subgraph is associated with the scheduleS = {s1, s2, · · · , s|S|} â Szm,fs, where |S| is the degree of S, i.e., |S| =âbnâB |Ïbnzm |. The optimal power levels PLs (Pb1zm , · · · , PbBzm) that max-imize the throughput for that vertex v are the solution to the followingproblemmaxPbnzmâbnâB|Ïbnzm | â minuiâÏbnzm log2(1 + SINRuibnzm(P))s.t. 0 6 Pbnzm 6 Pmaxbnzm , âbn â B, (2.8)where the optimization is over the power levels Pbnzm , âbn â B. The poweroptimization problem (3.5) is a well-known non-convex problem [151] andcan be solved optimally [152]. However, such a solution requires a highcomputation complexity and converges slowly. To find a reasonable solutionto (3.5) with a low computational load, we use one of the power optimizationalgorithms proposed in [151].The joint coordinated scheduling and power allocation algorithm can beimplemented at the CBS as follows.First, we design the CRAN-CLNC graph as follows. For each RRBzm â Z, we configure the power control subgraph Gzm by generating eachvertex v â Gzm corresponding to the feasible schedule S â Szm,fs usingconditions LC1 and LC2. Afterward, we calculate the optimal PLs foreach vertex by solving the optimization problem (3.5). Then, we append thecomputed PLs of each vertex and the corresponding rates to that vertex. Werepeat steps above for all RRBs zm â Z. We merge all subgraphs of all RRBsand connect them using condition GC. Second, in each iteration, we find themaximum-weight clique among all other maximal cliques in CRAN-CLNCgraph G, which can be implemented as follows. We compute the verticesâweights using (2.6). Then, we select the maximum-weight vertex vâ and addit to C, i.e., C is initially empty. Then, we update the graph G by removingvâ and all the vertices that are not adjacent to it so as the next chosenvertex is not in feasible transmission conflict with the already chosen onesin C. We execute this process until no more vertices exist in G. Clearly, the492.3. Joint Scheduling and Power Adaptation Solution using CLNCAlgorithm 1: Joint coordinated scheduling and power allocationalgorithmData: U ,F ,B,Z,Hui ,Wui and huibnzm , (ui, bn, zm) â U Ã B Ã Z;Initialization: maximum-weight clique C = Ï.for zm â Z doInitialization: Gzm = Ï.for each S = {s1, s2, · · · , s|S|} â Szm,fs doSolve (3.5) to calculate the optimal power levelsP = {(P âb1zm , P âb2zm , · · · , P âbBzm)}.Create v = {{(s1, Râb1zm , P âb1zm), · · · , (s|Ïb1zm |, Râb1zm , P âb1zm)},· · · , {(sB, RâbBzm , P âbBzm), · · · , (s|ÏbBzm |, RâbBzm, P âbBzm)}}.Compute w(v) using (2.6).Set Gzm = Gzm âª {v}.endendSet G = âzmâZGzm .Connect vertices of G using GC.Solve maximum-weight clique problem over G.Output C.number of vertices in the selected maximum-weight clique is at most Z. Thedetailed procedures of the solution are provided in Algorithm 1.For understanding the design of the CLNC-CRAN graph in Figure 2.2and Algorithm 1, please refer to the illustration in Appendix B.2.3.3 Complexity Analysis of Joint SolutionThe computational complexity of the aforementioned joint solution isdivided into two phases: i) the complexity of constructing the CRAN-CLNCgraph, and ii) the complexity of finding the maximum weight clique. Thesephases are explained as follows.Phase I: CRAN-CLNC construction complexity: The computa-tional complexity of constructing the CRAN-CLNC graph is divided into thefollowing steps: i) generating a single subgraph for each RRB, ii) computingthe power levels of the RRHs, and iii) connecting all the subgraphs in the502.3. Joint Scheduling and Power Adaptation Solution using CLNCsystem to construct the CRAN-CLNC graph. These steps are explained asfollows.First step: The complexity of this step corresponds to the computationalcomplexity of generating all vertices in any subgraph. Consider computingthe complexity of subgraph Gzm of the zm-th RRB. As explained in Sec-tion 2.3.1, the total number of vertices in each subgraph is the total numberof possible feasible schedules |Szm,fs|. Each schedule S â Szm,fs containsmany possible associations that represent IDNC file combinations to betransmitted to a set of users from a set of RRHs with their correspond-ing transmission rates/powers. |Szm,fs| depends on all possible IDNC filecombinations SIDNC in the system. Any possible IDNC combination con-tains combined files correspond to associated requesting users. We considerthe worst-case complexity of generating the IDNC combinations as follows.First, note that each associated user with any IDNC file combination canreceive at most one file. In other words, each user can instantly decode atmost one file from its associated IDNC combination. Therefore, the max-imum number of associations in any IDNC combination is min(U,F ). Inour setting, the number of files is greater than the number of users. Thus,the upper bound of the IDNC combinations is F choose U , which can becomputed as F !(FâU)!U ! . For simplicity, it can be denoted by C =F !(FâU)!U ! .Second, note that Gzm corresponds to the zm-th RRB across all RRHs. Sinceall RRHs cache the whole set of files, each RRH can generate the same set ofIDNC combinations that can be generated by the other RRHs. Further, thesame IDNC combination and its corresponding users can not be associatedto different RRHs in the same schedule S as this violates the condition LC2that explained in Section 2.3.1. Hence, the possible IDNC combinationsfor all RRHs in the system can be permuted between all RRHs, and eachpermutation represents schedule S. As previously mentioned, schedule S isrepresented by vertex v in Gzm . Therefore, the total number of vertices inGzm is the number of permutations of these IDNC combinations among BRRHs, which is C!(CâB)! .Second step: To compute the power levels, we solve (3.5) for each ver-tex v in each subgraph. Solving (3.5) for each v depends on the number512.3. Joint Scheduling and Power Adaptation Solution using CLNCof RRHs, number of users in S, and interference pricing messages from theRRHs. The number of users in each schedule S is upper bounded by U , i.e.,the case when all usersâ files can be combined using NC. For the worst-casecomplexity of computing (3.5), Algorithm 1 needs for each scheduled userin RRH bn to compute the interference of all other RRHs, i.e., bnâ² 6= bnand the pricing messages from each RRH bnË 6= bnâ² . Thus, the computa-tional complexity of calculating the power allocation is upper bounded byO (U(B(B â 1) +B(B â 1))) = O(2U(B2 âB)) = O (2UB2).Third step: The number of subgraphs is the number of RRBs in thesystem. Thus, Z subgraphs constitutes the CRAN-CLNC graph, and ithas O(C!(CâB)!Z)vertices. Therefore, the computational complexity of con-structing the CRAN-CLNC graph and computing the power allocations isO(C!(CâB)!Z(2UB2)).Phase II: Maximum-weight search complexity: First, we buildthe adjacency matrix of the CRAN-CLNC graph. Particularly, we need tocheck the General Condition (GC) that explained in Section 2.3.1 of eachpair of C!(CâB)!Z vertices to determine whether they should be connectedby an edge. This adjacent connection between vertices needs a complex-ity of O((C!(CâB)!Z)2). The computational complexity of the maximum-weight search algorithm can be decomposed in sum weights and vertexsearch computations as follows. Each iteration requires a complexity ofO(C!(CâB)!Z)for weight calculations of its maximum-weight clique. Notethat each maximum-weight clique has at most Z vertices as each subgraphcan contribute at most with one vertex per transmission. Therefore, buildingthe adjacency matrix and executing the maximum-weight search have a com-plexity of O((C!(CâB)!Z)2+ C!(CâB)!Z + Z)= O((C!(CâB)!Z)2). Given theaforementioned computational complexities of the different algorithm com-ponents, the total per-iteration computational complexity of Algorithm 1 interms of main systemâs parameters is upper bounded byOï£«ï£­ ( F !(FâU)!U !)!(F !(FâU)!U !âB)!Z(2UB2)+( (F !(FâU)!U !)!(F !(FâU)!U !âB)!Z)2ï£¶ï£¸. Since the second termdominates the overall complexity, we can write the upper bound overall522.4. Iterative Optimization for Coordinated Scheduling and Power Adaptationcomplexity as Oï£«ï£­( ( F !(FâU)!U !)!(F !(FâU)!U !âB)!Z)2ï£¶ï£¸. This complexity can be approxi-mated using Stirlingâs approximation as O(( â2piC(Ce)Câ2piK(Ke)KZ)2), where K =(C â B)!. In general, the computational complexity of the joint solution isless than that as not all files can be combined due to the instant decodabilityconditions that explained in Section 2.2.2. In the uncoded case [109], thecomputational complexity is O(U !(UâB)!Z(2B3)+(U !(UâB)!Z)2). For thehigh implementation complexity of the joint solution in large networks, wedevelop in the next section an efficient and alternative coordinated schedul-ing solution that has low implementation complexity.Remark on the complexity of the joint solution: If we increase the num-ber of files without changing the number of users and RRHs, the complexityof the whole system will decrease. This is because for a large number of files,any set of randomly picked uncoded files by the RRHs has a high chance tosatisfy all users. Thus, no need to perform network coding in this scenario.2.4 Iterative Optimization for CoordinatedScheduling and Power AdaptationWe present in this section a low-complexity iterative solution to theoptimization problem (2.5). In particular, we solve the coordinated NCschedule and power control separately and iteratively upon convergence.Towards that target, we fix the power levels PLs in (2.5) and solve thefollowing simplified problem to refine NC and user-RRB/RRH schedulemaxâbnâBâzmâZâuiâUXuibnzm minuiâ²âÏbnâ²zmâ²Ruiâ²bnâ²zmâ²(2.9a)s.t. (2.5b), (2.5c), (2.5e). (2.9b)The optimization is carried over the variables Xuibnzm , Yuibn, and κbnzm . Then,we use the resulting NC and user-RRB/RRH schedule in (2.5) and solve the532.4. Iterative Optimization for Coordinated Scheduling and Power Adaptationfollowing problem per RRBs basismaxPbnzmâbnâB|Ïbnzm | â minuiâÏbnzm log2(1 + SINRuibnzm(P))s.t. 0 6 Pbnzm 6 Pmaxbnzm , âbn â B, (2.10)where Pbnzm ,âb â B is the set of optimization parameters, B is the set ofRRHs, and ui is the user that belongs to the set of targeted users Ïbnzm thathave associations in the resulting schedule. In what follows, we show howto solve problems (2.9) and (2.10), respectively.2.4.1 Coordinated Scheduling: Solution to Problem (2.9)Let S be the set of all possible associations (all pairs) between RRHs,RRBs, users, files and the achievable capacity, i.e., S = BÃZÃUÃFÃR, ands is an element in S. For example, s = (bn, zm, ui, fk, R) â S represents theRRH bn, RRB zm, user ui, file fk, and rateR. Let the coordinated schedulinggraph be denoted by G(V, E) wherein V and E refer to the set of vertices andedges of this graph, respectively. This graph is constructed by generating avertex v for each possible association s â S. In the same zm-th RRB andbn-th RRH, two vertices v â V associated with s â S and vâ² â V associatedwith sâ² â S are connected by an edge if one of IDNC conditions (C1 or C2)in Section 2.3.1 and R(s) = R(sâ²) are satisfied. This satisfaction ensuresthat all users represented by the associations have the same transmissionrate, and receive always decodable transmission. Similarly, two differentvertices belonging to two different RRHs/RRBs are then set adjacent by anedge if their combination results in a feasible schedule. Let vertex v â G becorresponding to the association s â S and vertex vâ² â G corresponding tothe association sâ² â S. The vertices v, vâ² are adjacent if one of the generalconditions (GC) is satisfied.â GC1: ui(s) = ui(sâ²) and bn(s) = bn(sâ²), â(s, sâ²) â S. This conditionrepresents that the same user can be served from multiple RRBs withinthe same RRH.542.4. Iterative Optimization for Coordinated Scheduling and Power Adaptationâ GC2: (bn(s) = bn(sâ²) and fk(s) = fk(sâ²)) OR (bn(s) = bn(sâ²) and fk(s)â Hui(sâ²) andfk(sâ²) â Hui(s)). This condition guarantees that the en-coded combinations of the same users can be served by multiple RRBswithin the same RRH.â GC3: ui(s) 6= ui(sâ²) and (bn(s), zm(s)) 6= (bn(sâ²), zm(sâ²)). Thiscondition completes the adjacencies in the graph for any two verticesnot opposing the CC1 constraint for any two different users.Example 2: We show in this example the coordinated scheduling graph andits corresponding cliques of the network presented in Example 1. In Fig-ure 2.4, each vertex v is labeled by the subscripts nmikR of the associations = (bn, zm, ui, fk, R), where n, m, i, k and R represent the indices of RRHs,RRBs, users, files, and rates, respectively. The dashed lines in Figure 2.3 rep-resent either NC conditions (C1, C2) or rate condition (R(s) = R(sâ²)), andthe solid lines represent GC1. There are many possible maximal cliques in Gthat are represented by connected vertices. Each clique represents the poten-tial network-coded scheduling of the RRHs/RRBs that maximizes through-put. For example, the potential cliques in this example represented in Fig-ure 2.4 by solid lines are: {11111, 21221},{21332, 11111}, {21221, 11332},{21111, 21221, 21331}, {11111, 11221, 11331}, {21112, 11222, 11332}, and{11223, 21112, 21332}. The achieving total throughputs of these cliques are:2, 3, 3, 3, 3, 6, and 7 bits/s, respectively. Clearly, the vertices (circles)connected by red solid lines represent the last maximal clique, and shouldbe the one selected as it offers the maximum throughput. It can be notedthat any clique in Figure 2.4 satisfies the instant decodablity transmissionto all users have vertices in it.The following theorem characterizes the solution to the coordinatedscheduling problem (2.9).Theorem 2.2. The coordinated scheduling problem in (2.9) is equivalentto a maximum-weight clique problem over the coordinated scheduling graph,wherein the weight of a vertex v â V corresponding to the association s =552.4. Iterative Optimization for Coordinated Scheduling and Power Adaptation213322111211223212211133211222 2111121331111111122111331Ru1b1z1 = 1, Ru2b1z1= 3, Ru3b1z1 = 2Ru1b2z1 = 2, Ru2b2z1= 1, Ru3b2z1 = 2Figure 2.4: The coordinated scheduling graph of the network presented inFigure 2.3 using Algorithm 2.(bn, zm, ui, fk, R) â S is given byw(v) = R. (2.11)Problem in Theorem 2.2 is NP-hard. Therefor, we make use one of theexiting algorithms, e.g., [148], [149], [150], to solve the problem in The-orem 2.2 heuristically in linear time with respect to its size as shown inAlgorithm 2.2.4.2 Power Allocation: Solution to Problem (2.10)Given the resulting NC and user-RRB/RRH schedule in problem (2.10),finding the power level PL of each RRB is a non-convex problem. Thus, wefocus on a numerical solution to achieve at least a local optimum solutionusing the Karush-Kuhn-Tucker (KKT) iteration approach. In particular,the corresponding power levels for the resulting NC and user-RRB/RRHschedule must satisfy the first derivative, i.e., KKT condition. Therefore,the objective function of the problem (2.10) which is optimized over the set562.4. Iterative Optimization for Coordinated Scheduling and Power AdaptationAlgorithm 2: Coordinated NC scheduling algorithmData: U ,F ,B,Hui ,Wui , Pbnzm ,R, and huibnzm ,(bn, zm, ui, fk) â B Ã Z Ã U Ã F ;Initialization: maximum-weight clique C = Ï.Construct G using Section 2.4.1.Solve maximum-weight clique problem over G as follows.while G 6= Ï doCompute w(v) using (2.11), âv â G.Select vâ = maxvâG{w(v)}.Set C = C âª vâ and set G = G(vâ).Continue only with the vertices adjacent to vâ.endOutput C.of powers on an RRB-by-RRB basis, can be expressed asR(Pb1zm , ..., PbBzm) =âbnâBâuiâÏbnzmlog2(1 +Pbnzm |huibnzm |2Ï2 +âbnâ² 6=bnPbnâ²zm |huibnâ²zm |2)s.t. 0 6 Pbnzm 6 Pmaxbnzm , âbn â B. (2.12)The steps of solving the power optimization problem in (2.10) is given asfollows.First, we take the first derivative of the objective function (2.12) withrespect to Pbnzm as in (2.14) and (2.15) at the top of the next page. Second,we let the gradient in (2.14) equal to zero. Then, by manipulating theoptimality condition, we obtain this manipulation for optimizing the power1PbnzmâuiâÏbnzm(SINRuibnzm1 + SINRuibnzm)=âbnâ² 6=bnâuiâ²âÏbnâ²zm|huiâ²bnzm |2Pbnâ²zm |huiâ²bnâ²zm|2((SINRuiâ²bnâ²zm)21 + SINRuiâ²bnâ²zm)(2.13)572.4. Iterative Optimization for Coordinated Scheduling and Power AdaptationâRâPb nz m=ââPb nz mâuiâÏbnzmlog2( 1+Pb nz m|huib nz m|2Ï2+âb nâ²6=b nPb nâ²zm|huib nâ²zm|2)+ââPb nz mâb nâ²6=b nâuiâ²âÏbnâ²zmlog2( 1+Pb nâ²zm|huiâ²b nâ²zm|2Ï2+âb nË6=bnâ²Pb nËz m|huiâ²b nËz m|2) =1Pb nz mâuiâÏbnzm( SINRuib nz m1+SINRuib nz m)ââb nâ²6=b nâuiâ²âÏbnâ²zm|huiâ²b nz m|2Pb nâ²zm|huiâ²b nâ²zm|2( (SINRuiâ²b nâ²zm)21+SINRuiâ²b nâ²zm) ,(2.14)where,SINRuiâ²b nâ²zm=( 1+Pb bâ²zm|huiâ²b nâ²zm|2Ï2+âb nË6=bnâ²Pb nËz m|huiâ²b nËz m|2)(2.15)anduiâÏ bnz manduiâ²âÏ bnâ²zmarethescheduledusersoftheb n-thRRH,andtheb nâ² -thRRHatthez mthRRBforâbn,bnâ²âB,respectively.582.4. Iterative Optimization for Coordinated Scheduling and Power AdaptationTherefore,Pbnzm =âuiâÏbnzm(SINRuibnzm1+SINRuibnzm)âbnâ² 6=bnâuiâ²âÏbnâ²zm|huiâ²bnzm |2Pbnâ²zm |huiâ²bnâ²zm|2((SINRuiâ²bnâ²zm)21+SINRuiâ²bnâ²zm) (2.16)Finally, we compute the optimal [Pbnzm ]Bn=1 by interpreting the powercondition iteratively. More precisely, given the power allocation at the firstiteration, the right-hand side of (2.16) can be computed using the currentpower, then the new results are used to update the new power allocations.Furthermore, to account for the RRB power constraint, an additionalprojection on [.]Pmax0 can be taken such that in each iteration, the powerlevel Pbnzm is updated according to the followingPbnzm,new =ï£®ï£¯ï£¯ï£¯ï£°âuiâÏbnzm(SINRuibnzm1+SINRuibnzm)âbnâ² 6=bntbnâ²zmï£¹ï£ºï£ºï£ºï£»Pmax0, (2.17)where,tbnâ²zm =âuiâ²âÏbnâ²zm|huiâ²bnzm |2Pbnâ²zm |huiâ²bnâ²zm|2((SINRuiâ²bnâ²zm)21 + SINRuiâ²bnâ²zm)(2.18)and the notation [a]xy represents a upper bounded above by x and lowerbounded below by y. Note that the iterative process of (2.17) must convergeto a point either lie in the interior of the constrained set or on the boundary,so as to satisfy the âKKT conditionâ of the optimization problem (for detailssee [151], [153]). It is important to note that, the nominator on the right-hand side of (2.17) represents the effect power of zm-th RRB in bn-th RRHon all corresponding RRHs in the schedule, i.e., it is the derivative of thebnâ²-th RRHs terms with respect to the zm-th RRB power in the bth RRH.In other words, it summarizes the interfering effect of Pbnzm on the bnâ²th592.4. Iterative Optimization for Coordinated Scheduling and Power AdaptationAlgorithm 3: Overall iterative approach for solving problem (2.5)Initialization: Set the initial values for Pbnzm â(bn, zm) â B Ã Zand set t = 1.Repeat:â Solve problem (2.9) based on Algorithm 1 andobtain the NC and user-RRB/RRH association according toTheorem 2.2.â Solve problem (2.10) as in Section 2.4.2 and obtainthe power levels of the corresponding RRBs.â t = t+ 1Until convergenceRRH. Moreover, it depends on the transmit power, SINR, and the ratio ofthe direct and the interfering channel gains. The dominator on the right-hand side of (2.17) shows the effect of the combined noise and interferencein zm-th RRB of bn-th RRH.The overall two-step algorithm to problem (2.5) is summarized in Algo-rithm 3.Complexity AnalysisIn this part, we analyze the complexity of constructing the coordinatedscheduling graph, i.e., generating the vertices and connecting them, andexecuting the maximum-weight search.First, we construct the scheduling graph by generating O(UF |R|) ver-tices, where |R| = UZ. These vertices represent the requested popular filesby users, which can be targeted by one RRB with one of the achievable rates.However, vertices representing different rates cannot be part of one cliquein each RRB in the same RRH. Clearly, avoiding such vertices reduces thecomplexity to O(UF ). Generalizing this to the whole system has a complex-ity of O(UFZB). Then, we iteratively search over these vertices for eachrate as will be explained later. The adjacency matrix that connects verticesby edges needs O (U2F 2ZB) for coding conditions, and O(U2F 2Z2B2) for602.4. Iterative Optimization for Coordinated Scheduling and Power Adaptationgeneral conditions. Thus, the complexity of building the adjacency matrixis O(U2F 2ZB + U2F 2Z2B2)= O(U2F 2Z2B2).Second, the maximum-weight search algorithm iteratively search overall vertices for each rate of each RRB in each RRH. This needs at most|R| maximal cliques. Since each user cannot be scheduled to more than oneRRH, each maximal clique has at most U vertices. Further, each user canbe targeted by at most one file (i.e., one vertex) from one RRB across allRRHs. Thus, the calculation of the weights in each maximal clique and itsnumber of vertices (considering the lowest rate that involves all users ) hasa complexity of O(B|R|[(UF +U)]). In the whole system, the complexity isO(BZ|R|[(UF + U)]).Finally, combining all the complexities of the different algorithm ele-ments yields the total complexity of the algorithm per iteration ofO(UFZB+U2F 2Z2B2 + BZ|R|[(UF + U)]). Overall, roughly, the second term domi-nates the total complexity as |R| 6 UZ, which abstracts the complexity ofAlgorithm 2 to O(U2F 2Z2B2).Communication and Storage OverheadsIt is important to recall that the whole process in this work is done bythe CBS. Furthermore, the CBS knows usersâ side information and storesthem in a log ledger. Therefore, compared to the standard uncoded solu-tion, coded scheme needs nothing. However, the coding scheme may needoverhead for the headers of each encoded transmission (to notify users ofthe XORed files in each transmission), but this will not exceed a few bytes.It is also worth noting that the encoded file has the same size as the sourcefiles, which simplifies both the coding overhead at the RRBs/RRHs and theusersâ decoding complexity [44]. On the other hand, for storage overheads,users need to cache some files to be used later as side information. Suchcached file is refreshed over a short period of time so as it does not in-crease with time, i.e., newer popular files are replacing older non-used files.Furthermore, increasing the capabilities of devices as well as reducing theirmemory costs enable that easily. Thus, as long as the number of cached filesis bounded, i.e., window size in our case, the cached files would not consider612.5. Numerical ResultsTable 2.1: Numerical parametersBandwidth 10 MHzCellular layout HexagonalChannel estimation PerfectChannel model SUI-Terrain type BPath loss model 128.1 + 37.6 log10(dis.[km])Background noise power -168.60 dBm/HzShadowing variance 0 dBDistribution of users Uniformas overheads (for more details about caching, see for example [122]).2.5 Numerical ResultsIn this section, we validate our developed joint CRAN-CLNC and itera-tive schemes using numerical results. We consider a downlink C-RAN systemthat described in Section 2.2 and plotted in Figure 2.1. The system settingin this section follows the setup studied in [82] and [109]. The number ofRRHs is fixed to 3 unless stated. The additional numerical parameters aresummarized in Table 2.1. Each presented value in each plot for the joint andthe iterative schemes is obtained by averaging the throughput expressions inTheorem 2.1 and Theorem 2.2 over a large number of iterations, respectively.At each run, usersâ side information is randomly generated. To assess theperformances of our proposed schemes, we simulate various scenarios: num-ber of users U , number of RRBs per each RRHâs frame, maximum powerPmax, and cell size D. For numerical comparison, the proposed solutionsare compared with the following two baseline schemes.â Classical IDNC: This scheme optimizes the selection of XOR filecombinations with the absence in physical layer aspects. For full fileâsreception, the RRBâs transmission rate is limited by the weakest userwho experiences the lowest transmission capacity.â RLNC: This scheme associates users to a single RRB to which it hasthe maximum capacity. RLNC is employed for each RRB that has622.5. Numerical Resultsmultiple associated users. The encoding is done by mixing all fileswith different random coefficients, and the selected transmission ratein each RRB is limited by the minimum achievable capacity of theassigned users.For completeness of our work, we also compare our proposed schemeswith the recent RA-IDNC and uncoded schemes that were studied in [82],[109], respectively.4 4.5 5 5.5 6 6.5 7 7.5 8Number of Users U01020304050607080Average Sum Throughput in bits/HzCRAN-CLNC JointCRAN-CLNC IterativeUncodedMaximum Power RA-IDNCRA-IDNCRLNCClassical-IDNCAverage Sum Throughput in bits/HzFigure 2.5: Average sum throughput in bits/Hz. vs the number of users U .In Figure 2.5, we plot the average sum throughput versus the number ofusers U for a C-RAN composed of 2 RRBs per RRHâs frame, F = 10 files,a file size of 1Mb, a maximum transmit power Pmax = â42.60 dBm, and acell size D = 500m. From the figure, we see that the performance gain ofthe proposed joint and iterative schemes outperform the performances of theother schemes in terms of throughput maximization. In particular, when Uis sufficiently small (U = 4, 5), the uncoded scheme works closely to the pro-posed schemes, i.e., joint CRAN-CLNC scheme offers 28% improvement overuncoded for U = 5. This is due to the fact that the proposed CRAN-CLNCschemes suffer from a small number of encoded scheduling opportunities ineach RRB/RRH. In contrast, when U is moderate (U = 7, 8), the proposed632.5. Numerical Resultsjoint scheme achieves an appreciable performance improvement (53% forU = 7 and 63% for U = 8) over the uncoded scheme. This is because theencoded opportunities of mixing usersâ flow in each RRB/RRH increases asthe number of users U increases.25 30 35 40 45 50 55 60 65Number of Users U01002003004005006007008009001000Average Sum Throughput in bits/HzCRAN-CLNC JointCRAN-CLNC IterativeUncodedMaximum Power RA-IDNCRA-IDNCRLNCClassical-IDNCAverage Sum Throughput in bits/HzFigure 2.6: Average sum throughput in bits/Hz. vs a large number of usersU .In order to evaluate the performance of the proposed schemes in a largeC-RAN, Figure 2.6 illustrates average sum throughput versus a large numberof users U for a C-RAN composed of 6 RRHs, 5 RRBs per RRHâs frame,and F = 68 files, each with a size of 1Mb. The figure suggests that, for theuncoded strategy, the average throughput increases as the number of usersU increases, but uncoded scheme serves only one user per RRB (serves intotal ZB users), which limits the overall gain in the average throughput.Conversely, if the number of users is large enough compared to ZB, jointCRAN-CLNC scheme achieves significant gain over the uncoded scheme (theaverage throughput is twice for U = 30 and almost three times higher forU = 60). We can also see that, with the limitation of rate equality forall RRHs, RA-IDNC scheme offers improved performance as compared tothe uncoded scheme at sufficiently large U . Finally, the maximum powerRA-IDNC scheme, which exploits the NC abilities, serves a good number of642.5. Numerical Resultsusers in each transmission. Thus, it works better than the uncoded one ina large C-RAN system.In Figure 2.7, we investigate the impact of the number of RRBs Z on theC-RANâs average sum throughput. We set the parameters U = 7, F = 10,N = 1Mb, Pmax = â42.60 dBm, and D = 500m. From this figure, itcan be seen that the average throughput of all schemes increases as thenumber of RRBs Z increases. This is because all schemes agree on servingthe same set of users in different RRBs in the same RRH. However, theperformances of the proposed joint scheme over the uncoded and the RA-IDNC scheme is pronounced. In fact, the proposed joint scheme emphasizesthe different relative behavior of the uncoded and RA-IDNC schemes. Inparticular, the uncoded scheme only focuses on the high achievable ratesat the expense of transmitting at most one file to a single user from eachRRB in all RRHs. The RA-IDNC scheme leverages the potential of rate-aware codes in maximizing the throughput, but it limits the transmissionrate of the same RRB in all RRHs to the minimum, which affects the overallgain. Moreover, the proposed joint scheme offers improved performance ascompared to the iterative one for larger Z as the search space becomes largerfor larger Z. This becomes more advantageous for the proposed CRAN-CLNC joint algorithm.In Figure 2.8, we plot the average sum throughput versus the maximumpower Pmax, for a C-RAN setting composed of 2 RRBs in each RRHâstransmit frame, 7 users, 9 files, a file sizeN = 1Mb, and a cell sizeD = 500m.We can see from the figure that the achieved throughput of the CRAN-CLNCjoint scheme with a larger Pmax is significantly outperformed the iterativestrategy. This is because, in the regime of large Pmax, i.e., high inter-RRHsinterference, the iterative scheme does not consider the whole search spacein the system and rather partial consideration. In contrast, the joint schemeas a method of power optimization considers the overall interferenceâs effectin the system.In Figure 2.9, we show the average sum throughput versus the cell sizeD, for a C-RAN setting composed of 7 users, 9 files, 2 RRBs in each RRHâstransmit frame, each RRB has a maximum transmit power Pmax = â26.98652.5. Numerical Results1 1.5 2 2.5 3 3.5 4 4.5 5Number of RRBs per RRH020406080100120140Average Sum Throughput in bits/HzCRAN-CLNC JointCRAN-CLNC IterativeUncodedMaximum Power RA-IDNCRA-IDNCRLNCClassical-IDNCAverage Sum Throughput in bits/HzFigure 2.7: Average sum throughput in bits/Hz. vs. the number of radioresource blocks Z.-50 -45 -40 -35 -30 -25 -20 -15 -10Maximum Power Pmax050100150Average Sum Throughput in bits/HzCRAN-CLNC JointCRAN-CLNC IterativeUncodedMaximum Power RA-IDNCRA-IDNCRLNCClassical-IDNCAverage Sum Throughput in bits/HzFigure 2.8: Average sum throughput in bits/Hz. vs maximum power Pmax.dBm, and a file size N = 1Mb. The figure confirms the result in Figure2.8 that if the cell size is sufficiently small, i.e., high interference level, theproposed joint scheme can provide high gain in average throughput overthe iterative one. As the cell size increases, i.e., low interference level, the662.5. Numerical Results0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5Cell Size in Km020406080100120140160180Average Sum Throughput in bits/HzCRAN-CLNC JointCRAN-CLNC IterativeUncodedMaximum Power RA-IDNCRA-IDNCRLNCClassical-IDNCAverage Sum Throughput in bits/HzFigure 2.9: Average sum throughput in bits/Hz. vs cell size D in Km.5 10 15 20 25Number of iterations4550556065Average Sum Throughput in bits/HzCRAN-CLNC IterativeAverage Sum Throughput in bits/HzFigure 2.10: Average sum throughput in bits/Hz. vs the number of itera-tions.performance of the proposed joint solution over the iterative one decreasesand gains only 10% improvement.We further study the convergence behavior of the iterative approach thatexplained in Algorithm 3. We set the parameters U = 8, M = 10, Z = 2,672.5. Numerical ResultsPmax = â26.98 dBm, N = 1Mb, and cell size D = 500m. We plot theaverage sum throughput versus the number of iterations, as shown in Figure2.10. As we can see from the figure, solving the coordinated scheduling andthe power allocation problems converges iteratively. This confirms the factthat both problems are increasing in the objective function.5 5.5 6 6.5 7 7.5 8 8.5 9Number of Users U012345678910Average Number of Scheduled UsersClassical-IDNCCRAN-CLNC JointCRAN-CLNC IterativeUncodedAverage Number of Scheduled UsersFigure 2.11: Average number of scheduled users vs the total number ofusers U .Finally, we study the number of scheduled users by the RRBs/RRHsversus the number of total number of users in C-RAN system. We set theparameters M = 9, Z = 1, Pmax = â26.98 dBm, N = 1Mb, and cell sizeD = 500m. It can be seen from Figure 2.11 that the number of scheduledusers in the classical IDNC scheme is larger than the number of sched-uled users in all other schemes. This confirms the fact that classical IDNCscheme works well from the network layer perspective. However, selectingthe minimum rate of the scheduled users to the RRBs/RRHs degrades itsthroughput performance as explained in the aforementioned figures. Theuncoded scheme always severs BZ users as shown in the figure. As ex-pected, the proposed schemes strike a balance between the classical IDNCand uncoded schemes in terms of the number of scheduled users.It is worth remarking that classical IDNC scheme offers completion time682.6. Chapter Summaryreduction of a frame of files in a number of NC works. However, as mentionedbefore that serving many users in each RRB while limiting the transmissionrate of the RRB to the minimum exhibits a poor performance from a cross-layer perspective. Therefore, by means of extensive numerical results, weshowed in this work that CRAN-CLNC joint and iterative schemes providea more effective way to use NC, power adaptation, and simultaneous trans-missions in C-RAN setting than all other schemes.2.6 Chapter SummaryIn this chapter, the cross-layer throughput maximization problem thatconsiders network-coded scheduling and transmit power adaptation in C-RAN downlink communication has been investigated. Two schemes havebeen developed using graph theory technique, namely joint and iterativeCRAN-CLNC schemes. Our numerical results have showed that the pro-posed schemes achieve improved performances (53% for small C-RAN sizeand almost three times higher for large C-RAN) over the uncoded solution.69Chapter 3Cross-Layer Cloud Offloadingwith Quality of ServiceGuarantees in F-RANsIn Chapter 2, we introduced a cross-layer NC framework that maximizesthe throughput in C-RANs setting. However, the developed framework didnot consider the caching strategy at the RRHs and required minimum ratefor usersâ QoS. To this end, in this chapter, we study the joint design of CBSand edge processing for F-RAN setting in which the eRRHs are equippednot only with the functionalities of standard RRHs in C-RAN, but also withlocal cache. Therefore, the introduced framework in Chapter 2 for C-RANsetting is developed to solve the immediate file delivery in F-RAN with thegoal of maximizing the CBS offloading while guaranteeing users QoS, subjectto the eRRHâs cached files and minimum required rate. The organizationof this chapter is given as follows. We summarize the accomplished worksand research contributions in Section 3.1. The system model and general as-sumptions are discussed in Section 3.2. The joint cross-layer CBS offloadingand QoS guarantee problem is modeled and formulated in Section 3.3. InSection 3.4 and Section 3.5, we develop joint and iterative cross-layer CBSoffloading and QoS guarantee approaches. In Section 3.6, we present someselected numerical results, and in Section 3.7, we summarize the chapter.703.1. Accomplished Works and Research Contributions3.1 Accomplished Works and ResearchContributionsOur contributions in this chapter are summarized as follows.1. In the first part of this chapter, we formulate the joint cross-layerCBS offloading and QoS guarantee problem in an F-RAN setting usingover an ONC graph. This formulated problem is divided into twosubproblems, namely the inner throughput maximization problem andthe outer CBS consumed time reduction problem.2. In the second part of this chapter, we show that the inner problemis equivalent to a maximum-weight independent set problem over anew designed graph, herein called the FRAN-CLNC graph. The de-signed graph jointly considers the main optimization parameters ofthe inner problem that are mentioned as follows: 1) User Associa-tion Mechanism: Each vertex represents a group of users assignedto one of the RRBs of the eRRHs, given that their requests can becombined using NC and that they can be served in this RRB withthe required minimum rate; and 2) Power Level: Each vertex repre-sents a power control solution of a specific RRB that achieves a givenrate for its targeted users, given the interference caused by the sameRRB in different eRRHs. Afterward, given the developed joint solu-tion of the inner problem, we propose a greedy coloring solution to theouter problem. In addition, we explain the required computationalcomplexity of our proposed joint scheme.3. In the third part of this chapter, we propose a low-complexity itera-tive approach to mitigate the high complexity of the above joint ap-proach. Extensive simulations are finally performed to illustrate thepotential CBS offloading and user throughput trade-offs of the pro-posed approaches. Our simulation results reveal the following threeinsights: (i) the cross-Layer QoS-unaware technique performs fairlywell in terms of offloading the CBSâs resources, but it exhibits a poor713.2. System Model and Assumptionsperformance from usersâ QoS perspective and ii) our developed solu-tions strike a balance between the CBS offloading and QoS guaranteeby targeting users that have weak channel capacities from the CBS bythe eRRHs with the required QoS, and then scheduling the unsched-uled users from eRRHs to CBSâs channel with minimum possible CBSconsumed time.3.2 System Model and AssumptionsAs illustrated in Figure 3.1, we consider the downlink communication inF-RAN, where B eRRHs, denoted by the set B = {b1, b2, · · · , bB}, in coop-eration with the CBS serve U users, denoted by the set U = {u1, u2, · · · , uU}.It is assumed that the B eRRHs communicate with the CBS using low-rate fronthaul links. The library F of popular files, denoted by the setF = {f1, f2, · · · , fF }, constitutes the set of most possible files to be re-quested by the users for within a given time frame. The considered modelgeneralizes the C-RAN set-up studied in [82], [109]. In addition to the con-ventional RRHsâ functions in C-RAN, each eRRH bn in F-RAN is equippedwith a cache, which can pre-fetch a subset of files Hbn that represents theeRRH Has set. We assume that the number of cached files in any eRRHis equal, i.e., |Hbn | = µF,â bn â B, where µ is the caching ratio, which isdefined as the ratio of the number of files in the Has set of each eRRH tothe total number of files in the library F . It is also assumed that B eRRHscollectively cache all files in the library, i.e.,âBn=1Hbn = F , the distributionof files among eRRHs is fixed, and the same file can be stored in differ-ent eRRHâs caches. Each eRRHâs transmit frame consists of Z orthogonaltime/frequency RRBs. Let Z = {z1, z2, · · · , zZ} be the set of RRBs of theframe of the eRRH, in which each RRB is maintained at a fixed duration T ,as shown in Figure 3.2(a). Therefore, the total number of available RRBsin the system is Ztot = Z. The CBS has multiple C orthogonal channels,denoted by the set C = {c1, c2, · · · , cC}, as shown in Figure 3.2(b).On the user side, each user ui has some stored files from prior downloadsin its Has set Hui , and is interested to download only one file from a library723.2. System Model and Assumptionsof F popular files, denoted as the Wants setWui of ui. All files are assumedto be equally sized of N bytes, and are delivered by the eRRHs across anumber of RRBs (or possibly by the CBS across a number of channels).It is important to note that if the transmission rate of any RRB is notsufficient to guarantee the successful download of the requested file, user uiwill download that file in parts from the same eRRH by listening to variousRRBs that denoted by Zui until completion. If user requests multiple filessimultaneously, he/she will get them from the same eRRH by listening tomultiple RRBs, each RRB would deliver each file if its transmission rate iscapable of doing so. Since the proposed schemes send the requested popularfiles with the maximum possible throughput (the least number of RRBs), itwould provide more available RRBs for serving other users. If some usersstill require more files, they can receive them either from the CBS (each userwill get one file) or from the eRRHs in the next transmissions.The eRRHs are designed to be cost-efficient devices, so their role is con-fined to sending all the relevant information to the CBS through low rate-wireless fronthaul, such as the indices of the requested/downloaded files byeach user. On the other hand, the CBS, which has sufficient processing ca-pabilities and memory, stores all the information received from the eRRHsin a log file so as to determine which files should be XORed and transmittedto the users, i.e., users-eRRH/CBS resources associations. It is further re-sponsible for synchronizing the transmission of the different frames across alleRRHs and determining the power control policies of the network. There-fore, the whole process in this work is carried at the CBS in a fully centralizedfashion. Furthermore, since the CBS is responsible to do the whole process,it is the one that needs to track the download history of users, which isknown in the NC literature by the side information. Thus, the CBS cantemporarily store this side information of users and use them later to com-bine files using ONC XOR operations. Even if user moves from one CBSto another, its log entries of the current popular files can be transferred aspart of this userâs handover procedure.733.3. Modeling and Problem FormulationFigure 3.1: A fog radio access network composed of CBS, 11 users, and 3eRRHs. Only low-rate fronthaul links are required to connect the CBS withthe eRRHs.3.3 Modeling and Problem FormulationThis section formulates the joint CBS offloading and QoS guarantee opti-mization problem in the downlink F-RAN, given its cross-layer architecture(i.e., physical and network layers) and the well-known ONC graph [22].3.3.1 Physical-LayerFor eRRH-user transmission strategy, files are transmitted over differentRRBs via a wireless link. The achievable rate of the ui-th user assigned tothe zm-th RRB in the bn-th eRRH at the t-th transmission can be expressedRuibnzm(t) = log2(1+SINRuibnzm(P)), where SINRuibnzm denotes the correspond-ing signal-to-interference plus noise-ratio experienced by the ui-th user when743.3. Modeling and Problem FormulationPb2,z1PbB ,z1 PbB ,zZPb2,zZPb1,zZPb11,z1RRB zZNon-orthogonalRRBs and theirpower levels.eRRH trans-mission framesPower levelof RRB z1 ineRRH b1T(a) eRRHs transmission frames.132ch. 3ch. 2ch. 1 ch. CCBS Channel IndexTimeinSeconds(b) CBSâs resources.Figure 3.2: Illustration of the transmission frames of the eRRHs and CBSâsresources, i.e., time in seconds of the CBSâs orthogonal channels.it is assigned to the RRB zm in the bn-th eRRH. This SINRuibnzmis given bySINRuibnzm(P) =Pbnzm |huibnzm |2âbbâ² 6=bnPbbâ²zm |huibbâ²zm |2 + Ï2, where huibnzm denotes the complexchannel gain from the zm-th RRB in the bn-th eRRH, Pbnzm is the powerallocation level (PL) of the zm-th RRB in the bn-th eRRH, P = [Pbnzm ]is the B Ã Z matrix containing the PLs of the considered network, and Ï2denotes the AWGN variance. For brevity, the time argument t is often omit-ted when it is clear from the context. It is assumed that the channel gains{huibnzm}bnâB,zmâZ,uiâU are mostly affected by the location of the users withinthe service area and can be affected by other channel impairments, e.g., shortterm fading and shadowing. Thus, each user-RRB/eRRH pair has a differ-ent channel condition, i.e., {huibnzm}bnâB,zmâZ,uiâU . Such channel model leadsto heterogeneous physical-layer rates from different RRBs/eRRHs to differ-ent users. From practical constraints, the power level of RRB zn in eRRHbn is subject to the maximum power Pmaxbnzmi.e., Pbnzm 6 Pmaxbnzm . Since thetransmit frame of each eRRH consists of Z orthogonal RRBs, SINRuibnzm(P)depends solely on the scheduled users in z-th RRB across the remainingbnâ² 6= bn eRRHs and the corresponding power level Pbnâ²zm .At the CBS, usersâ requests (if any) are transmitted via multiple orthog-753.3. Modeling and Problem Formulationonal channels. So, the achievable rate of the ui-th user from the CBS isexpressed asrCBSui (t) = log2(1 +P |hui |2Ï2), (3.1)where hui denotes the channel gain from the CBS to the ui-th user, and Pis the transmitted power of the CBS, and assumed to be fixed during thewhole transmission process. We consider the standard assumption that both{huibnzm}bnâB,zmâZ,uiâU and {hui}uiâU remain constant during each transmis-sion interval and change from one transmission interval to another transmis-sion interval. The zm-th RRB of bn-th eRRH and the ck-th channel of theCBS can transmit at a rate which is at most equal to the minimum achievablecapacity of their assigned users, i.e., Rbnzm 6 Rubnzm and rCBSck6 rCBSui , whereck â C. The set of achievable capacities of all users in all RRBs across all eR-RHs can be represented by the set as followsR = â(bn,zm,ui)â BÃZÃU Ruibnzm ,where the symbolârepresents the product of the set of the achievable ca-pacities.3.3.2 Opportunistic Network Coding in the Network-LayerIn [145], the authors introduced the ONC graph as a design to representall usersâ demands and their possible ONC combinations. The generationof the ONC file combinations κ relies on the fact that the multiplexed-usersÏ can be served by one combined (encoded) file. Therefore, two distinctvertices vui,fl and vuiâ² ,flâ² are linked with a coding conflict edge if the followingconnectivity condition (CC) is satisfied.â CC: fl 6= flâ² and (fl, flâ²) /â Hui ÃHuiâ² . This condition represents thefact that both users do not want the same file and at least one of theusers inducing either vertices does not have what other user wants.Clearly, this condition ensures that any file combinations κ generated by thevertices of any independent set I is always decodable to the targeted usersÏ having vertices in the ONC graph. Thus, each I in that graph consists oftwo components, i.e., I = (Ï, κ).763.3. Modeling and Problem FormulationExample 3: We provide an example for a better illustration of the con-struction of both ONC and color graphs that will be used throughout thischapter. As shown in Figure 3.3, a system containing of 1 eRRH, 1 RRB,and 5 users.Example 4: To illustrate the concept of CLNC and the performance met-rics that are considered in this chapter, let us consider the same examplein Figure 3.3. Given a certain power allocation to the eRRH and the CBS,assume that the achievable capacities of the 5 users to the RRB of the eRRHand to the CBS are given in the right side of Figure 3.3. In order to maximizethroughput and offload the CBS for this example, there are many possiblesolutions.One possible solution is that the eRRH targets the set of users Ïb1z1 = u2,u3 and u4 in one RRB by XORing f1, f2 and f3 into an encoded combinationκb1z1 = f1 â f2 â f3 and sends κ11 with an achievable transmission rate of2 bits/s. Therefore, the encoded combination κ11 is instantly decodable bythe set of targeted users Ï11 and both components are represented by anindependent set, i.e., Ib1z1 = (Ïb1z1 , κb1z1). The decoding operation at theusersâ side can be performed as follows: u2 retrieves f1 by XORing κ11 withf2 and f3, u3 retrieves f2 by XORing κ11 with f1 and f3, and u4 retrieves f3by XORing κ11 with f1 and f2. The achievable overall throughput in thisscenario is 6 bits/s as each of u2, u3, and u4 simultaneously can receive 2bits/s worth of throughput. Such throughput improves upon the 2.5 bits/sthroughput achievable without coding. Indeed, the eRRH targets the userthat has the maximum achievable capacity among all other users, i.e., u4with a rate of 2.5 bits/s. Next, given this smart user-scheduling and NCprocess by the eRRH, the CBS schedules the remaining users to its channelsso as to minimize its physical-resources consumed time. Thus, CBS targetsu1 by sending f2 with transmission rate of 2.5 bits/s, which gives a consumedtime of N2.5 seconds, and targets u5 by sending f3 with transmission rate of5 bits/s, which gives a consumed time of N5 seconds. As a result, the CBSreserves channel 1 and channel 2 for the duration of sending file κ1 = f2 andκ2 = f3 to Ï1 = u1 and Ï2 = u5, respectively. Therefore, the overall CBStotal consumed time is the sum of its channel consumed times N2.5 +N5 =3N5773.3. Modeling and Problem Formulationseconds that used to serve u1 and u5. Clearly, the smallest this expression,the more CBSâs channels can be used to serve other users, thus yielding toa better CBS offloading improvement.Another possible solution is that the eRRH targets u1, u2, and u3 in oneRRB by sending the encoded file f1 â f2 with a transmission rate of 0.5bits/s (the lowest rates of u1, u2 and u3), and the CBS targets u4 and u5in one channel by sending the file f3 with transmission rate of 1.25 bits/s.Scheduling u1, u2, and u3 to the eRRH, which can be performed from thecoding/decoding perspective, would achieve an even worse throughput andCBS consumed time results than the above solution. Indeed, it will notonly limit the rate sent by the eRRH to 0.5 bits/s that results to an overallthroughput of 1.5 bits/s, but will also require N1.25 seconds to complete thefile delivery from the CBS, longer than the above solution that needs twotransmissions from the CBS. This clearly exhibits the effectiveness of CLNCin maximizing the throughput and minimizing the CBS actual-consumedtime. This result can be further improved by optimizing the power assign-ment and the corresponding rate selection for each RRB in each eRRH, aswill be used in this work through these two important and novel features ofCLNC.3.3.3 Problem FormulationGiven the aforementioned configurations, we are now ready to formu-late the joint CBS offloading and QoS guarantee optimization problem inan F-RAN setup as follows. Let, Ibnzm , bn â B and zm â Z, be an indepen-dent set, whose encoded XOR file κbnzm will be combined and transmittedby RRB zm in eRRH b to serve the users in Ïbnzm . These independentsets represent the transmissions by eRRHs/RRBs that serve users with therequired QoS. Our problem is then reduced to finding the set of indepen-dent sets P = Ich , · · · , IcC , so as to target the remaining users with theminimum consumed CBSâs resources. In other words, P is the set of allindependent sets of the ONC graph after removing Ibnzm , â bn, zm, i.e.,(G \u00E2Bn=1âZm=1 Ibnzm). Now, let us define P as a subset in P, i.e., P â P,783.3. Modeling and Problem FormulationONC Graphu1, f2u4, f3u5, f3u3, f2u2, f1Color Graphu4, f3u5, f3f3 f4f3 f4f3 f4f1f2f4u1u2u3u4u5eRRH b1 f4f2f3 f4f2CBSSide-informationf2f2f3Ruib1z1u1u2u3u4u50.5222.51Achievable capacities of usersrCBSui2.52.521.255f1f1f1f5f5f5f5f5f5f1Figure 3.3: A system containing 5 users, in which each user requestsone file. Each independent set in the ONC graph represents a feasi-ble ONC combination. For example, one possible independent set I is:{(u1, f2), (u2, f1), (u3, f2)} that corresponds to transmitting the combina-tion κb1z1 = f1 â f2 to the targeted users Ïb1z1 = u1, u2 and u3, i.e.,Ib1z1 = {(u1, u2, u3), (f1 â f2)}. The color graph corresponds to the mini-mum number of coded transmissions to target the remaining users. Eachcoded transmission is represented by vertices having the same color (yel-low) and can be sent by one CBS channel. In particular, both vertices{(u4, f3), (u5, f3)} have the same color and correspond to transmitting filef3 to both users via one CBS channel.and S(P ) is a set of independent sets in P . Thus, the joint CBS offload-ing and QoS guarantee optimization problem in F-RAN settings is thenexpressed asminIbnzm , Â·Â·Â· , IbBzZPâPâIchâS(P )NminuiâÏchrCBSui(3.2a)s. t.ï£±ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£²ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£³Ibnzm = arg max ÎºbnzmâHbnâuiâÏbnzm log2(1 + SINRuibnzm(P)),âZm=1 Ïbnzm â©âZm=1 Ïbnâ²zm = Ï, â (bn, bnâ²) â B,Ïbnzm ={ui â Uâ£â£|Îºbnzm â©Wui | = 1 & Rbnzm 6 Ruibnzm} ,T.âzmâZui Rbnzm 6 N, â ui â U ,âZm=1 κbnzm â Hbn , â bn â B,Rbnzm â¥ Rth, â (bn, zm) â B Ã Z,0 â¤ Pbnzm â¤ Pmaxbnzm , (bn, zm) â B Ã Z,κbnzm , κch â P(F), (bn, zm) â B Ã Z,(3.2b)793.3. Modeling and Problem Formulationwhere the optimization is carried over the variables κbnzm , κch , Rbnzm andPbnzm . Second constraint states that the sets of targeted users in all RRBs ineRRH bn and bnâ² are disjoint, where bn 6= bnâ² . In other words, the same usercannot be served from two different eRRHs. Third constraint states that allusers belonging to the targeted sets Ïbnzm â bn â B and zm â Z must receivean instantly decodable transmission. To do so, each RRB should adopt itstransmission rate to satisfy the successful reception of all its assigned users.However, this adopted transmission rate may not be able to deliver the wholefile/content to the assigned users, given the fixed duration T of the RRB.Thus, such assigned users need to be scheduled to different RRBs, denotedby Zui , in the same eRRHs so as to guarantee the successful download oftheir requested file, given the total number of RRBs in the eRRHâs frame.In other words, user ui will be scheduled to a set of RRBs Zui as long as itswanted file had not delivered yet, i.e., the fourth constraint. If one RRB iscapable of delivering such request to user ui, this user will not be scheduledto any other RRBss in the same eRRH. Fifth constraint ensures that allfiles/requests to be combined using XOR and served by all RRBs Z ineRRH bn are stored in its cache. Sixth constraint guarantees the minimumtransmission rate Rth required to achieve the QoS requirements. Finally,the last constraint accounts for the fact that the transmission power of eachRRB in each eRRH is bounded.The objective function (3.2a) of the optimization problem (3.2) repre-sents the outer CBS consumed time reduction problem, and the constraints(3.2b) represent the inner throughput maximization problem. Finding theglobal optimal solution to the joint optimization problem (3.2) requires asearch over all the sets of targeted users, their possible ONC combinations,and the optimal power levels and the corresponding transmitted rates ofeach RRB and each CBS channel. As such, finding an optimal solution to(3.2) is challenging and not feasible. Furthermore, finding the global solutionto only (3.2b), i.e., joint user-scheduling and power optimization problem ischallenging, and it is NP-hard problem in general [154], [155]. In order toseek an efficient solution to (3.2), we propose to use a graph representation.As such, (3.2b) is shown to be equivalent to a maximum-weight independent803.4. CBS Offloading and QoS Guarantee: Joint Approachset problem over a novel FRAN-CLNC graph, and (3.2a) is minimum col-oring problem over a color graph. In order to construct the FRAN-CLNCgraph, the rest of this subsection introduces the used variables as follows.Let Sbn be the set of all possible associations between users and files thatcached by eRRH bn, i.e., Sbn = UÃHbn . Let Ïui and Ïfl be a family of map-pings from the set Sbn to the set of users U and the set of filesHbn . The math-ematical definition of these mappings given the element y = (ui, fl) â Sbnare Ïui(y) = ui and Ïfl(y) = fl. The set of all possible ONC file combina-tions SIDNC,bn in eRRH bn is created based on the fact that the associationss in Sbn can be served by one XOR encoded file. Intuitively, s, sâ² in Sbn arecombined if the non-instant decodability condition (CC) not satisfied. TheONC file combinations set of the whole F-RAN system is simply the unionof ONC file combinations of all eRRHs, i.e., S = âbnâBSIDNC,bn . Let Abn bethe set of all possible associations between RRBs, ONC file combinations,and achievable capacities of the bn-th eRRH, i.e., Abn = Z Ã SIDNC,bn ÃR.Let Ïzm , Ïs, and Ïr be a family of mappings from the set Ab to the set ofRRBs Z, the set of ONC file combinations SIDNC,bn , and the set of achiev-able capacities R. Given the element y = (z, s, R) â A, the mathematicaldefinition of the mappings are Ïz(y) = z, Ïs(y) = s, i.e., s = (κ, Ï), andÏr(y) = R, respectively. Similarly, the set of all possible associations ofthe whole system is simply the union of possible associations of all eRRHs,i.e., A = âbnâBAbn . Let Azm represent the associations relative to the zm-thRRBs across all eRRHs, i.e., y â Azm â Ïzm(y) = zm.3.4 CBS Offloading and QoS Guarantee: JointApproach3.4.1 FRAN-Cross-Layer NC GraphThe FRAN-CLNC graph is introduced as a cross-layer NC design thatjointly optimizes NC combinations, users-eRRHs/RRBs assignments, andtransmission power of the RRBs in the downlink F-RAN setup. The FRAN-813.4. CBS Offloading and QoS Guarantee: Joint ApproachCLNC graph, denoted by G(V, E), is constructed by first generating all theZ RRB subgraphs, in which the vertex set of the FRAN-CLNC graph is theunion of vertices of all the subgraphs, i.e., V = âzmâZVzm .Let the subgraph of the zm-th RRB in the network be denoted byGzm(Vzm , Ezm) where Vzm and Ezm refer to the set of vertices and edgesof this subgraph, respectively. In order to represent the ONC file combina-tions s = (Ï, κ), the transmission rate R of each eRRH in the RRB zm, afeasible schedule S is generated. The generation of S is done by merging allpossible associations s â Azm for the different eRRHs under the constraintthat the same user cannot appear more than once in S. Therefore, eachvertex v â Vzm associated with S â Sfs,zm satisfies Ïbn(s) 6= Ïbn(sâ²) andÏui(s) 6= Ïui(sâ²) for all s 6= sâ² â S, where Sfs,zm is is the set of all possiblefeasible schedules corresponding to the zm-th RRB. The fundamental stepof merging the set of all possible associations s â Azm relies on the fact thatusers in these associations can be served simultaneously. Therefore, eachvertex v â Vzm representing the association S satisfies the following.â Two associations s, sâ² â S representing the same RRB z and the sameeRRH bn have the same transmission rate, i.e., Ïr(s) = Ïr(sâ²).â Two associations s, sâ² â S representing different eRRHs have differentset of targeted user(s), i.e., Ï â© Ï â² = â .In mathematical terms, each vertex v â Vzm representing the associationS satisfies the following local conditions (LC).â LC1: â (s, sâ²) â S, Ïbn(s) = Ïbn(sâ²) and Ïr(s) = Ïr(sâ²).â LC2: â (s, sâ²) â S, Ïbn(s) = Ïbn(sâ²) and Ï â© Ï â² = â .Clearly, the above verticeâs configurations point out the fact that each vertexin the RRB subgraph reflects partial contribution to the network. In otherwords, it totally represents that specific RRB, and each pair of vertcies vand vâ² â Vzm is connected by a conflict edge.823.4. CBS Offloading and QoS Guarantee: Joint ApproachGiven the configuration of the vertices and the edges between themwithin the same RRB subgraph, in the following, we will describe the re-maining edges corresponding to different RRB subgraphs. Two vertices vand vâ² corresponding to S and Sâ² and belonging to two different subgraphsGzm and Gzmâ² , respectively, are linked by a conflict edge if the resultingcombination satisfies one of the following events.â At least one user appears in both s â S and sâ² â Sâ², i.e., Ï â© Ï â² 6= â .â The transmission rate of any RRB to the targeted user(s) Ï is sufficientto successfully download their encoded file κ from only one RRB.In mathematical terms, two vertices v and vâ² are linked by a conflict edge ifthe associations they represent satisfy one of the following general conditions(GC).â GC1: â (s, sâ²) â SÃ Sâ², Ï â© Ï â² 6= â and Ïbn(s) 6= Ïbn(sâ²).â GC2: â (s, sâ²) â SÃ Sâ², Ï = Ï â² and Ïb(s) = Ïb(sâ²) and T.Rbnzm â¥ N .Assuming that the power distribution P of all RRBs in the system willbe computed later, a vertex v representing the associations S â Sfs,zm hasa secondary weight that reflects the partial throughput contribution to thenetwork, i.e., the secondary weight of v can be expressed asws(v) =âsâSminÏui (s)âÏÏbn (s),Ïzm (s)log2(1 + SINRÏui (s)Ïbn (s)Ïzm (s)(P)). (3.3)Now a vertex v representing the associations S has a primary weight thatreflects the degree of priority of users in S to be served from RRBs/eRRHs,i.e., the primary weight of v can be expressed aswp(v) =âsâSNrCBSui. (3.4)In particular, a larger primary value of wp(v) offers a larger download timefrom the CBS (lower rate from the CBS) of each represented file in S. Theweighting design of each vertex can be summarized as follows. A larger value833.4. CBS Offloading and QoS Guarantee: Joint Approachof ws(v) and wp(v) in (3.3) and (3.4), respectively, leads to a cross-layer en-coded transmission that offers a better performance of throughput and CBSoffloading. In particular, the higher the primary weight (3.4), the largerthe physical-layer resource consumed time of the CBS channels. This yieldsto a smart scheduling of users representing the corresponding vertex witha higher secondary weight (3.3), which in turn maximizes the throughput.Therefore, any maximal independent set in FRAN-CLNC graph representsa set of coded transmissions that satisfies the following criterion: 1) the rep-resented users by vertices in the maximal independent set are experiencingthe lowest rates from the CBS, 2) all targeted users satisfy the required min-imum rate, and can decode the requested file from the transmission scheduleof all RRBs and eRRHs, 3) users are listening to multiple RRBs in the sameeRRH as long as the successful download of their requited files is not guaran-teed, and 4) each RRB identified by the vertices in a maximal independentset adopts the transmission rate identified by the vertex. Such rate is lessthan or equal to the channel capacities of all users served by that RRB.Given the optimal power allocation P and the weighting design of eachvertex, the following theorem characterizes the solution of the inner through-put maximization problem by allocating users to the RRBs of each eRRHand adapting the power levels, such that the userâs QoS is guaranteed.Theorem 3.1. The inner throughput maximization problem (3.2b) is equiv-alent to a maximum-weight independent set problem over the FRAN-CLNCgraph, and can be written asarg maxIâIâvâIws(v), (3.5)where I is the maximum-weight independent set in the FRAN-CLNC graph,I is the set of all possible maximal independent sets of degree Z, and theweight of a vertex v â V is defined in (3.3).Proof. The proof of this theorem can follow the same steps that used ininvestigating Theorem 2 in [109]. The main difference is that we multiplexusers that have cached files in eRRHs to the RRBs instead of assigning one843.4. CBS Offloading and QoS Guarantee: Joint Approachuser in each RRB. Interested readers can read the proof in Appendix A.The set of targeted users and the file combination of the zm-th RRBacross all eRRHs is obtained by combining the vertices of the maximal-weight independent set Izm corresponding to the RRB subgraph Gzm , inwhich Izm is the union of all maximal-weight independent sets for that RRBin each eRRH, i.e., Izm =âBn=1 Ibnzm . Therefore, I =(âBn=1âZm=1 Ibnzm).3.4.2 Greedy AlgorithmIt can be noted that the optimization problem (3.2) is formulated usingONC graph. The global solution is, therefore, equivalent to a maximum-wight independent set over FRAN-CLNC graph and a minimum weightcoloring over a color graph, which is an NP-hard problem [74], [156], and sois the problem (3.2). However, it is established that it can be near optimallysolved with a reduced complexity as compared the O(|V|2.2|V| + V log(V))naive exhaustive search methods, e.g., the algorithms in [149], [150], and[156]. The maximum-weight independent set and the color problems canbe solved sequentially in a linear time with their sizes in simple heuristicsolution as explained in this subsection. While the proposed solution isnot necessarily optimum, it works well for solving (3.2) for one particulartransmission.The joint cross-layer CBS offloading and QoS guarantee optimizationalgorithm is executed at the CBS at each transmission and broken into twophases as follows.Phase I: This phase solves the inner throughput maximization problem(3.2b) in two steps, the FRAN-CLNC graph design step and the maximum-weight search step.First step: The FRAN-CLNC graph can be designed as follows. A subgraphGzm is generated for each RRB zm â Z using LC1 and LC2. Afterwards,for each RRB zm â Z across all eRRHs, a vertex v â Gzm correspondingto the feasible schedule S â Sfs,zm is generated for all possible associations.The optimal PLs of each association are, then, computed by solving theoptimization problem (2.10). The vertex in the subgraph Gzm is generated by853.4. CBS Offloading and QoS Guarantee: Joint Approachappending the computed PLs and the corresponding rates to that vertex asshown in Section 3.4.1. The same steps above are repeated for all RRBs zm âZ. The FRAN-CLNC graph is, then, designed by merging all subgraphs andadding connections according to GC1 and GC2.Second step: The algorithm finds the maximum independent set I amongall the maximal independent sets I in FRAN-CLNC graph. Each iteration offinding I is implemented as follows. The algorithm computes the secondaryweight of all generated vertices using (3.3). Now let the primary weightsof these generated vertices are computed using (3.4). The vertex with themaximum-primary weight vâ is labeled and find its corresponding vertexthat has the maximum-secondary weight vââ among all other correspondingvertices. The selected vertex vââ is, then, added to I, i.e., I is assumed to beinitially empty. Afterwards, FRAN-CLNC G graph is updated by removingthe selected vertices vââ and its adjacent vertices. As such, the next selectedvertex is not in coding nor transmission conflict with the already selectedones in I. The process continues until no more vertices exist in FRAN-CLNC graph G. Since each RRB subgraph contributes by a single vertex,the number of vertices in I is Z.Phase II: Second phase solves the outer CBS consumed time reductionproblem (3.2a) by serving users that are unserved by the eRRHs, so thatthey can be served by the least consumed time of CBS physical resources.Mathematically, this phase serves(U âbnâBâzmâZÏbnzm)users. Therefore,in each transmission, phase II removes all vertices from the ONC graphthat represent these served users by the eRRHs, i.e., ONC graphI. Theremaining vertices are, then, sorted in a list M in descending order based ontheir corresponding weights, in which the weight of each remaining vertexvui,fl =NrCBSui. Given the weight of each remaining vertex, a greedy coloringscheme is performed as follows. First, it picks the highest weight vertexvâ and colors it with a certain color c1. Then, it scans all vertices in thatlist, searching in each step for any vertex not adjacent to vâ, and coloringit with c1. The scheme continues until no more vertices are not adjacentto all previously colored vertices in c1. The scheme, then, removes the863.4. CBS Offloading and QoS Guarantee: Joint Approachselected vertices having color c1, and repeating the above steps again withanother color c2. This process continues until no vertices have not coloredyet in M. The key idea in this scheme is to color the vertices of userssatisfying the NC conditions and experiencing the lowest rates by the samecolor. Each group of same-color vertices will thus be served in one CBSorthogonal channel. The overall two-phase algorithm to the problem (3.2)is summarized in Algorithm 43.4.3 Computational Complexity of Joint ApproachIn each transmission of FRAN-CLNC, the CBS requires to compute thecomplexity of phase I and phase II in Algorithm 4.Phase I Complexity: Each eRRH b requires to find all its file combina-tion possibilities |SIDNC,bn | that satisfy CC and relate these combinationsto its RRBs, which give the total file combinations in the system S. Sinceeach feasible schedule in the network may involve associating different usersto different eRRHs (i.e., satisfy LC1 and LC2), the number of feasibleschedules can be computed by permutating S among all eRRHs. Thus, thetotal number of these schedules is SPB, which is represented by the ver-tices in the RRB subgraph. Further, calculating the optimal power needsto execute the optimization problem (2.10) on each vertex. Thus, the com-plexity of obtaining a RRB subgraph is SPBc(A), where c(A) is the com-putational complexity of solving the power allocation problem (2.10) withA variables. The total number of RRB subgraphs is Z, thus introducingan FRAN-CLNC graph design complexity of SPBc(A)Z. To connect all thegenerated vertices SPBZ in FRAN-CLNC graph using GC1 and GC2, thealgorithm needs (SPBZ)2. Now, solving the maximum-weight independentset in FRAN-CLNC graph requires weight calculations and vertex searchmethod of f(SPBZ), where f(x) is the complexity of solving the maximum-independent set in a graph containing x vertices. The overall phase I com-plexity is then O(SPBZ[c(A) + SPBZ] + f(SPBZ)).Phase II complexity: Given the solution to the inner problem, the num-ber of remaining users having vertices in ONC graph is V = ONC graphI.873.4. CBS Offloading and QoS Guarantee: Joint ApproachAlgorithm 4: Joint Cross-Layer CBS Offloading and QoS Guar-antee Optimization AlgorithmData: U ,F ,B,Z,Hbn ,Hui ,Wui , hui and huibnzm , (ui, fl) â U Ã F ,(bn, zm, s) â B Ã Z Ã S;Construct the ONC graph using Section 3.3.2.Phase I: Solve the inner throughput maximization problem(3.2b).â Initialize the maximum-weight independent set I = Ï.for zm = {z1, z2, · · · , zZ} doInitialize the cluster Gzm = Ï.for each S = {s1, s2, · · · , sS} â Sfs,zm doSolve (2.10) to compute the optimal power allocationsP = {(pâb1zm , pâb2zm , · · · , pâbBzm)}.Create: v = {{(s1, râb1zm , pâb1zm), · · · , (s|Ïb1zm (κb1zm )|, râb1zm , pâb1zm)}, · · · , {(sbB , râbBzm , pâbBzm), · · · , (s|ÏbBzm (κbBzm )|, râbBzm , pâbBzm)}Calculate ws(v) using (3.3).Set Gzm = Gzm âª {v}.endendâ Set G = âzmâZ Gzm and connect vertices of G using GC1 and GC2â Solve the maximum-wight independent set problem in G to find I as followswhile G 6= Ï doSelect the maximum-primary weight vâ = maxvâG{wp(v)} and find itscorresponding vertex with the maximum-secondary weightvââ = maxvâG{ws(v)}.Set I = I âª vââ and G = G(vââ) and continue only with vertices notlinked to vââ in G.endPhase II: Solve the outer CBS consumed time reductionproblem (3.2a).â Set h = 1.â â vertex vuifl â ONC graphI: calculate w(vuifl) = NrCBSui and sort them ina list M in descending order.while M 6= Ï doInitialize the independent set Ich = Ï.Select the first vertex vâ and color it with Cc.Set Ic = Ich âª vâ.Continue coloring all vertices not adjacent to vâ with ch and addingthem to Ich and set M = M Ich .Set h = h+ 1.endResult: I and I1, I2, · · · 883.5. CBS Offloading and QoS Guarantee: Iterative ApproachThus, the greedy coloring step requires to calculate the weights of vertices Vand sort them, which has a computational complexity of O(V + (V log(V )))[30].Therefore, the overall per-transmission computational complexity of FRAN-CLNC is O(SPBZ[c(A)+SPBZ]+f(SPBZ)+V [1+log(V )]). In the uncodedcase, the per-transmission complexity reduces to O(UPBZ[c(A) +UPBZ] +f(UPBZ)+V ). We note that the computational complexity of FRAN-CLNCis sensitive to the number of NC possibilities. Consequently, FRAN-CLNChas higher complexity which justifies our resorting to the iterative simpleapproach. Finally, the transmission overhead that the CBS needs to exe-cute Algorithm 4 can be analyzed as follows. Since the eRRHs report to theCBS about the cached and the non-downloaded files at the users, all sideinformation is known to the CBS. Clearly, this needs a few bytes of con-trol signaling. Thus, compared to the standard LTE uncoded solution, noadditional overhead is needed for the coded users-eRRHs/CBS schedulingscheme. However, the coded solution may need overhead for the headers ofeach eRRHs/CBS encoded transmission (to inform users of the XORed filesin any transmission), which is negligible in size compared to the entire fileâssize.3.5 CBS Offloading and QoS Guarantee:Iterative ApproachThis section recommends that instead of solving (3.2b) jointly which re-quires high computational complexity, one way to mitigate such high com-plexity is to solve (3.2b) iteratively. In particular, (3.2b) is solved itera-tively in such a way that for a given fixed transmit power of each RRB,the throughput optimization problem is solved as a coordinated schedulingproblem. Afterward, the power allocation problem is solved numericallyfor the resulting NC and user-RRB/eRRH schedule. The process iteratesbetween these two steps until convergence. Given the iterative solution tothe inner problem, the outer CBS time reduction problem (3.2a) is solved893.5. CBS Offloading and QoS Guarantee: Iterative Approachusing greedy coloring scheme as in the joint approach. Towards that goal,this section first addresses the optimization problem (3.2) as a coordinatedscheduling problem only, and can be written asminIbnzm , Â·Â·Â· , IbBzZPâPâIcâS(P )NminuâÏcrui(3.6a)s. t.ï£±ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£²ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£³Ibnzm = arg max ÎºbnzmâHbâuâÏbz RbnzmâZm=1 Ïbnzm â©âZm=1 Ïbnâ²zm = Ï,â(bn, bnâ²) â B,Ïbnzm ={ui â Uâ£â£|Îºbnzm â©Wui | = 1 & Rbnzm 6 Ruibnzm} ,T.âzmâZuui Rbnzm 6 N, âui â U ,âZm=1 κbnzm â Hbn , âbn â B,Rbnzm â¥ Rth, â(bn, zm) â (B,Z).(3.6b)The optimization is carried over the variable Rbnzm , κbnzm . On the otherhand, for the resulting NC and user-RRB/eRRH schedule, the inner opti-mization problem (3.2b) can be considered as a power allocation step andsimplifies on a per RRB basis. For each RRB zm, the optimization problem(3.2b) can be written as in (2.10).Coordinated Scheduling GraphSimilar to our preliminary work [128] the scheduling graph is formed by gen-erating a vertex vbn,zm,ui,fl,r for each bn â B, each zm â Z, for every user uirequests a file fl, and for each achievable rate for that user r â¥ Rth. The con-figuration of the set of edges in the scheduling graph is divided into codingand transmission conflict edges. Two vertices vbn,zm,ui,fl,r and vbn,zm,uuâ² ,flâ² ,râ²representing the same RRB zm and the same eRRH bn are adjacent by acoding conflict link if the transmission is non decodable to one of them (sat-isfy the condition in Section 3.3.2 or the transmission rate is different (i.e.,r 6= râ²). Similarly, two vertices vbn,zm,ui,fl,r and vbnâ² ,zmâ² ,uiâ² ,flâ² ,râ² representingdifferent RRB zm and different eRRH bn are adjacent by a transmissionconflict link if one of these conditions is true:903.5. CBS Offloading and QoS Guarantee: Iterative ApproachAlgorithm 5: Coordinated Scheduling AlgorithmData: U ,F ,B,Hb,Hui ,Wui , Pbnzm ,R and huibnzm ,(bn, zm, ui, fl) â B Ã Z Ã U Ã F .Initialize the maximum-weight independent set I = Ï.Construct G and solve the maximum-weight independent setproblem over G as follows:while G 6= Ï doâ vertex v â G: calculate the primary weight wp(v) and thesecondary weight wËs(v) as illustrated in Section 3.5.Select the maximum-primary weight vâ = maxvâG{wp(v)} andfind its corresponding vertex with the maximum-secondaryweight vââ = maxvâG{wËs(v)}.Set I = I âª vââ and continue only with the vertices not adjacentto vââendResult: I.â ui = uiâ² and (bn, zm) = (bnâ² , zzâ²), we have T.Rbnzm > N . This condi-tion schedules user to multiple RRBs in the same eRRH as long as itsrequested file has not received completely.â ui = uiâ² and (bn, zm) 6= (bnâ² , zmâ²). This condition insists that the sameuser cannot be scheduled to different eRRHs in all RRBs.Consider the primary weight of each vertex vbn,zm,ui,fl is defined as wp(v) =NrCBSui. Thus, the vertexâ weight becomes large when its file download timefrom the CBS is large, thus representing a lower rate from the CBS. Giventhe above configuration of the scheduling graph and the weighting designof each vertex, it can be established that any maximal independent set inthat graph satisfies that all users have vertices in the selected set receivean instantly decodable transmission that meets QoS requirements, and thencan decode a new file.The following theorem characterizes the solution of allocating users, sat-isfying the required minimum rate and having the worst download rates fromthe CBS, to the RRBs across all eRRHs, such that the received throughputis maximized.913.6. Numerical ResultsTheorem 3.2. The coordinated scheduling problem (3.6) is equivalent to amaximum-weight independent set problem over the scheduling graph, whereinthe secondary weight of a vertex vbn,zm,ui,fl,r is given byw(v) = r. (3.7)The set of targeted users and the file combination of the zm-th RRB in theb-th eRRH is obtained by combining the vertices of the maximum-weightindependent set I in the coordinated scheduling graph.Heuristic SolutionMaximum-weight independent set problems are NP-hard problems wherethe complexity of solving these problems optimally needs |V|2.2|V| cost of anexhaustive search solvers where V is the set of vertices of graph G. However,it is established that it can be efficiently solved with a reduced complex-ity α|V| where α is the complexity constant [29, 30]. Even though suchcomplexity is less than an exhaustive search, it is still high for moderatesize networks. Thus, the maximum-weight independent set problem can besolved here in a linear time with its size in a simple heuristic solution as inAlgorithm 5. Let w(v) the raw weight of vertex v in the scheduling graphas expressed in Theorem 3.2. The modified weight wËv of vertex v can bedefined aswËs(v) = w(v)âvâ²âVvw(vâ²), (3.8)where Vv is the set of vertices not connected to vertex v by neither codingnor transmission conflict edges. The appropriate design of the weights showsthat wËs(v) reflects the contribution of the vertex to the network as it has alarge raw weight and non-adjacent to a large number of vertices induced byusers with high raw weight.3.6 Numerical ResultsIn this section, we present some numerical results that compare the per-formance of both proposed schemes with the baseline algorithms in [109],923.6. Numerical Results[126] and [127]. We consider a downlink F-RAN system where the positionsof 3 eRRHs are fixed and users are distributed randomly within a hexagonalcell of radius 500m. The channel gains are generated according to SUI-Terrain type B. The channels are assumed to be perfectly estimated. Thenoise power and the maximumâ RRB/CBS power are set to Ï2 = â168.60dBm/Hz and Pmaxbnzm = P = â42.60 dBm/Hz, respectively. The bandwidthis 10 MHz, the shadowing variance is 6 dB, and the eRRH caching ratio µ isset to 0.6. To evaluate the performance of the proposed solutions at differ-ent thresholds, we simulate various scenarios: number of users, number ofpopular files, and number of RRBs per eRRHâs frame. In these evaluations,the average throughput and the CBS consumed time are computed over acertain number of iterations, and the average values are presented. For thesake of comparison, we implement following schemes.â Upper-Layer (denoted by UL): This scheme jointly optimizesthe selection of ONC file combinations for each RRB in each eRRHand each CBSâ channel without considering the physical-layer rates ofusers. This scheme is proposed in [126].â Uncoded: The transmission strategy in this scheme is performedirrespective of the available information at the network layer, i.e., priordownload files. The user-RRB association in this scheme is proposedin [109].â Cross-Layer QoS-unaware (denoted by CL): In this scheme, allusers experiencing low rates from the CBS are multiplexed based ontheir requests and targeted from RRBs/eRRHs randomly. This schemeis proposed in [127].â Proposed FRAN-CLNC: This scheme is described in Section 3.4.â Proposed Iterative: This scheme is described in Section 3.5.In Figure 3.4, we show the total CBS consumed time and the averagethroughput versus the number of users U for M = 10 files, each with a sizeof 10 MB, and 3 RRBs in each eRRHâs frame. As we can see from Figure933.6. Numerical Results9 10 11 12 13a - Number of users U10152025303540Total CBS consumed time in secondFRAN-CLNC Joint, R th=5UncodedFRAN-CLNC Joint, R th=0.5ULFRAN-CLNC Joint, R th=0.05CLNC-FRAN Iterative, R th=0.05CLTotal CBS consumed time in second9 10 11 12 13b - Number of users U60080010001200140016001800Average throughput in bits/secondFRAN-CLNC Joint, R th=5FRAN-CLNC Joint, R th=0.5FRAN-CLNC Joint, R th=0.05FRAN-CLNC Iterative, R th=0.05UncodedULCLAverage throughput in bits/secondFigure 3.4: Total CBS consumed time and average throughput inbits/second versus number of users U .3.4-b, both proposed schemes offer improved performance in terms of maxi-mizing the number of received bits as compared to the other schemes. Thissignificant gain is due to the role of the joint FRAN-CLNC and the iterativeone that smartly multiplexes users, selects the best transmission rate of eachRRB, and controls the power for interference mitigation. In particular, theperformance of the CL scheme decreases as the number of users increases.This is due to the fact that it distributes users to RRBs randomly and usesthe minimum rate of all assigned users to each RRB. As this number in-creases, the minimum rate further decreases thus drastically affecting theaverage throughput of the scheme. On the other hand, the uncoded schemefocuses only on the highest rate at the expense of transmitting at most onefile to a single user from each RRB. As the number of users increases, itsperformance improves slightly. This can be explained by the fact that whenthe number of users goes beyond the total number of RRBs in the system,i.e., ZB, the scheme does not gain from the increased number of users andbenefits only from the diversity of the set of users. Clearly speaking, despitethe overloading of users experiencing low rates (their achievable capacitiesfrom RRBs are less than the threshold Rth = 0.05) on the CBS, Figure 3.4-a943.6. Numerical Resultsmarks an appreciable performance improvement by 90% - 93% on averageof the CL scheme. However, the gains are more significant when U = 12, 13,which are around 97% and 96%, respectively. This is because that proposedschemes focus mainly on the critical set of users who experience low ratesfrom CBS to be served by the eRRHs.8 9 10 11 12a - Number of files F10152025303540Total CBS consumed time in secondFRAN-CLNC Joint, R th=5UncodedFRAN-CLNC Joint, R th=0.5ULFRAN-CLNC Joint, R th=0.05FRAN-CLNC Iterative, R th=0.05CLTotal CBS consumed time in second8 9 10 11 12b - Number of files F600700800900100011001200130014001500Average throughput in bits/secondFRAN-CLNC Joint, R th=5FRAN-CLNC Joint, R th=0.5FRAN-CLNC Joint, R th=0.05FRAN-CLNC Iterative, R th=0.05UncodedULCLAverage throughput in bits/secondFigure 3.5: Total CBS consumed time and average throughput inbits/second versus number of files F .In Figure 3.5, we compare the total CBS consumed time and the averagethroughput versus the number of files F each with a size of 10 MB, U =10 users, and 3 RRBs in each eRRHâs frame. Similar to what we havediscussed in Figure 3.4, the joint and the iterative schemes show significantgain on the throughput maximization regime in Figure 3.5-b compared toall schemes. Also, both proposed schemes show a certain degradation in theCBS consumed time regime in Figure 3.5-a as compared to the CL scheme.It is worth remarking that the increase in the number of files increases theCBS consumed time for all coded schemes. This is due to the fact that thenumber of conflict edges between vertices increases as the number of filesincreases. This results in a smaller ONC opportunities to mix files, thusleading to a large number of colors to cover the CBS graph. For the samereason, the received throughput of all coded schemes improves slightly.953.7. Chapter Summery1 2 3 4 5a - Number of RRBs per eRRH10152025303540Total CBS consumed time in secondFRAN-CLNC Joint, R th=5UncodedFRAN-CLNC Joint, R th=0.5ULFRAN-CLNC Joint, R th=0.05FRAN-CLNC Iterative, R th=0.05CLTotal CBS consumed time in second1 2 3 4 5b - Number of RRBs per eRRH0200400600800100012001400160018002000Average throughput in bits/secondFRAN-CLNC Joint, R th=5FRAN-CLNC Joint, R th=0.5FRAN-CLNC Joint, R th=0.05FRAN-CLNC Iterative, R th=0.05UncodedULCLAverage throughput in bits/secondFigure 3.6: Total CBS consumed time and average throughput inbits/second versus number of RRBs Z.In Figure 3.6, we present the total CBS consumed time and the averagethroughput versus the number of RRBs Z for U = 10 users, F = 8 files, withfileâs size of 10 MB. Clearly, figure 3.6-b shows that the received throughoutof all schemes are increased with the increase in the number of RRBs. Infact, all schemes in agreement with serving the same set of users in differentRRBs of the same eRRH. The proposed solutions, however, benefit frommixing the userâs flows and selecting the best transmission rates which makesthe average throughput increase highly noticeable compared to the othersolutions. On the other hand, Figure 3.6-a depicts that the CBS consumedtime of all solutions decreases with the increase in the number of RRBs.This is due to the fact that as the number of RRBs increases, more usersare targeted, which in turn reduces the overload on the CBS to target theremaining users.3.7 Chapter SummeryIn this chapter, we have introduced a cross-layer optimization frameworkfor the immediate file delivery phase with the goal of maximizing the CBS of-963.7. Chapter Summeryfloading while guaranteeing users QoS. Presented numerical results revealedthat both proposed schemes achieve significant gains in users throughputcompared to the existing solutions. Compared to the QoS un-aware algo-rithm, our proposed schemes have a certain degradation in CBS consumedtime.97Chapter 4Completion TimeMinimization in F-RANsusing D2D Communicationsand Rate-Aware NCIn Chapter 3, we studied the CBS offloading and QoS guarantee prob-lem in F-RAN setting. However, the performance of F-RAN can be furtherimproved by implementing D2D communications. Therefore, we considerin this chapter a more practical 5G mobile network of D2D-aided F-RANthat integrates both F-RAN and D2D communications. In particular, wedevelop a framework that exploits the cached files at eRRHs, their transmis-sion rates/powers, and previously downloaded files by the different users todeliver the requesting files from both the eRRHs and transmitting users tothe requesting users with a minimum completion time in D2D-aided FRAN.This chapterâs organization is given as follows. The accomplished worksand research contributions are summarized in Section 4.1. The C-RAN andcross-layer NC models are discussed in Section 4.2. The completion timeminimization metric is detailed in Section 4.3 and its problem formulationand decorations is provided in Section 4.4. In Section 4.5 and Section 4.6, wedevelop joint and iterative scheduling and power adaptation approaches. InSection 4.7, we present some selected numerical results, and in Section 4.8,we provide some concluding remarks.984.1. Accomplished Works and Research Contributions4.1 Accomplished Works and ResearchContributionsThe contributions of this chapter are summarized as follows. For a D2D-aided F-RAN, we develop a framework where eRRHs and users collaborateto minimize the completion time. In particular, given the intractability ofsolving the completion time minimization problem over all possible futureNC decisions, we reformulate the problem at each transmission with theconstraints on user scheduling, their limited coverage zones, transmissionrates, maximum power allocations, and QoS rate guarantee. By analyzingthe problem, we decompose it into two subproblems. The first subproblemaims to obtain the possible completion time in eRRHs transmissions throughminimizing the transmission time. To solve it, we design an interference-aware IDNC (IA-IDNC) graph that efficiently solves the user schedulingand power allocation problem jointly under the completion time constraints.Based on this, the transmission time achieved by eRRHs is revealed forsolving the second subproblem. Then, we introduce a new D2D conflictgraph to heuristically solve the second subproblem, i.e., maximizing thenumber of users that can be scheduled on D2D links. The aforementionedgraph-based solutions of the corresponding subproblems will be referred asjoint approach. Since the IA-IDNC graph in the joint approach grows fastwith the NC combinations in large network size, we propose an alternativeand efficient low-complexity coordinated scheduling approach that solves thecompletion time problem using graph theoretic method. We compare ourproposed schemes with the existing coded and uncoded (i.e., without NC)schemes. Selected numerical results demonstrate that the proposed schemescan effectively improve completion time performance.4.2 System ModelNetwork Model OverviewWe consider a D2D-aided F-RAN system, shown in Figure 4.1, that consistsof one CBS, B single antenna eRRHs, and U users. The sets of eRRHs994.2. System Model User 1eRRH 1Cellular Links Cloud Base Station (CBS)User 2 eRRH 2Cellular Link User 9 eRRH 3Cellular Links User 6 User 7 User 8 User 10 Fronthaul Links Selected Potential Transmitting Users D2D linkUser in Interference RegionCacheUser 4 User 3 User 5 Figure 4.1: Illustration of the D2D-aided F-RAN model with 13 users, 3eRRHs and 1 CBS.and users are denoted by B = {b1, b2, · · · , bB}, U = {u1, u2, · · · , uU}, re-spectively. The CBS is responsible for making the NC decisions, powerallocation, delivering the instructions to eRRHs and transmitting users forexecutions. It also communicates with eRRHs through fronthaul links. Sinceusers are allowed to transmit at a certain amount of power, each device haslimited coverage zone, denoted by Cui , which represents the service areaof the ui-th user to transmit data within a circle of radius R. Note thatuser and device are used interchangeably throughout this chapter. The setof devices within the transmission range of the ui-th device is defined byCui = {uj â U|dd2dui,uj â¤ R}, where dd2dui,uj is the distance between the ui-thand uj-th devices. Devices can use the same frequency band and transmitencoded files simultaneously via D2D links. We assume there is a set of Fpopular files, denoted by F = {f1, f2, · · · , fF }. This data frame constitutesthe set of most frequent requested files by the users within a given time dura-tion in a hotspot area. Following the caching model in [129], the bn-th eRRHcaches a subset Hbn that represents its cache, i.e., |Hbn | = µF,âbn â B,1004.2. System Modelwhere 0 â¤ µ â¤ 1 is the fractional cache size. Further, we assume that alleRRHs collectively cache all files in the frame, i.e.,âBn=1Hbn = F . The dis-tribution of files among eRRHs is assumed to be given, and some commonfiles can be cached in different eRRHsâ caches. In this work, each device isassumed to be equipped with single antenna and used half-duplex channel.Thus, each device can access to either a D2D channel or cellular channel,and accordingly, it can either transmit or receive at a given time instant.Moreover, the allocated channels for D2D communications are assumed tobe orthogonal (out-of-band) to those used by eRRHs, i.e., an overlay D2Dcommunication model is adopted [24].Physical Layer ModelThe achievable rate at the ui-th user when receives file from the bn-theRRH is given by Rcbn,ui = log2(1 + SINRbn,ui(P)),âbn â B,âui â U , whereSINRbn,ui(P) is the corresponding signal-to-interference plus noise-ratio ex-perienced by the ui-th user when it is assigned to the bn-th eRRH. This SINRis given by SINRbn,ui(P) =Pbn |hcbn,ui |2N0 +âbnâ²âB,bnâ² 6=bn Pbnâ² |hcbnâ² ,ui |2, where hcbn,uidenotes the channel gain between the ui-th user and bn-th eRRH, N0 denotesthe noise power, Pbn denotes the transmit power of bn-th eRRH, and P =[Pbn ], âbn â B is a row vector containing the power levels of the eRRHs in theconsidered network. The set of usersâ rates across all eRRHs can be writtenas R = â(bn,ui)â BÃU Rcbn,ui , where the symbol â represents the product ofthe set of the achievable rates. Similarly, let hd2duk,ui denote the channel gainfor the D2D link between the uk-th and ui-th users and Puk denote the trans-mit power of the uk-th user. Then, the achievable rate of D2D pair (uk, ui) isgiven by rd2duk,ui = log2(1 +Puk |hd2duk,ui |2N0 +âukâ²âUtra,ukâ² 6=uk Pukâ² |hd2dukâ² ,ui |2),âuk, ukâ² âUtra, and ui â Cuk â© Cukâ² , where Utra is the set of transmitting users viaD2D links. We assume hcbn,ui and hd2duk,uito be fixed during a single eRRHand D2D transmissions but change independently from one file transmis-sion to another file transmission. The channel capacities of all pairs of D2Dlinks can be stored in an U Ã U capacity status matrix (CSM) r = [ruk,ui ],1014.3. Completion Time Minimization for D2D-aided F-RAN Systemsâ(uk, ui). Since uk-th user does not transmit to itself and cannot transmitto other users outside its coverage zone, rd2duk,uk = 0 and rd2duk,ul= 0, âul /â Cuk .4.3 Completion Time Minimization forD2D-aided F-RAN Systems4.3.1 Network Coding in the Network-LayerWe assume that users are interested in receiving the whole frame F , andthey have already acquired some files in F from prior broadcast transmis-sions (i.e., without NC) [68]. The previously acquired files by ui-th user isdenoted by the Has set Hui , and its requested files is denoted by the Wantsset, i.e., Wui = F Hui . Taking advantage of the acquired and requestedfiles by different users, each eRRH and D2D transmitter can perform XORoperation on these files and send the combined XORed files to the inter-ested users. As such, the requested files are delivered to requesting userswith minimum completion time. We use the subscript t to represent theindex of transmission/time slot, e.g., t = 1 refers to the first transmissionslot. After each transmission, each user feedbacks to the eRRHs and neigh-boring users an acknowledgment for each received file, and accordingly, theHas and Wants sets are updated by the CBS [67], [68]. The set of usershaving non-empty Wants sets at the t-th transmission slot is denoted byUw,t, which is defined as Uw,t = {ui â U|Wui,t 6= â }. When a user receivesits requested files, it can act as a D2D transmitter to provide its receivedfiles to the interested neighboring users.Let κcbn,t and κd2duk,tdenote the XOR file combinations to be sent by thebn-th eRRH and uk-th D2D transmitter, respectively, to the sets of sched-uled users Ï(Îºcbn,t) and Ï(Îºd2duk,t) at the t-th transmission. For simplicity,the subscript transmission index t is often omitted when it is clear fromthe context. These file combinations κcbn and κd2dukare elements of thepower sets P(Hbn) and P(Huk), respectively. At every transmission slott, each scheduled user in Ï(Îºcbn) can re-XOR κcbnwith its previously re-ceived files to decode a new file. To ensure successful reception at the users,1024.3. Completion Time Minimization for D2D-aided F-RAN Systemsthe maximum transmission rate of a particular transmitting eRRH/useris equal to the minimum achievable capacity of its scheduled users. Fordiscussion convenience, the term âtargeted usersâ is referred to a set ofscheduled users who receives an instantly-decodable transmission. There-fore, the set of targeted users by bn-th eRRH is expressed as Ï(Îºcbn) ={ui â Uwâ£â£|Îºcbn â©Wui | = 1 and Rcbn â¤ Rcbn,ui}. Similarly, for D2D transmis-sions, the set of targeted users by uk-th D2D transmitter is expressed asÏ(Îºd2duk ) = {uj â Uwâ£â£|Îºd2duk â© Wuj | = 1 and uj â Cuk and rd2duk â¤ rd2duk,uj}.Without loss of generality, the set of all targeted users when |Utra| D2Dtransmitters transmit the set of combinations κd2d(Utra) is represented byÏ(Îºd2d(Utra)), where uk, κd2duk , Ï(Îºd2duk ) are elements in Utra, κd2d(Utra), andÏ(Îºd2d(Utra)), respectively.4.3.2 Transmission Time Analysis and Expression of theCompletion TimeThis subsection provides an analysis of the transmission time for sendingcoded files from the eRRHs and D2D transmitters to a set of scheduled users,which leads to an expression of the completion time in D2D-aided F-RAN.The transmission time for sending the coded file κcbn from the bn-th eRRHwith rate Rcbn to the set of targeted users Ï(Îºcbn) is T cbn =NRbnseconds, whereN is the size of the file in bits. Without loss of generality, let us assume thatthe bnâ-th eRRH has the minimum rate at the t-th transmission slot that isdenoted by Rbnâ . The corresponding transmission duration is Tcbnâ =NRbnâseconds. Since different eRRHs will have different transmission rates, theywill have different transmission durations. Thus, the portion of the timethat not being used by bnâ²-th eRRH at t-th transmission slot is referred toas the idle time of the bnâ²-th eRRH and denoted by Tcbnâ² idle. This idle timecan be expressed as T cbnâ² idle= (T cbnâ â T cbnâ² ) seconds. Such idle time can beexploited by the scheduled users of bnâ²-th eRRH via D2D links if it ensuresthe complete delivery of files, i.e., T cbnâ² idleâ¥ T d2dum , where T d2dum = Nrd2duk isthe transmission duration for sending κd2dum from the um-th D2D transmitterwith adopted rate rd2dm , âum â Ï(Îºcbnâ² ). The unscheduled users by the eRRHs1034.3. Completion Time Minimization for D2D-aided F-RAN SystemsFigure 4.2: Transmission time structure for eRRHs and potential D2D trans-mitters for one time slot.can also use D2D links to transmit files, and accordingly, the transmissionduration for sending κd2duk from the uk-th D2D transmitter with adoptedrate rd2dk is Td2duk= Nrd2dukseconds, âuk /â Ï(Îºcbn), âbn â B. Based on theabove discussion, ul-th user experiences one of three possible delays at eachtransmission, as shown in Figure 4.2, and described below.1. The time delay for ul-th user receiving a non-instantly decodable trans-mission from bnâ-th eRRH, this delay is Tcbnâ ,ul , âul /â Ï(Îºcbnâ ).2. The time delay for ul-th user receiving a non-instantly decodabletransmission from bnâ²-th eRRH, this delay is Tcbnâ² ,ul, bnâ² â B andul /â Ï(Îºcbnâ² ).3. The time delay for ul-th user being transmitting or receiving a non-instantly decodable transmission from any D2D transmitter in the setUtra, this delay is denoted as T d2duk,ul , where (ul = uk) â Utra or (ul /âÏ(Îºd2d(Utra)) and uk â Utra).Note that for ul-th user, Tcbnâ² ,ulis less than T cbnâ ,ul and maxukâUtra(T d2duk,ul). Thus,the maximum delay experienced by ul-th user, which is not scheduled atthe t-th transmission slot, is equal to Tmax,t = max(Tcbnâ , maxukâUtra(T d2duk )).Consequently, users that are not scheduled at transmission slot t, experienceTmax,t seconds of delay in a cumulative manner defined as follows.1044.3. Completion Time Minimization for D2D-aided F-RAN SystemsDefinition 4.1. A user with non-empty Wants set experiences Tmax,t sec-onds of time delay if it does not receive any requested file at t-th transmissionslot. The accumulated time delay of ul-th user is the sum of Tmax,t secondsat each transmission until t-th transmission slot, and denoted by Dul,t. Itcan be expressed asDul,t = Dul,tâ1 +ï£±ï£´ï£´ï£´ï£²ï£´ï£´ï£´ï£³Tmax,t if ul /â(u(fcbnâ ,t) âª Ï(Îºcbnâ² ,t)),âbnâ , bnâ² â BTmax,t if (ul = uk) â Utra,t or (ul /â Ï(Îºd2d(Utra,t))and uk â Utra,t)(4.1)Definition 4.2. The completion time of ul-th user, denoted by Tul , is thetotal time required in seconds to receive all its requested files. The overallcompletion time To is the time required to receive all files by all users, andis given by To = maxulâUw{Tul}.Definition 4.3. A transmission schedule T = {(κcbn,t, Rcbn), (uk, κd2duk,t, rd2duk )}ât â {1, 2, ......., |T |},âbn â B, âuk â Utra,t is a collection of transmitting eR-RHs/D2D transmitters, their file combinations and adopted rates at everyt-th transmission index to receive all files by all users.The completion time minimization problem in a D2D-aided F-RAN sys-tem can be expressed as followsT â = arg minT âT{To(T )} = arg minT âT{maxulâUw{Tul(T )}}, (4.2)where T â is the schedule that optimally minimizes the overall completiontime and T is the set of all possible transmission schedules. The followingtheorem expresses the optimal schedule T â in terms of time delay definedin definition 1.Theorem 4.4. The optimal schedule T â that minimizes the overall comple-1054.3. Completion Time Minimization for D2D-aided F-RAN Systemstion time in a D2D-aided F-RAN system can be written as followsT â = arg minT âT{maxulâUw{N.|Wul,0|RËul(T )+ Dul(T )}}, (4.3)where |Wul,0| is the initial Wants size of ul-th user, Dul(T ) is the accumula-tive time delay of ul-th user in schedule, and RËul(T ) is the harmonic meanof the transmission rates of transmissions that are instantly decodable forul-th user in schedule T .Proof. The proof of Theorem 4.4 is omitted in this work as it can followthe same steps that proofed Theorem 1 in [82] for C-RAN networks withoutD2D communications. Therefore, only a sketch of the proof is given asfollows. We first show that the completion time can be expressed as thesum of instantly and non-instantly decodable transmission times from |B|and |Utra| transmitters via cellular and D2D links, respectively. Afterward,we need to proof that the number of instantly decodable transmissions to ul-th user is equal to the number of its requested files |Wul,0| and the number ofnon-instantly decodable transmissions matches the time delay in definition1. Finally, we extend the results of the optimal schedule in Theorem 1 in[82] that used in PMP system with a single transmitter to the coordinatedD2D-aided F-RAN setting with multiple transmitters.Solving the completion time problem in (4.2) optimally is intractable[82]. In fact, the transmission schedule at the current transmission slot doesnot depend only on the future transmission schedules, but also on usersâachievable capacities and eRRHsâ transmit powers. Therefore, we pay ourspecial attention to solve such problem at each transmission, where filesare transmitted with high transmission rates. If some eRRHs cannot sendXOR files to a set of users with the rate threshold Rth, these users can bescheduled on D2D links. To this end, our main objective is to minimize thecompletion time at each transmission, known as the anticipated completiontime [115], through minimizing the time delay. This anticipated userâs com-pletion time at each transmission in D2D-aided F-RAN system is given inthe next corollary.1064.3. Completion Time Minimization for D2D-aided F-RAN SystemsCorollary 4.5. The anticipated completion time of ul-th user at t-th trans-mission slot is given byTul,t âN.|Wul,0|RËul,t+ Dul,t, (4.4)where Dul,t is the accumulative transmission delay as given in (4.1), andRËul,t is the harmonic mean of the transmission rates that are instantly de-codable for ul-th user until t-th transmission.The anticipated completion time in Corollary 4.5 depends on the numberof requested files by ul-th user, its accumulated time delay and harmonicmean RËul,t. Clearly, this metric is intimately related to the duration oftime that all files are delivered to all users, which can be illustrated in thefollowing example.Example 5: This example considers the model in Figure 4.3 that consistsof 2 eRRHs, 6 users, usersâ received and requested files and their rates. Forexample, u2 receives f1, f4 and requests f2, f3. The sets of files that storedin eRRHsâ caches are Hb1 = {f1, f4, f3}, Hb2 = {f2, f3, f4}. Each file isassumed to have a size of 10 bits. To minimize the completion time for thisexample, one possible schedule is given as follows.First time slot: The b1-th and b2-th eRRHs transmit κcb1,1= f1 â f4 andfc2 = f3âf4 with rates Rcb1 = 2.5 and Rcb2 = 5 bits/s, respectively, to the setsu(κcb1,1) = {u4, u6} and Ï(Îºc,1b2) = {u2, u3}. The u1-th user transmits κd2du1,1 =f4 with rate rd2du1 = 5 bits/s to the set Ï(Îºd2du1,1) = {u5}. Given this, we havethe following transmission durations of b1-th eRRH, b2-th eRRH, and u1-thtransmitting user, respectively: T cb1 =102.5 = 4, Tcb1= 105 = 2, Td2du1 =105 = 2seconds. Since user u4 receives f4 from b1-th eRRH in 4 seconds, it can usethe idle time of b1-th eRRH, i.e., Tcb1idle= 2 seconds, to send f2 to u6 withrate rd2du4 = 5 bits/s. Therefore, the updated Wants sets after the first timeslot are: Wu2,1 = {f2}, Wu3,1 = â ,Wu4,1 = â , Wu5,1 = {f3}, Wu6,1 = â .Note that Tmax,1 = max(Tcb1, T cb2 , Td2du1 ) = 4 seconds.Second time slot: The b2-th eRRH transmits fc,2b2= f2 â f3 with rateRce2 = 2.5 bits/s to the set Ï(Îºc,2b2) = {u2, u5} which requires transmission1074.4. Problem Formulation and Problem Decompositionf1f1f1f1f2f2f2f2f3f3f3f4f4f4u1Usersâ received and requested filesA possible schedulef1Rb1,ul Rb2,ulUsersâ rates2.5142.52.5335512.52eRRH b1:eRRH b2:Ist time-slot 2nd time-slotu1:4 secondsf4User 4:f1âf2 f34 s.f3Usersâ partial connections and rates2110.5111.521.55 4545433u1 13 546f3âf4eRRH b2:f1âf4u2u3u4u5u6u2u3u4u5u6Figure 4.3: D2D-aided F-RAN system containing 2 users and their corre-sponding requested/received files and rates.time T cb2 = Tmax,2 =102.5 = 4 seconds. By the end of second time slot, allusers will have their wanted files. Therefore, the total transmission time isTmax,1 + Tmax,2 = 8 seconds.4.4 Problem Formulation and ProblemDecompositionProblem FormulationIn order to minimize the completion time at each transmission slot, weneed to develop a rate-aware network coding framework that decides: i) theadopted transmission rate/power at the en-th eRRH, {Rcbn , Pbn}, to transmitits XOR combination κcbn,t to a set of targeted users Ï(Îºcbn,t), âbn â B, andii) the set of D2D transmitters Utra,t for sending κd2duk,t to the users Ï(Îºd2d,tuk ),and their adopted transmission rates rd2duk ,âuk â Utra,t. As such, all filesare delivered to all users with minimum completion time. Therefore, thecompletion time minimization problem in D2D-aided F-RAN system can beformulated as on the top of next page. The constraints are explained as fol-lows. C1 states that the set of scheduled users to all eRRHs are disjoint, i.e.,each user must be scheduled to only one eRRH. C2 makes sure that each usercan be scheduled to only one potential D2D transmitter and no user can bescheduled to a D2D transmitter and eRRH at the same time instant. C3 en-sures the successful delivery of files from D2D transmissions within the idle1084.4. Problem Formulation and Problem DecompositionP1 : minκcbn,t,κd2duk,t,Pbn ,Utra,tâP(U){maxulâUw,tTul,t}subject toï£±ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£²ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£´ï£³C1: Ï(Îºcbn,t) â© Ï(Îºcenâ² ,t) = â ,âbn 6= bnâ² â B;C2: Ï(Îºd2duk,t) â© Ï(Îºd2dukâ² ,t) = â & Ï(Îºd2duk,t) â© Ï(Îºcbn,t) = â ,âuk 6= ukâ² â Utra,t, bn â B;C3: rd2duk .Tcbnâ² idleâ¥ N, âuk â Utra,t, âbnâ² â B;C4: κcbn,t â P(Hbn) & κd2duk,t â P(Huk,t), â(bn, uk) â B Ã Utra,t;C5: 0 â¤ Pbn â¤ Pmax,âbn â B;C6: Rcbn â¥ Rth; C7: rd2duk â¥ Rth,âbn â B, âuk â Utra,t.time of the eRRHs. C4 ensures that all files to be combined using XOR op-eration at all eRRHs and D2D transmitters are stored in their Caches andHas sets, respectively. C5 bounds the maximum transmit power of eacheRRH, and C6 and C7 satisfy the minimum transmission rates required tomeet the QoS rate requirement Rth. The optimization problem in P1 con-tains the NC scheduling parameters Ï(Îºcbn,t), Ï(Îºd2duk,t),âbn â B, âuk â Utra,t,power allocations of eRRHs Pbn , âbn â B, potential set of transmitting usersUtra,t and their transmission rates. We can readily show that problem P1is NP-hard and intractable [116]. However, by analyzing the problem, wecan decompose it into two subproblems and solve them individually and ef-ficiently using graph theory technique.Problem DecompositionSince the main objective is to minimize the maximum completion time ofusers, which depends on the time delay increase at each transmission slot, wecan first focus on minimizing the transmission duration for the eRRH-userNC transmissions. In particular, we can get the possible completion time byjointly optimizing the NC user scheduling and power allocations of eRRHs.The mathematical formulation for minimizing the transmission duration for1094.5. Joint Solution for Completion Time Minimization ProblemeRRH-user NC transmissions can be expressed asP2 : min0â¤Pbnâ¤PmaxTcbn,t (4.6a)subject toï£±ï£²ï£³Ï(Îºcbn,t) â© Ï(Îºcbnâ² ,t) = â ,âbn 6= bnâ² â B;κcbn,t â P(Hbn); Rcbn â¥ Rth, âbn â B.Note that this subproblem contains usersâ associations and power allocationvariables and a joint solution will be developed in Section 4.5. After obtain-ing the possible transmission duration from eRRH-user NC transmissions,denoted by T cbnâ ,t of bnâ-th eRRH, by solving P2, we can now formulate thesecond subproblem. In particular, we can maximize the number of users Ztthat are not been scheduled to the eRRHs Uw,t\u00CF(Îºcbnâ ,t) within T cbnâ ,t by us-ing D2D communication. In addition, users being scheduled to bnâ²-th eRRHfrom subproblem P2, have the opportunity to be scheduled on D2D linkswithin the idle times of their corresponding eRRHs at the t-th transmissionslot, âbnâ² 6= bnâ â B. Therefore, the second subproblem of maximizing thenumber of users to be scheduled on D2D links can be expressed as followsP3 : maxUtra,tâP(U\u00CF(Îºcbnâ ,t))Îºd2duk,tâP(Huk,t)Zt (4.7a)subject toï£±ï£´ï£´ï£´ï£²ï£´ï£´ï£´ï£³(C2); rd2duk .(Tcbnâ ,t â T cbnâ² ,t) â¥ N, âuk â Utra,t, â(bnâ , bnâ²) â B;T d2duk â¤ T cbnâ ,t, âuk â Utra,t;|Ï(Îºd2d(Utra,t))|+ |Utra,t| â¤ Zt.4.5 Joint Solution for Completion TimeMinimization ProblemIn this section, we propose a joint approach to solve the subproblems inP2 and P3 using designed interference-aware IDNC and new D2D conflictgraphs, respectively. Specifically, we design interference-aware IDNC in thefist subsection to solve the sub-problem P2. We then introduce a new D2D1104.5. Joint Solution for Completion Time Minimization Problemconflict graph to solve the sub-problem P3 as shown in the second subsection.4.5.1 Solution to Sub-problem P2Interference Aware-IDNC GraphInterference-Aware IDNC (IA-IDNC) graph, denoted by GIA-IDNC(V, E), isdesigned to systematically select an IDNC combination, transmission rate,and power allocation of each eRRH at the t-th transmission slot. Unlike thegraph in [82] that resulted in one rate for fixed power eRRHs, our designedIA-IDNC graph leads to different transmission rates/powers from differenteRRHs. This gives flexibility to each eRRH to choose its IDNC combinationand transmission rate that satisfy a set of scheduled users.Consider generating all possible associations (pairs) representing usersand their corresponding requested files that cached by bn-th eRRH, denotedby Sbn = Uw Ã Hbn , i.e., s â Sbn = (ul, fh) represents the association oful-th user and its fh-th requested file. The corresponding files of a set ofassociations in Sbn can be encoded into one IDNC combination if these filesare instantly decodable to the corresponding associated users. The set of allIDNC combinations is denoted by SIDNC,bn . In particular, the correspondingfiles of any two different associations s â Sbn and sâ² â Sbn are encoded if oneof the following IDNC conditions is satisfied.â IDNC-C1: ul,s 6= ulâ²,sâ² and fh,s = fh,sâ² This condition represents thatthe same file fh is requested by two distinct users ul and ulâ² .â IDNC-C2: ul,s 6= ulâ²,sâ² and fhâ²,sâ² â Hul,s and fh,s â Hulâ² ,sâ² . Thiscondition represents that different files fhâ² and fh are requested bytwo different users ulâ² and ul, respectively. Meanwhile, the requestedfile of each user is in the Has set of the user in the other association. Weuse l, s in ul,s as subscripts to represent ul-th user in s-th association.For example, the element s = (κcbn , Ï(Îºcbn)) â SIDNC,bn represents theset of scheduled users Ï(Îºcbn) that will receive the IDNC combination κcbnfrom bn-th eRRH. Let Abn be the set of all possible associations betweenthe IDNC combinations SIDNC,bn and achievable capacities Rbn â R, i.e.,1114.5. Joint Solution for Completion Time Minimization ProblemAbn = SIDNC,bn ÃRbn . In other words, S = (s, R) â Abn is a schedule thatconsists of a set of associations representing the IDNC combination, set ofscheduled users, and rate R of en-th eRRH, i.e., S = (s, R) = s1, s2, · · · , s|S|,where |S| is the total number of scheduled users in S. Note that s1 representsone user, one file, and rate of bn-th eRRH. Now, any two associations s1 âS, s2 â S representing the bn-th eRRH should have an equal adopted ratethat is greater than or equal to Rth. That is, the Rate Condition (RC)is satisfied Rs1 = Rs2 and Rs1 â¥ Rth.The aforementioned procedures are applied to all eRRHs in the network.Thus, the set of all possible IDNC combinations SIDNC,bn and schedulesAbn in the network are SIDNC =âbnâBSIDNC,bn and A =âbnâBAbn , respec-tively. These schedules A can be exactly represented by unique vertices V inGIA-IDNC(V, E) such that we transfer the subproblem P2 to a graph-theorybased problem. Therefore, the Si-th schedule in S is represented by the Vi-thunique vertex in GIA-IDNC (i = 1, 2, · · · , |S|). This schedule-to-vertex map-ping makes any IDNC combination sent from the bn-th eRRH with adoptedrate to its corresponding associated users is decodable. Two vertices Vi andViâ² representing two different schedules Si â Sbn and Siâ² â Abnâ² are adja-cent by an edge in GIA-IDNC, if the associations they represent satisfy thefollowing condition.â Transmission Condition (TC): Ï â© Ï â² = Ï, â(s1, s2) â Si Ã Siâ² .This condition ensures that the same user can be scheduled only to aunique eRRH.Assuming that the power allocation of the eRRHs in the network will becomputed later; then the weight of a given vertex V representing a scheduleS is expressed byw(V ) =âsâSminul,sâÏ(Îºcbn ) log2(1 + SINRbn,s,ul,s(P))N. (4.8)The weight of each vertex reflects the contribution of each eRRH towardsminimizing the completion time of its associated users. Actually, the trans-mission rate plays a crucial role in minimizing the transmission duration T cbn .1124.5. Joint Solution for Completion Time Minimization ProblemThus, a larger value in (4.8) leads to minimize the transmission duration ofdelivering IDNC files to users, which minimizes their completion times. Thedesign of the IA-IDNC graph makes any maximal weight clique representsa set of transmissions satisfying the following three features: i) each user isscheduled only to a single eRRH that cached one of its requested files, ii)each eRRH delivers an IDNC file with an adopted transmission rate/powerthat satisfies a lower completion time for a potential set of users. Suchadopted rate satisfies the QoS rate guarantee and no larger than the chan-nel capacities of all scheduled users, iii) the weight of each vertex strikesa balance between the adopted rate and the number of scheduled users toeach eRRH.The following theorem characterizes the solution of subproblem P2 basedon the designed IA-IDNC graph.Theorem 4.6. The transmission duration minimization subproblem P2 isequivalently represented by the maximum weight clique problem in the IA-IDNC graph, and can be expressed asarg maxCâCâViâCw(Vi), âi = 1, 2, · · · , |C|, (4.9)where C is the maximum weight clique of a maximum degree |B| in the IA-IDNC graph and C is the set of all possible maximal cliques.Proof. A sketch of proof of Theorem 4.6 is provided as follows. First, weneed to show that there is a unique one-to-one mapping between each sched-ule Si â S and each vertex Vi â V in GIA-IDNC (i = 1, 2, · · · , |S|). Then, weemphasize that each maximal clique in the IA-IDNC graph that consists of aset of vertices satisfying all edge conditions represents feasible coded trans-missions from the eRRHs. Finally, the proof can be concluded by showingthat the contributed weight of the maximum weight clique C for minimizingthe transmission duration is: w(C) =âViâCw(Vi) =âbnâBâSiâSw(Si) =âbnâBâsâSiminul,sâÏ(Îºcbn )log2(1+SINRbn,s,ul,s (P))N , âi = 1, 2, · · · , |C|, where Sis the set of the selected potential schedules. Therefore, the subproblem P2is equivalent to the maximum weight clique problem among the maximal1134.5. Joint Solution for Completion Time Minimization Problemcliques in the IA-IDNC graph.The problem in Theorem 4.6 is clearly NP-hard problem, and solving itoptimally is intractable [74]. However, we heuristically and efficiently solveit in the next subsection.Development of Greedy AlgorithmWe solve the problem in Theorem 4.6 by characterizing the joint solutionto the NC user scheduling and power allocation problem while designing theIA-IDNC graph. A proper power allocation for each eRRH leads to suppressthe interference in the system, thus a better transmission rate is achieved.As a result, the transmission duration for delivering files to the scheduledusers is minimized.Consider a power-clique (PC) in GIA-IDNC that is associated with anetwork-coded user scheduling S = {S1,S2, · · · ,S|B|}, where S1 is the sched-ule of e1-th eRRH, which consists of a set of associations s1, s2, · · · , s|S1|, and|S1| = |Îº(Ï cbn)|. Our goal is to obtain a local optimal eRRH power allocationvector, denoted as (P âb1 , · · · , P âbB ) for that PC. The power allocation prob-lem is formulated as an optimization problem of maximizing the weighedsum-rate. As such, all scheduled users receive files sent by their associatedeRRHs with minimum transmission duration, which can be expressed asP4 : maxPbnBân=1|Ï(Îºcbn(Sn))|Nâ minulâÏ(Îºcbn (Sn))(log2(1 + SINRbn,ul(P))) ,s. t. 0 6 Pbn 6 Pmax, ân = 1, 2, · · · , B, (4.10)where Ï(Îºcbn(Sn)) is the set of scheduled users in n-th schedule correspond-ing to bn-th eRRH. The power allocation problem in P4 is a non-convexoptimization problem. Therefore, similar to the works in literature (see forexample, [147, 148] and references therein), we focus on finding the localoptimal solution.The proposed solution to the problem in Theorem 4.6 is executed at theCBS at each transmission slot and divided into two stages: designing the1144.5. Joint Solution for Completion Time Minimization ProblemIA-IDNC graph and finding its corresponding maximum PC.First stage: The IA-IDNC graph is designed as follows. Using IDNC-C1, IDNC-C2, and RC conditions that explained in Section 4.5.1, wegenerate all schedules A and represent them by vertices in V. Afterwards,we check the connection between any two pairs Vi and Viâ² of vertices inGIA-IDNC based on the transmission condition TC in Section 4.5.1. Any con-nected vertices result in a feasible network-coded scheduling to the eRRHs.Then, we evaluate the power allocation of such network-coded scheduling{S1,S2, · · · ,SB} by solving the optimization problem (4.10). By the com-puted power allocation and corresponding rate, we compute the weights ofthe corresponding vertices in GIA-IDNC as expressed in (4.8). We repeat theabove process to all network-coded schedules in the IA-IDNC graph.Second stage: The second stage finds the maximum weight PC C amongall other maximal PCs in GIA-IDNC graph. In the first step, we select vertexVi â V, (i = 1, 2, · · · , |V|) that has the maximum weight w(V âi ) and add it toC (at this point C = {V âi }). Then, the subgraph GIA-IDNC(C), which consistsof vertices in graph GIA-IDNC that are adjacent to vertex V âi is extracted andconsidered for the next vertex selection process. In the next step, a newmaximum weight vertex V âiâ² (i.e., Vâiâ² should be in the corresponding PC ofV âi ) is selected from subgraph GIA-IDNC(C). Now, C = {V âi , V âiâ² }. We repeatthis process until no further vertex is adjacent to all vertices in the maximalweight PC C. The selected C contains at most B vertices.4.5.2 Solution to Sub-problem P3New D2D Conflict GraphWe introduce a new D2D conflict graph, denoted by Gd2d(V, E), thatconsiders all possible conflicts for scheduling users on D2D links, such astransmission, network coding, half-duplex conflicts. This leads to feasibletransmissions from the potential D2D transmitters |Utra|, where each uk âUtra transmits the IDNC combination κd2duk to the scheduled users Ï(Îºd2duk )with the transmission rate rd2duk .Let Ud2d denote the set of unscheduled users to the eRRHs, i.e., Ud2d =1154.5. Joint Solution for Completion Time Minimization ProblemU\u00E2Bn=1 Ï(Îºcbn), and let Ud2d,w â Ud2d denote the set of users that stillwants some files. Hence, the D2D conflict graph is designed by generatingall vertices for uk-th possible D2D transmitter, âuk â Ud2d. The vertex setV of the entire graph is the union of vertices of all users. Consider, for now,generating the vertices of uk-th user. Note that uk-th D2D transmitter canencode its IDNC file κd2duk using its previously received files Huk . Therefore,each vertex is generated for each single file fh â Wui â©Huk that is requestedby each user ui â Ud2d,w â© Cuk and for each achievable rate r of uk-th userthat is defined below.Definition 4.7. The set of achievable rates Rd2duk,ui from uk-th user to ui-th user is a subset of achievable rates Rd2duk that are less than or equal tochannel capacity rd2duk,ui . It can be expressed by Rd2duk,ui = {r â Rd2duk |r â¤rd2duk,ui and ui â Ud2d,w â© Cuk and r â¥ Rcbnâ}.The above definition emphasizes that ui-th user in the coverage zone Cukcan receive a file from uk-th D2D transmitter if the adopted transmissionrate r is in the achievable set Rd2duk,ui and no less than the minimum trans-mission rate of bnâ-th eRRH. Therefore, we generate |Rd2duk,ui | vertices for arequesting file fh â Hukâ©Wui ,âui â Ud2d,wâ©Cuk . In summery, a vertex vkr,i,fis generated for each association of a transmitting user uk, a rate r â Rd2duk,ui ,and a requesting file fh â Huk â©Wui of user ui â Ud2d,w â©Cuk . Similarly, wegenerate all vertices for all users in Ud2d.All possible conflict connections between vertices (conflict edges betweencircles) in the D2D conflict graph are provided as follows. Two vertices vkr,i,hand vkâ²râ²,iâ²,hâ² are adjacent by a conflict edge in Gd2d, if one of the followingconflict conditions (CC) is true:â IDNC (CC1): (uk = ukâ²) and (fh 6= fhâ²) and (fh, fhâ²) /â Hukâ² ÃHuk .A conflict edge between vertices is connected as long as the files theyrepresent are not-instantly decodable to a set of scheduled users to thesame uk-th D2D transmitter.â Rate (CC2): (uk = ukâ²) and (r 6= râ²). All adjacent vertices cor-respond to the same uk-th D2D transmitter should have the sameachievable rate.1164.5. Joint Solution for Completion Time Minimization Problemâ Transmission (CC3): (uk 6= ukâ²) and (ui = uiâ²). The same usercannot be scheduled to two different D2D transmitters uk and ukâ² .â Half-Duplex (CC4): (uk = uiâ²) or (ukâ² = ui). The same user cannottransmit and receive in the same transmission slot.Given the aforementioned designed D2D conflict graph, the followingtheorem reformulates the subproblem P3.Theorem 4.8. The subproblem of maximizing the number of scheduled userson D2D links in P3 at the t-th transmission is equivalently represented bythe maximum weight independent set (IS) selection among all the maximalsets in the Gd2d graph, where the weight Ï(vkr,i,h) of each vertex vkr,i,h is givenbyÏ(vkr,i,f ) = |Cuk â© Ud2d,w(Huk)|(rN). (4.11)The above weight metric shows two potential benefits: i) |Cukâ©Ud2d,w(Huk)|represents that the uk-th transmitting user is connected to many other usersthat are requesting files in Huk and ii)(rN)provides a balance between thetransmission rate and the number of scheduled users on D2D links.Details of Greedy SolutionThe proposed solution here greedily maximizes the number of scheduledusers on D2D links within T cbnâ by maximizing the number of vertices in anyIS in the D2D conflict graph. In order to maximize the number of verticesin any IS, we update the weight of each vertex. An appropriate design of theupdated weights of vertices leads to selection of a large number of verticesand each vertex has high original weight that defined in Theorem 4.8.Let piv,vâ²3 define the non-adjacency indicator of vertices v and vâ² in theGd2d graph such that:piv,vâ² =ï£±ï£²ï£³1 if v is not adjacent to vâ² in Gd2d,0 otherwise. (4.12)3For notation simplicity, we replace vir,k,l by v and viâ²râ²,kâ²,lâ² by vâ².1174.5. Joint Solution for Completion Time Minimization ProblemNow, let the weighted degree nv of vertex v is defined by nv =âvâ²âGd2d piv,vâ² .Ï(vâ²),where Ï(vâ²) is the original weight of vertex vâ² defined in Theorem 4.8. Hence,the modified weight of vertex v is defined asw(v) = Ï(v)nv = Ï(v)âvâ²âGd2dpiv,vâ² .Ï(vâ²). (4.13)The modified weight of a vertex v in (4.13) points two attractive features:(i) it has a large original weight, and (ii) it is not adjacent to a large numberof vertices that have high original weights. Based on this, we iteratively andheuristically execute a greedy vertex search scheme as follows. Initially, avertex vâ that has the maximum weight w(vâ) is selected and added to themaximal IS I (i.e., I = {vâ}). Then, the subgraph Gd2d(I), which consistsof vertices in graph Gd2d that are not adjacent to vertex vâ, is extracted andconsidered for the next process. In the next step, a new maximum weightvertex vâ²â is selected from subgraph Gd2d(I) (at this point I = {vâ, vâ²â}).We repeat this process for all transmitting users so that no further vertex isnot adjacent to all the vertices in I. The selected D2D transmitters in themaximum IS I generate coded files and broadcast them to all neighboringusers on D2D links.The overall two-solution joint approach that are explained in Section 4.5.1and Section 4.5.2, respectively, is provided in Algorithm 6.Example 6: We illustrate in this example how to design the IA-IDNCand D2D conflict graphs that shown in Figure 4.4 of the network presentedin Figure 4.3.â In Figure 4.4(a), we plot the IA-IDNC graph, where each vertex repre-sents a possible NC combination that consists of combined associationsin each eRRH. For plotting simplification, we did not include the ver-tices that represents one association (i.e., no NC). The connections be-tween vertices (circles) is based on the TC condition that explained inSection 4.5.1. There are many possible maximal PCs in GIA-IDNC thatare represented by connected vertices. Each one represents the poten-tial network-coded scheduling of the eRRHs that minimizes the com-1184.5. Joint Solution for Completion Time Minimization ProblemAlgorithm 6: Proposed Joint Approach1: Require N , F , K, Cbn , Hul,0, Wul,0, Pmax, Puk , N , hcbn,ul , hd2duk,ul ,âuk, ul â U , âbn â B.2: Initialize C = â and I = â .3: Solution of Subproblem P2: eRRH-user Transmission4: Design GIA-IDNC according to Section 4.5.1.5: for each S do6: Calculate P = {P âb1 , P âb2 , · · · , P âbB} by solving (4.10).7: Obtain Vi = {(Râbi , P âbi , sbi), · · · , (Râbi , P âbi , s|Ï(Îºcbi )|)} (i = 1, · · · , B)according to P.8: Calculate w(Vi) using (4.8).9: end for10: GIA-IDNC(C)â GIA-IDNC.11: while GIA-IDNC(C) 6= â do12: V âi = arg maxViâG(C){w(Vi)}.13: Set Câ C âª V âi and GIA-IDNC(C)â GIA-IDNC(V âi ).14: end while15: Solution of Subproblem P3: D2D Transmission16: Design Gd2d according to Section 4.5.2.17: Gd2d(I)â Gd2d.18: while Gd2d(I) 6= â do19: âv â Gd2d(I): calculate Ï(v) and w(v) using (4.11) and (4.13),respectively.20: vâ = arg maxvâGd2d(I){w(v)}.21: Set Iâ I âª vâ and obtain Gd2d(I).22: end while23: Obtain C and I.pletion time of users. For example, one possible maximal PC shown inred color in Figure 4.4(a) is {s1RâP â53, s1RâP â61, s2RâP â22, s2RâP â34}. Thefive indices b1, Râ, P â, 5, 3 in the first association represent first eRRH,its transmission rate and power level, scheduled user and its requestedfile, respectively.â To ease the understanding of the D2D conflict graph, we plot it onlyfor the first three users {u1, u2, u3} of the network presented in Figure4.3 and irrespective to the possible scheduled users to the eRRHs.1194.6. Coordinated Scheduling Solution for Completion Time Minimization ProblemInterference-Aware IDNC (IA-IDNC) graphs1RâP â23s1RâP â34s2RâP â54s2RâP â44s2RâP â34s1RâP â23s1RâP â44s1RâP â23s1RâP â53s1RâP â34s1RâP â44s1RâP â33s1RâP â53s1RâP â23s1RâP â61s1RâP â34s1RâP â44s1RâP â54s1RâP â44s1RâP â54s1RâP â53s1RâP â61s2RâP â22s1RâP â34s2RâP â23s2RâP â44s2RâP â22s2RâP â44s2RâP â22s2RâP â54 s2RâP â53s2RâP â23s2RâP â62s2RâP â22s2RâP â34s2RâP â44s2RâP â34s2RâP â54s2RâP â54s2RâP â44s2RâP â62s2RâP â53Possible maximal-cliquePossible maximal-cliqueEdge represents TC conditionAssociations(a) The IA-IDNC graph.D2D Conflict Graphv11,2,2v11,2,3 v15,4,4v11,4,4v15,5,4v11,5,3v21,3,4v21,5,4v31.5,2,2v31.5,2,3v32,5,3v11,5,4v15,5,3v31.5,5,3(b) The D2D conflict graph.Figure 4.4: Illustration of both IA-IDNC and D2D conflict graphs of theexample presented in Figure 4.3.The D2D conflict graph is shown in Figure 4.4(b), where the conflictconditions CC1 and CC2 are represented by solid lines and conditionsCC3 and CC4 are represented by dash lines. By Theorem 4.8, onepossible maximal IS in this graph is {v15,4,4, v15,5,4, v31.5,2,2}. The firstvertex v15,4,4 represents the transmitting user u1, its rate r = 5, thescheduled user u4 and its requested file f4, respectively.4.6 Coordinated Scheduling Solution forCompletion Time Minimization ProblemIn this section, we propose a faster and simpler coordinated schedulingapproach. The need for this approach is invoked by the possibly large num-ber of IDNC combinations generated by the joint approach in large networksize. In such large networks, we can utilize this alternative approach to ob-tain fast and efficient solution. Let Pbn be a fixed power level of bn-th eRRH,âbn â B. The completion time minimization problem at t-th transmission1204.6. Coordinated Scheduling Solution for Completion Time Minimization Problemslot can be written as a coordinated scheduling problem as followsP5 : maxÎºcbnâP(Hbn )Ï(Îºcbn )â©Ï(Îºcbnâ² )=â RbnâRZt (4.14a)subject toï£±ï£´ï£´ï£´ï£´ï£´ï£´ï£²ï£´ï£´ï£´ï£´ï£´ï£´ï£³(Ï(Îºd2duk ), ruk) = arg min Utra,tâP(U)Îºd2dk âP(Huk )rukâRuk{maxulâUw,t Tul,t}, âuk â Utra,t;Ï(Îºd2duk ) â© Ï(Îºd2dukâ² ) = â , âuk 6= ukâ² â Utra,t;fd2duk â P(Huk); ruk â¥ Rth.(4.14b)The objective function (4.14b) of problem P5 represents the possible com-pletion time minimization that we can obtain from D2D transmissions and(4.7a) represents maximizing the number of users left to be scheduled toeRRHs.To solve the problem in P5, we develop a simple and fast approach thatfirst schedules users that have low channel capacities from eRRHs on D2Dlinks, and the remaining unscheduled users (if any) can be scheduled byeRRHs with high transmission rates. This solution not only minimizes thecompletion time of users, but also offloads the eRRHsâ radio resources. In-deed, after D2D transmissions, few users left to be scheduled by eRRHs.This approach is summarized in Algorithm 7, which consists of the follow-ing two stages at every transmission slot: i) users experience relatively weakchannels from the eRRHs should be scheduled to the potential D2D trans-mitters on D2D links, and ii) the eRRHs deliver encoded files to a set ofusers that have not previously scheduled on D2D links. The coordinatedscheduling approach is described below.First stage: Here, we focus on scheduling a set of users that have lowrates from the eRRHs to a set of potential transmitters via D2D links assuch we solve problem (4.14b) efficiently.First step: Inspired by Section 4.5.2, we follow the same procedures thatconstruct the new D2D conflict graph Gd2d(V, E). Thus, we generate a ver-1214.6. Coordinated Scheduling Solution for Completion Time Minimization Problemtex vkr,l,f for each transmitting user uk, a transmission rate ruk â Rd2duk,ui anda missing file fh â Huk â© Wul of a user ul â Uw â© Cuk . Further, the rateof each transmitting user in each generated vertex should be greater thanor equal to Rth. Similarly, we generate the vertices for U users and thenconnect them as in Section 4.5.2.Second step: We design two-layer weights for each generated vertex in theGd2d graph, named by secondary and primary weights. The secondaryweight of a vertex vkr,l,f is defined as w(vkr,l,f ) =rukB that shows a partialcontribution of that vertex in terms of reducing the completion time in thenetwork. The primary weigh of a vertex vul,fh is defined as w(vui,fh) =BminbnâKRbn,ul, âfh â Hbn . This primary weight characterizes the users basedon their channel capacities from the eRRHs to give them priority to bescheduled on D2D links. A vertex with high primary weight (low rate fromeRRHs) leads to prolonged file delivery time from eRRHs. Then the corre-sponding users of such vertices should be scheduled on D2D links with themaximum rate from any possible potential D2D transmitters. As such, thecompletion time of these users is minimized.Third step: We propose to iteratively perform maximum weight search toform the set of D2D transmitters and their scheduled users in the maxi-mal IS I as follows. First, we search for the vertex with the maximumprimary weight and find its corresponding maximum secondary weight. Iftwo or more vertices have equal weights, we select one vertex randomly.We continue this process until there are no other available vertices that canbe included in the selected IS. At the end, the final IS I consists of ver-tices that represent a set of potential D2D transmitters. Each of these D2Dtransmitters serves users that have low channel capacities from the eRRHs.Second stage: Here, we schedule users that are not scheduled on D2Dlinks to eRRHs using RA-IDNC. In particular, we solve problem (4.7a) bymaximizing the number of scheduled users to the eRRHs. First, we constructthe coordinated scheduling graph, denoted by Gcord(E ,V), by generating avertex Vbn,ui,fh,Rbn for each bn â B, for every file fh is requested by userui â Uw,tI, and for each achievable rate for that user Rbn â¥ rmin, wherermin is the minimum selected transmission rate of any transmitting user in Î.1224.6. Coordinated Scheduling Solution for Completion Time Minimization ProblemAlgorithm 7: Proposed Coordinated Scheduling Approach1: Require U , F , N , B, Hbn , Hul,0, Wul,0, Pbn , Puk , hcbn,ul , hd2duk,ul ,âuk, ul â U , âbn â B;2: First stage3: Initialize I = â and Gd2d(I)â Gd2d.4: âvkr,l,h â Gd2d: calculate w(vkr,l,h) =rukN and its correspondingw(vul,fh) =NminbnâKRbn,ul.5: while Gd2d(I) 6= c do6: Choose the maximum primary weight vâul,fh and finds itscorresponding maximum secondary weightvkâr,l,h = arg maxvkr,l,hâGd2d(I){w(vkr,l,h)}.7: Set I â I âª vkâr,l,h and Gd2d(I)â Gd2d(vkâr,l,h).8: end while9: Second stage10: Design Gcord according to Section 4.6.11: âVen,ui,fh,Ren â Gcord: calculate w(Ven,ui,fh,Ren ) =RenB.12: Obtain the maximum IS I as follows.13: Initialize I = â .14: for each Vbn,ui,fh,Ren â Gcord non-conflicting with I do15: Select V âbn,ui,fh,Ren = arg maxVbn,ui,fh,RbnâGcord{w(Vbn,ui,fh,Rbn )}.16: Iâ I âª V âbn,ui,fh,Rbn .17: end forThe configuration of the set of edges in the scheduling graph is divided intocoding (NC and rate edges) and transmission edge. Two vertices Vbn,ui,fh,Rbnand Vbn,uiâ² ,fhâ² ,Rbnâ²representing the same eRRH are adjacent by a conflictedge if they do not satisfy the IDNC and rate conditions in Section 4.5.1.Similarly, two vertices Vbn,ui,fh,Rbn and Vbnâ² ,uiâ² ,fhâ² ,Rbnâ²representing differenteRRHs are adjacent by a conflict transmission edge if the same user ui isscheduled to different eRRHs, i.e., ui = uiâ² and bn 6= bnâ² . Then, a maximumsearch process is executed in Gcord to obtain the maximum IS I as presentedin Algorithm 7.1234.7. Numerical Results4.7 Numerical ResultsThis section presents selected simulation results that compare the com-pletion time performances of our proposed two schemes with baseline al-gorithms. We consider a downlink D2D-aided F-RAN system where theeRRHs have fixed locations and users are distributed randomly at everytransmission within a hexagonal cell of radius 900m. We set the radius ofthe usersâ coverage zone R to 50m and the number of eRRHs B to 3. Weconsider the SUI-Terrain type B model in which the channel model of bothF-RAN and D2D communications is mostly affected by the location of theusers within the cell. Path loss is calculated as 148 + 40 log10(distance[km]).We consider that the channels are perfectly estimated. The noise powerand the maximumâ eRRH/user power are assumed to be â174 dBm/Hz andPmax = P = â42.60 dBm/Hz, respectively. The bandwidth is 1 MHz andthe eRRH caching ratio µ is 0.6. As discussed in Section 4.2, at the be-ginning of the D2D-aided F-RAN transmission, each user already has about45% and 55% of F files. To assess the performances of our proposed schemeswith different thresholds (Rth1 = 0.05, Rth2 = 0.5, and Rth3 = 5), we sim-ulate various scenarios with different number of users, number of files, andfile sizes.For the sake of comparison, our proposed schemes are compared withthe baseline RLNC and Classical IDNC schemes. For completeness of ourwork, we also compare our proposed schemes with the uncoded schemes.â Uncoded Unicast: This scheme schedules only one user to eacheRRH from which it receives an uncoded file with its maximum trans-mission rate. In addition, the untargeted users by the eRRHs is servedby implementing uncoded D2D transmissions.â Uncoded Broadcast-F-RAN: The eRRHs broadcast uncoded filessequentially as such all users are served. In this scheme, each eRRHtransmits with the lowest transmission rate of all scheduled users.â Uncoded Broadcast-D2D: In this scheme, set of transmitting usersis selected randomly to broadcast uncoded files from their Has sets1244.7. Numerical Results10 11 12 13 14 15 16 17 18Number of users U0102030405060Average Completion Time(seconds)Proposed Joint R th1, Rth2, Rth3Proposed Coordinated Scheduling Rth1RA-IDNCRLNCUncoded Broadcast-F-RANUncoded UnicastUncoded Broadcast-D2DClassical IDNCAverage Completion Time(seconds)Figure 4.5: Average completion time versus the number of users U .that are missing at the largest number of their neighboring users. Thetransmission rate is selected based on the minimum transmission of allscheduled users.Recently, RA-IDNC scheme is studied in [82] where all eRRHs use thesame transmission rate that corresponds to the minimum transmission rateof all scheduled users. In addition, the unscheduled users by the eRRHs arescheduled from transmitting users over D2D links with the same rate thatis used by the eRRHs. Thus, we include the RA-IDNC and compare it withthe proposed schemes.In Figure 4.5, we depict the average completion time versus the numberof users U . We consider a D2D-aided F-RAN model with a frame of 15files and a file size of 1 Mbits. From this figure, it can be seen that theproposed schemes offer improved performance in terms of completion timereduction as compared to the other schemes. This improved performance isdue to the joint and coordinated schemes that (i) judiciously schedule users,adopt the transmission rate of each eRRH and optimize the transmissionpower of each eRRH, and (ii) select potential users for transmitting coded1254.7. Numerical Resultsfiles over D2D links. In particular, the uncoded unicast suffers from tar-geting few users that have relative strong channel qualities. As a result, ahigher number of transmissions, at least (UF )/(B + |Utra|) transmissions,is needed for frame delivery completion, and it leads to a high completiontime. Uncoded broadcast schemes suffer from serving all users at the costof adopting the transmission rate of all eRRHs and transmitting users withthe minimum transmission rate of the served users. Furthermore, uncodedbroadcast D2D scheme offers a poor completion time performance as alltransmitting users do not benefit from the transmission, i.e., they cannottransmit and receive at the same time. RLNC is a rate-less scheme thattargets all users by sending encoded file with the lowest rate of all users.On the other hand, RA-IDNC scheme offers an improved performance com-pared to uncoded, RLNC, and classical IDNC schemes as mentioned in [82].This is because the coding decisions in RA-IDNC scheme not only dependson the file combinations, but also on the channel qualities of the scheduledusers. This effectively balances between the number of scheduled users andthe transmission rate of eRRHs/transmitting users. However, selecting onetransmission rate (the minimum rate) for all eRRHs and transmitting usersdegrades the completion time performance of the RA-IDNC scheme. This isa clear limitation of the RA-IDNC scheme in [82], as it does not fully exploitthe typical variable channel qualities of the different eRRHs/transmittingusers to their scheduled users. Our proposed joint and coordinated schemesfully utilize the eRRHs and transmitting usersâ resources to choose their owntransmission rates, XOR combinations, and scheduled users. Consequently,a better performance of our proposed schemes compared to the RA-IDNCscheme is achieved. Moreover, the joint scheme optimizes the employed ratesusing power control on each eRRH. Thus, it works better than our proposedcoordinated scheme. Note that the completion time performances of theclassical IDNC and uncoded broadcast D2D schemes are of orders 105 and103, respectively. Thus, we omit them from all the remaining figures.In Figure 4.6, we show the average completion time versus the numberof files F . The simulated D2D-aided F-RAN system composed of 15 usersand file size of 1 Mbits. Again, for the above-mentioned reasons in Figure1264.7. Numerical Results10 11 12 13 14 15 16 17 18Number of files F0510152025303540Average Completion Time(seconds)Proposed Joint R th1, Rth2, Rth3Proposed Coordinated SchedulingRA-IDNCRLNCUncoded Broadcast-F-RANUncoded UnicastAverage Completion Time(seconds)Figure 4.6: Average completion time versus the number of files F .4.6, our proposed schemes outperform the other schemes. It can be observedfrom the figure that increasing the frame size leads to an increasing in thecompletion time of all schemes. The opportunities of mixing files using NCin the RA-IDNC and proposed schemes are limited with few files. Therefore,all NC schemes have roughly similar performances. As the number of filesincreases, the increase in the completion time with our proposed schemes islow. This is in accordance with our results in Theorem 4.6 and Theorem 4.8,where it is shown that our proposed schemes judiciously allow each eRRHand each transmitting user to decide on a set of files to be XORed. Assuch, they are beneficial to a significant set of users that have relativelygood channel qualities. Even though uncoded broadcast and RLNC schemescompletes file transmissions in fewer transmissions (F transmissions) thanour proposed schemes, each of their transmission durations is longer thana single transmission of the proposed schemes. Thanks to their optimizedhigher rate/power and usersâ transmission that result in less completiontime.In Figure 2.6, we illustrate the impact of increasing the file size N onthe average completion time. In this figure, we simulate the D2D-aided F-1274.7. Numerical ResultsFigure 4.7: Average completion time versus file size N .RAN system composed of 12 users and 15 files. We can observe that theperformances of all schemes increase linearly with the file size. This is inaccordance with the completion time expression in Corollary 4.5, where itwas emphasized that To increases linearly with N . From physical-layer view,as N increases, more bits are needed for delivering files. Thus, time delay isincreased to receive files from eRRHs/transmitting users.Finally, some insights from our presented numerical results are given asfollows. First, it is advantageous to serve many users with NC files as in theclassical IDNC algorithm, but selecting the minimum transmission rate ofall scheduled users degrades its performance. Thus, this scheme is imprac-tical from physical-layer perspective. Second, although the uncoded unicastscheme uses the maximum transmission rate of each user, it needs a largenumber of transmissions for completion. Thus, its completion time per-formance is degraded. Third, RA-IDNC scheme overcomes the limitationsof the aforementioned schemes but suffers from selecting the lowest-rate ofthe fixed-power eRRHs in the system. This limitation further degrades thecompletion time performance of the RA-IDNC scheme in large network sizeswith large number of eRRHs. This due to the fact that RA-IDNC always1284.8. Chapter Summaryselects the lowest-rate of all eRRHs. Conversely, our transmission frame-work is more practically relevant as it enables different transmission ratesfrom different eRRHs/transmitting users and optimizes the employed ratesusing power control on each eRRH.4.8 Chapter SummaryIn this chapter, we have developed two frameworks that exploit thecached contents at eRRHs, their transmission rates, and previously receivedcontents by different users to deliver the requesting contents to users witha minimum completion time in D2D-aided F-RAN. Simulation results haveshown that our proposed frameworks can effectively minimize the framedelivery time as compared to conventional algorithms.129Chapter 5Coalition Formation Gamefor Cooperative ContentDelivery in Network CodingAssisted D2DCommunicationsIn Chapter 4, we considered a centralized system of D2D-aided F-RAN,where there is a centralized computing unit called the CBS. This CBS isresponsible for making the NC decisions, rate adaptation, delivering theinstructions to transmitting users and eRRHs for executions. The CBS isassumed to be within the transmission range of all users and has perfectknowledge of the network topology. Further, in order to make NC decisionsfor the transmitting eRRHs/users, the CBS has to track the downloadinghistory of all users after each transmission which requires a high computationcapability at the CBS. This is expensive for service providers to implementfixed infrastructures of many distributed CBS units. Importantly, in somescenarios of an extremely high user density, the CBS is fully loaded. To thisend, in this chapter, we consider D2D networks to develop a distributed anddecentralized framework that overcomes all the aforementioned limitationsof the centralized system. In fact, one of the major directions towards 5Gnetworks is D2D communications and cooperative packet recovery amongusers. This will offload traffic from the CBS can thus free up some spectrumfor it to serve more users. The organization of this chapter is given as fol-1305.1. Accomplished Works and Research Contributionslows. The accomplished works and research contributions are summarizedin Section 5.1. The D2D system model and problem formulation are dis-cussed in Section 5.2. In this section, we provide an example for illustratingthe completion time minimization. In Section 5.3, we model the completiontime minimization problem as a coalition game. Section 5.4 proposes a fullydistributed coalition formation game solution using merge and split rules.In Section 5.5, we analyze the convergence, stability, complexity, and com-munication overhead of the proposed algorithm. In Section 5.6, we evaluatethe completion time and game performances of our proposed solution, andin Section 5.7, we conclude this chapter.5.1 Accomplished Works and ResearchContributionsThe contributions of this chapter are summarized as follows. First, forpartially D2D networks, we develop a decentralize IDNC-assisted D2D gametheoretical framework to minimize the completion time while offloading theCBSs. In particular, the completion time minimization problem is formu-lated and modeled as a coalition game. Given the difficulty of expressingthe problem as a coalition game with non-transfer function (NTU), we relaxit to a coalition formation game (CFG). Second, given the relaxed CFG, weexpress the completion time metric as the utility function, which is trans-ferred to each playerâs payoff in each coalition. We, then, derive the rules forassociating players, selecting the transmitting player, and finding its packetcombination that is beneficial for a set of interested UDs in each disjointaltruistic coalition. Afterward, we develop a coalition formation distributedalgorithm in each transmission slot based on merge-and-split rules. Finally,we prove that the proposed coalition formation algorithm is converged toa Nash-stable equilibrium, and we theoretically analyze its complexity andcommunication overhead. We validate our theoretical finding using compre-hensive numerical simulations, which reveal that our distributed scheme cansignificantly outperform existing centralized and fully distributed methods.1315.2. System Overview and Problem Formulationu2u6u8u11u12u13 u1u3u4u5u9u10u7Ïu8u9Figure 5.1: Illustration of a partially connected D2D network with 13 UDs.For simplicity, only the coverage zones of the possibly transmitting UDs u2,u6, u8, and u11 are drawn.For the presented network setups, our proposed decentralized scheme offersalmost the same performance as the centralized F-RAN D2D scheme.5.2 System Overview and Problem Formulation5.2.1 System OverviewConsider a D2D-enabled wireless network, shown in Figure 5.1, that con-sists of U UDs, denoted by the set U = {u1, u2, · · · , uU}, that are interestedin receiving a delay-sensitive content representing a frame of M packets,denoted by the set P = {p1, p2, · · · , pM}. The size of the frame P dependson the sizes of the packet and content. This work assumes that UDs havealready acquired some packets in P from previous transmissions, i.e., Hukdenotes the Has set of packets acquired by uk-th UD. We assume UDs re-quest a set of packets, which is not included in their Has sets, from the frameP. This requested set will be referred as Wants set, i.e., Wuk = P Huk isset of wanted packets for uk-th UD. The Has and Wants sets of all UDs canbe summarized in a binary UÃM state matrix S = [suk,pl ] wherein the entrysuk,pl = 0 represents that the pl-th packet is successfully received at uk-thUD and 1 otherwise. In order for all UDs to obtain the whole frame P from1325.2. System Overview and Problem FormulationD2D communications, we assume that each packet pl, 1 â¤ l â¤M is receivedby at least one UD, i.e.,âukâU suk,pl â¥ 1 for all packets pl â P. At eachtransmission slot, each UD can be packets requester (receiver) or packetsholder (transmitter) that providing its received packets to other requestingUDs via D2D links. When any UD receives all its requested packets, it mostlikely acts as a transmitter to transmit its received packets to interestedUDs.This work considers a realistic partial network topology, where UDs canonly target the subset of UDs in their coverage zone, denoted by Cuk of uk-thUD. The network topology can be captured by a unit diagonal symmetricU ÃU adjacency matrix C represents the connectivity of the UDs such thatCukul = 1 if and only if ul â Cuk . The matrix C is updated after eachtransmission based on the connectivity index C, where C is a fractionalconnection ratio. We assume that no part of the network is disjoint, i.e.,the matrix Z is connected. Otherwise, the proposed algorithm is separatelyapplied to each independent part of the network. Upon successful receptionof a packet, each UD sends an error-free acknowledgment (ACK) to allUDs in its coverage zone to update their Has and Wants sets. Therefore,maintaining a feedback matrix of neighboring UDs required low complexityand low signaling overhead than the fully connected model.We focus only on the upper layer view of the network, where networkcoding is performed at the network layer, and a memory-less erasure channelabstracts the physical-layer. This abstraction is widely used in networkcoding literature, where a packet is either perfectly received or completelylost with certain average probability [44], [61], [62], [63], [64], [65], [66], [67],[68], [69]. Therefore, the physical channel between the uk-th and ul-th UDsis modeled by a Bernoulli random variable whose mean Ïukul indicates thepacket erasure probability from uk-th UD to ul-th UD. We assume that theseprobabilities remain constant during the transmission of a single packet pl âP, and they are known to all UDs. Due to the channelâs asymmetry betweenuk-th and ul-th UDs, the equality of Ïukul and Ïuluk is not guaranteed. Toclarify the system model and its most variables, Figure 5.1 shows a partiallyconnected D2D network with 13 UDs. The coverage zones of the possibly1335.2. System Overview and Problem Formulationtransmitting UDs and their targeted UDs are shown in Figure 5.1.We consider a slowly changing network topology, in which UDs havefixed locations during the IDNC packet transmission and change from onetransmission to another. However, after one transmission, the UDs canmove, and all the network variables will be updated. Our model, i.e., thecoalition formation solution, can be used with updated network parameters.It is important to note that in fully connected networks, each UD is con-nected to all other UDs in the network, and hence, it precisely knows theHas and Wants sets of all UDs. To avoid any collision in the network, onlyone UD is allowed to transmit an encoded packet at any transmission slot.In partial connected D2D networks, single-interface UDs can receive twotransmissions from different transmitting UDs, but this causes collisions.This collision is due to two or more UDs transmit simultaneously using thesame radio resource block, e.g., frequency. As such, the receiving UD can-not decode these collided packets correctly, see for examples [20], [21], [22],[23],, [24] and their references. Therefore, UDs are grouped in disjoint andindependent coalitions to avoid any collisions or conflict transmissions. Con-sidering the interference of transmissions caused by other UDs to the set oftransmitting UDs can be pursued in future work.5.2.2 Instantly Decodable Network Coding ModelIDNC XOR combination enables the complete packet reception at ev-ery time slot when each scheduled UD has at most one packet in thatXOR combination. Let puk be an XOR combination sent by the uk-thUD to the set of scheduled UDs u(puk). Note that the packet combina-tion puk â Huk is an element of the power set X of the received packetsat the uk-th UD. A transmission from the uk-th UD is instantly decod-able at the ul-th UD if: i) it contains only one packet from the Wants setof the ul-th UD, and ii) the ul-th UD is in the coverage zone of the uk-th UD. Therefore, the set of targeted4 UDs by uk-th UD is expressed asu(puk) ={ul â Uâ£â£|puk â©Wul | = 1 and ul â Cuk}. In that case, ul-th UD4The term âtargeted UDsâ is given for a set of scheduled UDs who receives an instantly-decodable transmission.1345.2. System Overview and Problem Formulationcan re-XOR the combination puk with Hul to retrieve one of its requestingpackets. Hence, we say that uk-th UD is a transmitting UD that provides aset of its received packets to a set of targeted UDs.Let Utra,t â U denote the set of transmitting UDs at the t-th transmis-sion and p(Utra,t) = (pu1 , · · · , pu|Utra,t|) denote the packet combinationsto be sent by UDs in Utra,t. For notation simplicity, the transmission in-dex t is often omitted when it is clear from the context. Let u(p(Utra)) =(u(puk), · · · , u(pu|Utra|)) denote the set of targeted UDs by the transmit-ting UDs wherein ul â u(puk(Utra)) implies that |Wul â© puk(Utra)| = 1 and{ul} â© Cuk â© Cum = δukum{ul} for all transmitting UDs um â Utra whereinδukum is the Kronecker symbol. Mathematically, δukum{ul} = ul if uk = umand 0 otherwise.Definition 5.1. The completion time of uk-th UD, denoted by Tuk , is thenumber of D2D transmissions required to get all its packets in Wuk . Theoverall completion time T = maxukâU{Tuk} represents the time required forall UDs to get all the packets.5.2.3 Completion Time Minimization Problem FormulationIn this subsection, we formulate the distributed completion time reduc-tion problem in IDNC-enabled D2D network. Let Uw be a binary vector ofsize U whose uk-th index is 1 if uk-th UD has non-empty Wants set, i.e.,Wuk 6= â and 0 otherwise, and let u(p(Utra)) = 1â u(p(Utra)) be the set ofthe non-targeted UDs by the encoded packets p(Utra). The different erasureoccurrences at the t-th transmission slot are denoted by Ï : Z+ â {0, 1}UÃUwith Ït = [Yukul ], for all (uk, ul) â U2, where Yukul is a Bernoulli randomvariable equal to 0 with probability Ïukul .Let nt = (n[u1], n[u2], · · · , n[uu]) be a binary vector of length U whosen[uk]-th element is equal to 1 if uk-th UD is transmitting, i.e., ânâ1 = |Utra|.Likewise, let D(nt) be the decoding delay experienced by all UDs in thet-th transmission slot. In particular, D(nt) is a metric quantifies the abilityof the transmitting UDs to generate innovative packets for all the targetedUDs. This metric increases by one unit for each UD that still wants packets1355.2. System Overview and Problem Formulationand successfully receives a nonuseful transmission from any transmittingUD in Ntra or for a transmitting UD that still wants some packets. LetI = (I [u1], I [u2], · · · , I [uU ]) be a binary vector of size N whose I [ul] entryis 1 if ul-th UD is hearing more than one transmission from the set Utra,i.e., ul â Cuk â© Cum where uk 6= um â Utra and 0 otherwise, and let O =(O[u1],O[u2], · · · ,O[uU ]) be a binary vector of size U whose O[ul] element is1 if ul-th UD is out of transmission range of any transmitting UD in Utra,i.e., ul /â Cuk ,âuk â Utra and 0 otherwise.Given the above configurations, the overall decoding delays D(nt) expe-rienced by all UDs, since the beginning of the delivery phase until the t-thtransmission, can be expressed as follows.D(nt) = D(ntâ1) +ï£±ï£²ï£³U if ântâ1 = 0I +O + nt +D(nt) otherwise. (5.1)As mentioned, the completion time is a difficult and intractable metricto optimize. However, in network coding literature, such metric is approx-imated by the anticipated completion time which can be computed at eachtransmission using the decoding delay. The anticipated completion timethat uses the decoding delay in (5.1) is defined as follows.Definition 5.2. The anticipated completion time of the uk-th UD is definedby the following expressionTuk(nt) =|Wuk,0|+ Duk(nt)â E[Ïuk ]1â E[Ïuk ], (5.2)where |Wuk,0| is the number of the requested packets in the Wants set of uk-th UD at the beginning of delivery phase and E[Ïuk ] is the expected erasureprobability linking uk-th UD to the other UDs in its coverage.Clearly, (5.2) represents the number of D2D transmissions that are re-quired for uk-th UD to receive all packets inWuk . In this context, completiontime is intimately related to the throughput of the system. Throughput ismeasured as the number of cooperative D2D transmission rounds required by1365.2. System Overview and Problem Formulationp1p1p1p1p1p2p2p2p2p3p3p3p3p4p4p4p4u1u2u3u4u5u6u1u2u3 u5u4u6First transmission slotu1:u6:ââp3 p4p4p1u1u2u3 u5u4u6Second transmission slotu1:u4:âp2 p4p2Ntra,1 = {u1, u6} Ntra,2 = {u1, u4}p1UDsâ acquired and wanted packetsFigure 5.2: A partially connected D2D network containing 6 UDs and 4packets.the UDs to receive all their requested packets. The overall anticipated com-pletion time can be written as T(nt) = maxuk(Tuk(nt)) = âT(nt)ââ. Therefore,the anticipated completion time minimization problem at the t-th transmis-sion slot in IDNC-enabled partially D2D network can be written as follows.minntâ{0,1}Up(Utra)â{0,1}MâT(nt)ââ. (5.3)Unlike a fully connected model that only requires optimization over a sin-gle transmitting UD and its corresponding packet combination, a partiallyconnected model needs to select the set of transmitting UDs Utra and theencoded packets p(Utra). As such, the probability of increasing the antici-pated completion time is minimized.Example of IDNC Transmissions in a Partially Connected D2DNetworkWe illustrates the aforementioned definitions and concepts with a simpleexample. Consider a simple partially connected D2D network containing6 UDs and a frame P = {p1, p2, p3, p4} as illustrated in Figure 5.2. Theacquired and wanted packets of all UDs are given on the left part of Figure5.2, and the coverage zone of each UD is represented by edges. For ease ofanalysis, we assume error-free transmissions. Assume that u1 transmits thecombination pu1 = p3 â p4 to u2, u3, u5 and u6 transmits the combinationpu6 = p1 â p4 to u4, u5 in the first transmission slot. In the second trans-1375.2. System Overview and Problem Formulationmission slot, assume that u4 transmits pu4 = p2 to u6, and u1 transmitspu1 = p2 â p4 to u2, u5. The decoding delay experienced by the differentUDs is given as follows.â The u5-th UD experiences one unit delay as it is in the intersectionof the coverage zone of transmitting UDs u1 and u6. In other words,u5 is in collision, i.e., u5 â I. Thus, u5-th UD would not be able todecode packet p6 transmitted by the u6-th UD.â The u6-th UD experiences one unit of delay as it transmits in the firsttransmission slot.Under this scenario, we have the following assumption.â First transmission slot: Uw = (0 1 1 1 1 1), the set of transmit-ting UDs Utra,1 = {u1, u6} = n1 = (1 0 0 0 0 1), the correspondingencoded packets p(Utra,1) = (pu1 , pu6), and the set of targeted UDsu(p(Utra,1)) = (u(pu1), u(pu6)) = {(u2, u3), (u4)}. The set of UDs thathearing more than one transmission I = (0 0 0 0 1 0), and the set ofUDs that out of transmission range of any UD in Utra,1 is O = 0. Thedecoding delay experienced by all UDs is D(n1) = (0 0 0 0 1 1). Theaccumulative decoding delay is D(n1) = (0 0 0 0 1 1).â Second transmission slot: Nw = (0 1 0 0 1 1), the set of trans-mitting UDs Utra,2 = {u1, u4} = n2 = (1 0 0 1 0 0), the correspondingencoded packets p(Utra,2) = (pu1 , pu4), and the set of targeted UDsu(p(Utra,2)) = (u(pu1), u(pu4)) = {(u2, u5), (u6)}. The set of UDs hear-ing more than one transmission I = 0, and the set of UDs that out oftransmission range of any UD in Utra,2 is O = 0. The decoding delay isD(n2) = 0 and the accumulative decoding delay D(n2) = (0 0 0 0 1 1).â The completion time of all UDs after the second transmission is T =(0 2 1 1 2 2). Thus, the maximum completion time is 2 transmissionslots which represents the overall completion time for all UDs to gettheir requested packets, i.e., Uw = 0.1385.3. Distributed Completion Time Minimization as a Coalition Game5.3 Distributed Completion Time Minimizationas a Coalition GameOur main goal is to develop a distributed framework that models thecollaborations among the UDs of IDNC-enabled partially D2D networks. Inorder to do that, we use game theory because it involves a set of playersthat interact with each other to form a coalition without any coordinationfrom the CP. The key idea of forming coalitions is to study the cooperativebehavior of UDs in coalitions. In particular, UDs are formed coalitions sothat they minimize their completion times compared to when they do notform coalitions as will be discussed in Section 5.4. Through coalitions andIDNC content delivery among players, the overall completion time can bereduced.In this section, we first model the completion time problem in IDNC-enabled partially connected D2D networks using coalition games [83]. Af-terward, we define and provide fundamental concepts in coalition games.These concepts are used in Section 5.4 to derive the proposed distributedcompletion time reduction solution.Completion Time Minimization as a Coalition GameWe use a coalition game to formulate the completion mentioned abovetime problem. In particular, our problem is modeled as a coalition gamewith a non-transferable utility (NTU) [83].Definition 5.3. A coalition game with a non-transferable utility is definedas a pair (N , Ï), where N is the set of players consisting of N UDs and Ïis a real function such that for every coalition Ss â N , Ï(Ss) is the payoffthat coalition Ss receives which cannot be arbitrarily apportioned between itsplayers.For the considered D2D completion time problem with colaition games,packets are transmitted simultaneously from a set of cooperative transmit-ting UDs Ntra. Each transmitting UD serves a group of interested andnearby UDs that constitutes a coalition. In the coalition game, each UD1395.3. Distributed Completion Time Minimization as a Coalition Gameacts as a game player and aims to join a coalition such that: i) it can receivepackets and minimize its completion time, ii) it does not increase the com-pletion time of its alliances in the coalition. Therefore, for each coalition,we need to determine the transmitting player and its packet combinationthat is beneficial to a set of interested players. As such, we minimize theincreasing of the completion time.Let Ï(Ss) = (Ïu1(Ss), · · · , Ïu|Ss|(Ss)) define a tuple wherein elementÏuk(Ss) represents the payoff of uk-th UD in coalition Ss, where Ss â N ,and |Ss| is the total number of players in Ss. We use s as the subscript toidentify coalitions. The |S|-dimensional vector represents the family of realvector payoffs of coalition Ss, which is denoted by Ï(Ss). Consequently, byadopting the cooperative D2D completion model described in the previoussection, the total payoff of any coalition Ss â U , âs = {1, · · · ,m} is givenbyÏ(Ss) = maxuk(Ïuk(Ss)) = âÏ(Ss)ââ, (5.4)where Ïuk(Ss) is the payoff of uk-th UD in a coalition Ss which is in ourproblem given byÏuk(Ss) = ââTuk(nt)ââ â âDuk(nt)â Duk(ntâ1)â1. (5.5)The payoff function in (5.4) represents the total payoff that a coalitionreceives due to self-organize players. For a player uk â Ss, the first term in(5.5) represents the maximum anticipated completion time among players inSs that is defined in (5.2). Similarly, the second term in (5.5) represents theaugmentation of the sum decoding delay that is defined in (5.1). Therefore,players in coalitions prefer to increase the payoff in (5.5) by minimizing theanticipated completion time through controlling the decoding delay. Notethat the negative sign indicates that the payoff of a coalition is inverselyproportional to the completion time.Property 1 : The proposed D2D completion time cooperative problem ismodeled as a coalition game with NTU (U , Ï) where U is the set of players1405.3. Distributed Completion Time Minimization as a Coalition Gameand Ï is the payoff function given by (5.4).Proof. From the nature of definition 1 and definition 2, the uk-th playerhas its own unique anticipated completion time and decoding delay, and,thus, it has a unique payoff Ïuk(Ss) within a coalition Ss. Therefore, thepayoff function in (5.4) cannot be arbitrarily apportioned between coalitionâsplayers. Thus (5.4) is considered as an NTU. Further, the overall completiontime is the maximum individual completion times of the players regardlessof the coalition. In other words, the dependency of Ï(Ss) in any coalitionstructure is not only on packet delivery of players inside Ss, but also onpacket delivery outside Ss, which concludes that the proposed game modelis NTU game.Although cooperation generally reduces the payoffs of players [38], it islimited by inherent information exchange cost that needs to be paid by theplayers when acting cooperatively. Consequently, for any coalition Ss â U ,players need to exchange information for cooperation, which is an increasingfunction of the coalition size. The problem becomes severe when all playersare in the same coalition, i.e., grand coalition (GC). However, given therealistic scenario of a partially connected network where each UD has limitedcoverage, it is highly likely that when attempting to form the GC, one ofthese scenarios will hold:â There exists a pair of uk-th, ul-th players in U that are distant enoughto receive packets within the GC. Thus, they have no incentive to jointhe grand coalition.â There exists a player uk â U with a payoff in GC Ïuk(U) that is lessthan its payoff in any coalition Ïuk(Ss). Hence, this player has anincentive to deviate from the GC.Further, the limited coverage players in the considered partially connectedD2D model would most likely form small coalitionsâ sizes, not large coali-tionsâ sizes. Therefore, the GC of all players is seldom formed, and thecooperation cost due to forming small coalitionsâ sizes would not have asignificant impact on the payoff functions.1415.3. Distributed Completion Time Minimization as a Coalition GameThe aforementioned discussion emphasizes that the proposed (N , Ï)game is classified as a coalition formation game (CFG) [134], where play-ers form several independent disjoint coalitions. Hence, classical solutionconcepts for coalition games, such as the core [83], may not apply to ourproblem. In summery, the proposed coalition game (U , Ï) is a CFG, wherethe objective is to develop an algorithm for forming coalitions.Coalition Formation ConceptsThis section provides some concepts of coalition formation games thatare used in the next subsection. CFG, a subclass of coalition games, hasbeen a topic of high interest in game theory research [134], [135], [138]. Thefundamental approach in coalition formation games is to allow players in theformation set to join or leave a coalition based on a well-defined and mostsuitable preference for NTU games, i.e., Pareto Order. Pareto Order is thebasis of many existing coalition formation concepts, e.g., the merge-and-splitalgorithm [136].Definition 5.4. A coalition structure, denoted as Ψ, is defined as Ψ ={S1, · · · ,Sm} for 1 < |Sm| < |U| independent disjoint coalitions Sm of Ψ.One can see from definition 5 that different coalition structures maylead to different system payoffs as each coalition structure Ψ has its uniquepayoff Ï(Î¨). These differences in Ψ and their corresponding payoffs Ï(Î¨) areusually ordered through a comparison relationship. In the coalition gameliterature, e.g., [136], comparison relationships based on orders are dividedinto individual value orders, and coalition value orders. Individual orderimplies that comparison is performed based on the playersâ payoffs. Thisis referred to as the Pareto Order. In particular, in such order, no playeris willing to move to another coalition when it has a negative effect on thepayoff of that coalition. In other words, the payoff of players would be worseoff after the new player joins. This is known as selfish behavior. Coalitionorder implies that two coalition structures are compared based on the payoffof the coalitions in these coalition structures. This is known as a utilitarianorder and is denoted by .. In other words, the notation Ψ2 .Ψ1 means that1425.4. Proposed Fully Distributed SolutionÏ(Î¨1) > Ï(Î¨2). Subsequently, the definition of the preference operator thatconsidered in this work is given as follows.Definition 5.5. A preference operator . is defined for comparing two coali-tion structures Ψ1 = {S1, · · · ,Sm} and Ψ2 = {R1, · · · ,Rn} that are parti-tions of the same set of players U . The notation Ψ2.Ψ1 denotes that playersin U are preferred to be in Ψ2 than Ψ1.5.4 Proposed Fully Distributed SolutionHere, we derive the constraints of forming a coalition that representsthe playersâ associations, transmitting player, and its packet combinationin a coalition. By the given constraints, we aim to propose a distributedcoalition formation algorithm using merge-and-split rules.5.4.1 Coalition Formation ConstraintsLet Us be the set of all associated players in Ss-th coalition and Us,wthe subset of Us that have non-empty Wants set. Let Ms be the sub-set of packets that in the Has set of each player in Us, which defined asMs =âukâUs Huk . Let Ss denote the set of all neighboring coalitions toSs-th coalition. For the Ss-th coalition, the unâs -th transmitting UD is theone that can achieve the least expected increase in the completion time.According to the analysis available in [69], a transmitting UD unâs and itspacket combination punâs sent to the set of users u(punâs ) can be obtained bysolving the following problemunâs = arg maxunâUtra,sLs|Cun â©Ns,w|+ arg maxpunâp(Utra,s)âulâLsâ©u(pun )log1Ïunul, (5.6)where Utra,s is the set of players in coalition Ss that are not in any coveragezone of all other players in Ss and Ls is the set of critical players that canpotentially increase the overall payoff of the coalition Ss. This set char-acterizes the players based on their anticipated completion times to givethem priority to be targeted in the next transmission. In other words, Ls,t1435.4. Proposed Fully Distributed Solutioncontains players that would potentially increase the maximum anticipatedcompletion time if they are not targeted in the t-th transmission. It can bedefined asLs,t ={uk â U â© Us,wâ£â£Tuk(ntâ1) + 11â E[Ïuk ] > âT(ntâ1)ââ}. (5.7)The set of targeted players in coalition Ss when device unâs transmits thecombination punâs isu(punâs ) ={uk â Ssâ£â£|punâs â©Wuk | = 1 and Cunâsuk = 1} .With the aforementioned variable definitions, we can reformulate the com-pletion time minimization problem in IDNC-based partially connected D2Dnetwork per coalition at each transmission slot as followsminntâ{0,1}|Us|pâ{0,1}|Ms|Ï(Ss) (5.8a)s. t. |u(punâs )| > 1, (5.8b)u(punâs ) â© u(pnâv) = â ,âunâs 6= unâv â Ss. (5.8c)Constraint (5.8b) says that the number of targeted players in each coalitionmust be more than one to ensure that at each transmission at least one playeris benefiting. Constraint (5.8c) states that all targeted players should notexperience any collision. To find the optimal solution to the problem in (5.8),we need to search over all the sets of optimal player-coalition associations,their different erasure patterns, playersâ actions, and their optimal IDNCpackets. As pointed out in [67] for a centralized fog system, this is anintractable problem. Further, the solution to (5.8) must go through theplayersâ decisions to join/leave a coalition at each stage of the game. Toseek an efficient solution to (5.8) that is capable of achieving significantcompletion time reduction, a distributed coalition formation algorithm isdeveloped.1445.4. Proposed Fully Distributed Solution5.4.2 A Distributed Coalition Formation AlgorithmWe develop a distributed coalition formation algorithm to obtain theminimum completion time of UDs. The key mechanism is to allow playersin the coalition formation process to make individual decisions for selectingpotential coalitions at any transmission slot. We first define two rules ofmerge-and-split that allow the modification of Ψ of the set N players asfollows.Definition 5.6. (Merge Operation). Any set of coalitions {S1, · · · ,Sm}in Ψ1 can be merged if and only if (mâs=1Ss,Î¨2) . ({S1, · · · ,Sm},Ψ1), wheremâs=1Ss and Ψ2 are the new set of coalitions and the new coalition structureafter the merge operation, respectively.Definition 5.7. (Split Operation). Any set of coalitionsmâs=1Ss in Ψ1 canbe split if and only if ({S1, · · · ,Sm},Ψ2). (mâs=1Ss,Î¨1), where {S1, · · · ,Sm}and Ψ2 are the new set of coalitions and the new coalition structure afterthe split operation, respectively.The merge rule means that two coalitions merge if their merger wouldbenefit not only the players in the united alliance but also benefit the overallcoalition structure value, i.e., the whole completion time. On the otherhand, a coalition split into smaller ones if its splitter coalitions enhance atleast the payoff of one player in that coalition. Therefore, using these twoknown rules, we present a distributed algorithm to solve the completion timeminimization problem in (5.3) as follows.Step 1 (Coalition Members Discovery): Players in the initialized randomcoalition structure Ψini discover their neighbors by utilizing one of differentknown neighbor discovery schemes, e.g., those used in wireless networks[157]. For example, the uk-th player broadcasts a message consisting of twosegments; each segment consists of one byte. While the first byte indicatesthe number of players in its coverage zone Cuk , the second byte indicatesthe ukâs completion time. Further, players use the collected aforementioned1455.4. Proposed Fully Distributed Solutioninformation to decide on the one who: i) has a large Has set that can serve alarge number of players in its coverage zone, and ii) not in the coverage zoneof any player in any other coalitions in Ψini. However, if such a player doesnot exist, the size of the coalition is increased until that player exists. Tosummarize, the unâs -th selected transmitting player in Ss-th coalition shouldsatisfy (5.8b) and (5.8c) and can be obtained by solving problem (5.6).Afterward, each player evaluates its potential payoff as in (2.6) to makean accurate decision in step 2. The unâs selected player in Ss-th coalition(âSs â Ψini) will do the analysis in step 2. This step significantly reducesthe search space for associating the players to the coalitions.Step 2 (Coalition Formation for Playersâ Association): This step opti-mizes the selection of the transmitting players and their packet combinationsin step 1 through many successive split-and-merge rules between coalitions.Therefore, step 2 is to associate players to potential neighboring coalitions,select the transmitting player, and find its packet combination, which canbe accomplished by the following. In this step, the index is updated toÏ = Ï + 1. The merge rules are implemented by checking the merging possi-bilities of each pair of neighboring coalitions Ss and Sv. Initially, Î¨Ï = Ψini.Thus, a coalition Ss â Î¨Ï can decide to merge with another coalition Sv â Ssto form a new coalition Sj . As such, the resulting structure guarantees bothmerge conditions (MC).â MC1: There exists at least one player satisfies (5.8b) and (5.8c).â MC2: At least one player in the merged coalition can enhance itsindividual payoff without negatively affecting the payoffs of all theremaining players.After all the coalitions have made their merge decisions based on the play-ersâ preferences, the merge rules end. This results in the updated coalitionstructure Î¨Ï . Similarly, the split rules performed on the players that donot benefit from being a member of that coalition. In other terms, coalitionSs â Î¨Ï can be split into coalitions of smaller sizes as long as the splittercoalitions guarantee both split conditions (SC).1465.4. Proposed Fully Distributed Solutionâ SC1: At least one player can strictly enhance its payoff without affect-ing the payoffs of all the remaining players.â SC2: In each split coalition, there exists at least one player satisfying(5.8b) and (5.8c).At the end of the split rules, the coalition structure Ψ1 is updated. Theindex Ï is updated along with a sequence of merge-and-split rules whichtake place in a distributed manner. Such sequence continues based on theresulting payoff of each player and coalition. It ends when there are nofurther merge-and-split rules required in the current coalition structure Î¨Ï ,which is the final converged coalition structure Ψfin.Step 3 (IDNC Packet Transmissions:) Each transmitting UD in each coali-tion broadcasts its IDNC packet to all UDs in its coverage zone. Accordingly,each targeted UD by any transmitter sends ACK to all its neighboring UDsindicating its packet reception status. Thus, the Has, and Wants sets of allUDs in the system are updated.The coalition formation algorithm is distributively executed at eachtransmission slot and summarized in Algorithm 8. It is repeated until allpackets are delivered to all UDs, as presented in Algorithm 9.Some remarks on executing Algorithm 8 are given below.â The merge-and-split rules enumerate only neighboring coalitions, andthis does not necessarily need significant computations. To further re-duce the computations, the players of a coalition Ss can avoid mergingwith other neighboring coalition Sv if the payoffs of the players in bothcoalitions are equal Ïuk(Ss) = Ïul(Sv), âuk â Ss and âul â Sv.â The connectivity constraints of UDs are incorporated in the coalitionformations by: i) forming disjoint coalitions of nearby UDs based ontheir preferences, and ii) selecting the potential transmitting UD thatcan only target its connected players in its coalition. As such, we makesure that connected UDs are grouped into a single coalition.â Forming coalitions only one time, i.e., at the beginning of the trans-mission round, is not guaranteed to deliver all packets to all players.1475.4. Proposed Fully Distributed SolutionAlgorithm 8: Coalition Formation AlgorithmInput: U , P, Huk , Wuk , Cuk , âuk â U .;Initialization: Ψini = {S1, · · · ,Sm}, Ï = 0, Î¨Ï = Ψini.;Step 1: Coalition Members Discoveryâ Each player discovers its neighboring players.for each Ss â Î¨ini,âs = {1, 2, · · · , m} doSelect the transmitting players Utra,s that satisfying (5.8b) and (5.8c).Solve (5.6) to find unâs and its packet combination punâs .Calculate Ïuk(Ss) as in (2.6), âuk â Us.endStep 2: Coalition Formationâ The optimization target in coalition Ss is minntâ{0,1}|Us|pâ{0,1}|Ms|Ï(Ss).â Obtain playerâs assignments based on the two main rules of merge and split:repeatUpdate Ï = Ï + 1.for each Ss â Î¨Ïâ1,âs = {1, 2, · · · ,m} dounâs analyzes all possible merge rules with Ss.If a merge occurs:1. Update Î¨Ïâ1.2. Solve (5.6) to update Utra,s and unâs .Set Î¨Ï = Î¨Ïâ1.endfor each Ss â Î¨Ï ,âs = {1, 2, · · · ,m} dounâs analyzes all possible split rules.If a split occurs:1. Update Î¨Ï .2. Update Utra,s and update unâs by solving (5.6).enduntil No further merge nor split rules;Output The convergence coalition structure Ψfin = Î¨Ï .Step 3: IDNC Packet Transmissionâ Each unâs in each coalition Ss broadcasts punâs to all players in its coveragezone, âs = {1, 2, · · · ,m}.1485.4. Proposed Fully Distributed SolutionAlgorithm 9: Overall Completion Time Approach for SolvingProblem (5.3)Data: U , P, Huk , Wuk , Cuk , Tuk = 0, Duk = 0, âuk â U and .Initialize: Transmission slot t = 1Repeat:â Execute Algorithm 8 to obtain Utra,t, p(Utra,t), and u(p(Utra,t)) inÎ¨fin.â For âunâs â Utra,t doâ Each uk â u(punâs ) re-XOR punâs with Huk .â Calculate the completion time of each uk â u(punâs ) as in (5.2).â Each uk â u(punâs ) broadcasts one bit ACK to all players in Cuk .â End forâ t = t+ 1.â Update Huk , Wuk , âuk â Uw.Until Wuk = Ï, âuk â Uw.Output: Transmission slot t.This is because each formed coalition has only some portion of pack-ets and does not have the requested packets of other players in othercoalitions. For packet delivery completion, each coalition is formed,at each transmission slot, based on the individual preference of itsalliances and irrespective of the Has sets of its alliances. Thus, eachtransmitting player has delivered some packets to each visited coalitionin previous transmissions.In the considered game, each player has two actions to take either totransmit a packet combination p or to listen to a transmission. Thus, the ac-tion of uk-th player at t-th game stage isACuk,t = {transmit puk , remain silent}.The asymmetry of the side information at each player generates a differentpacket combination to be sent by each player at each transmission slot. Thiscauses the asymmetry of the action space of each player. Also, in each trans-1495.5. Theoretical Analysis of the Proposed Gamemission, different players are associated with each coalition. All these makethe payoff of each coalition unique.5.5 Theoretical Analysis of the Proposed GameConvergence and StabilityThe stability of the coalition structures in coalition formation gamescorresponds to an equilibrium state known as Nash-equilibrium. Here, weprove that the resulting coalition structure from Algorithm 8 is converged,and it is a Nash-stable. The following theorem demonstrates that Algorithm8 terminates in a finite number of iterations.Theorem 5.8. Given any initial coalition structure Ψini, the coalition for-mation step of Algorithm 8 maps to a sequence of merge-and-split rules whichconverges, in a finite number of iterations, to a final coalition structure Ψfincomposed of a number of disjoint coalitions.Proof. To proof this theorem, we need to show that for any merge or splitrule, there exists a new coalition structure which results from the coalitionformation step of Algorithm 8. Starting from any initial coalition structureΨini, the coalition formation step of Algorithm 8 can be mapped to a se-quence of merge/split rules. As per definition 8 and definition 9, every mergeor split rule transforms the current coalition structure into another coalitionstructure, hence we obtain the following sequence of coalition structuresΨini â Ψ1 â Ψ2 â · · · Ψfin (5.9)where Ψi+1.Ψi, andâ indicates the occurrence of a merge-and-split rule.Since the Pareto Order introduced in definition 6 is irreflexive, transitive,and monotonic, a coalition structure cannot be revisited. Given the factthat the number of merge and split rules of a finite set is finite and themerge/split operations-coalition structure mapping, the number of coalitionstructure sequences in (5.9) is finite. Therefore, the sequence in (5.9) alwaysterminates and converge to a final coalition structure Ψfin.1505.5. Theoretical Analysis of the Proposed GameDefinition 5.9. A coalition structure Ψ = {S1, · · · ,Sm} is Nash-stable ifplayers have no incentive to leave Ψ through merge-and-split operations.This definition implies that any coalition structure Ψ is considered as aNash-stable coalition structure if and only if no player has an incentive tomove from its current coalition and join another alliance or make an indi-vidual decision by performing any merge/split rules. Further, the alliancesin the final coalition structure, Ψfin have no incentive to do more merge andsplit operations. A Nash-stable coalition structure is also an individuallystable coalition structure. In general, in a coalition formation game, Nash-stability is a subset of individual stability [158]. Specifically, no player leavesits current coalition through a split rule and form an empty coalition, i.e.,no singleton coalition is created if the following property holds.Property: There exists at least one coalition structure Ψ that satisfies bothNash-stability and individual stability if and only if âSs â Ψ such that|Ss| > 1.Proof. This property states that forming a singleton coalition cannot hap-pen. Indeed, since each player cannot send an encoded packet to itself, itbelieves that a better payoff can be obtained by being a member of anycoalition. Further, since the payoff of a non-targeted player in any coali-tion and a single player-coalition is the same, our proposed algorithm, asmentioned in the previous section, avoids making any merge-and-split rulesfor equal payoff values. Thus, according to Algorithm 8, a Nash-stable andindividual stable coalition structure can be obtained.As a consequence of Property 2, the final coalition structure Ψfin thatresults from Algorithm 8 is Dhp stable as the coalitions have no incentive todo further merge-and-split operations. Dhp stable is also known as merge-and-split proof [158]. Furthermore, Ψfin can be considered as Dc stable.This is because players have no incentive to leave Ψfin and form any othercoalitions [136].1515.5. Theoretical Analysis of the Proposed GameCoalition Formation ExampleIn order to better illustrate the proposed coalition formation algorithm andthe aforementioned stability concepts, consider the example presented inFigure 5.2. For ease of analysis, we assume error-free transmissions. Giventhe coverage zone of the players and their side information as in Figure 5.2,the resulting coalition structure Ψfin from Algorithm 8 for the network pre-sented in Figure 5.2 consists of two disjoint coalitions S1,S2 where only oneplayer transmits in each coalition. In particular, in coalition S1, player u4transmits packet p1 to player u6, and in coalition S2, player u1 transmitsthe combination p3 â p4 to players u2, u3, u5. The transmitting player ineach coalition is shown in a red circle; their targeted players and the packetcombinations are shown in Figure 5.3. Given the resulting coalition struc-ture Ψfin = {S1,S2} that shown in Figure 5.3, we now analyze its Nashstability. The coalition structure Ψfin is Nash-stable as no player has anincentive to leave its current coalition. For example, player u5 has a pay-off of Ïu5(S2) = â2 when being part of the coalition S2 = {u1, u2, u3, u5}.The payoff Ïu5(S2) is calculated as follows. Since player u5 receives aninstantly-decodable combination from player u1, it does not experience anydecoding delay increases. Thus, by (5.2), its anticipated completion time isTu5(nt) =|Wu5,0|+Du5 (nt)âE[Ïu5 ]1âE[Ïu5 ] = 2, and, by (5.5) its payoff is â2. If playeru5 switches to act non-cooperatively and joins S1, player u6 would be thenew transmitting player in S1. In this case, player u5 will be in the coveragezone of both transmitting players u1 in S2 and u6 in S1. Consequently, thepayoff of player u5 decreases to Ïu5(S1) = â3, and the payoff of player u6decreases from Ïu6(S1) = â3 to Ïu6(S1) = â4. Thus, player u5 does notdeviate form its current coalition S2 and join S1. Similarly, if players u2and u3 act non-cooperatively by leaving S2 and forming a singleton coali-tion for each, i.e., S3 and S4, their payoffs decrease from Ïu2({2}) = â2 andÏu3({3}) = â1 to Ïu2(S3) = â3 and Ïu3(S4) = â2, respectively. Clearly,Ψfin is an individual Nash-stable as it does not have any singleton coalition.Further, it is both Dhp and Dc stable as no further merge-and-split oper-ations can be performed by the coalitions and no player has incentive todeviate from Ψfin, respectively.1525.5. Theoretical Analysis of the Proposed Game-0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2 0.25Position in x (m)-0.25-0.2-0.15-0.1-0.0500.050.10.150.20.25Position in y (m)Position in y (m)Figure 5.3: A resulting coalition structure Ψfin = {S1,S2} from Algorithm8 for a partially connected D2D network that is presented in Figure 5.2.Computational Complexity and Communication OverheadHere, we analyze the complexity and communication burden of Algorithm8.Complexity: Each UD at any transmission slot generates its packet combi-nation, which depends on the packets that it previously received. Further,since a game with incomplete information, i.e., each UD knows only thereceived and requested packets of UDs in its coverage zone, every UD gen-erates its packet combinations of all other UDs in its coverage zone. Thisallows every UD to calculate the payoff function (5.5) of all other UDs in itscoverage zone. The complexity of generating the packet combination by theCBS using a maximum weight search method is given as follows. First, theCBS generates all the vertices that represent all users and their requestedpackets, which needs O(UM) operations. Note that a vertex is generatedfor each file pl is requested by each UD uk, âpl â P,âuk â N . The CBS,then, connects these vertices (circles) by edges that represent network codingconditions of O(N2M). Afterward, the CBS executes the maximum weightsearch method that computes the weight of O(UM) vertices and selects amaximum of N UDs. Hence, the overall complexity of finding the IDNC1535.5. Theoretical Analysis of the Proposed Gamepacket is O(UM) +O(U2M) +O(U2M) = O(U2M) operations [44]. In ourcase, the complexity for generating the packet combination at each UD isbounded by O(U2M). This is because the number of UDs in the coveragezone of each UD is less than the total number of UDs in the network.Communication Overhead: The communication overhead of Algorithm8 is related to perform the membersâ discovery step, transmitting player se-lection, and the analysis of merge-and-split rules. It is explained as follows.Step 1: Similar to many algorithms in the literature, e.g., [157], the mem-ber discovery step needs |U | 2-byte messages, in which each message is beingsent by every UD to all its neighbors which is denoted by U. Thus, the totalcommunication overhead for discovering the neighbor UDs is |2UU| bytes.Step 2: Selecting the transmitting player in each coalition can be per-formed in many different strategies, e.g., based on playersâ attributes [159],[160]. In Algorithm 8, coalitionâs members initially exchange an advertise-ment message among them, and the one that satisfies the conditions inSection 5.4.2 would be chosen as a transmitting player in that coalition.The same process is applied for selecting/updating the transmitting playerin step III. Since it is connected to most players in the coalition, the trans-mitting player is responsible for ensuring that the rest of the coalitionâsmembers received an acknowledgment (ACK). As such, they update theirHas and Wants sets after each D2D transmission.Step 3: The communication overhead due to forming coalitions is basedon the number of merge-and-split operations. This is mainly related to thetotal number of decisions made by each of the U players. As previouslymentioned in Section 5.4.2, the merge-and-split operations enumerate onlythe neighboring coalitions Ss. Thus, two extreme cases can occur:â If all coalitionsâ alliances decide to leave their current coalitions andjoin other coalitions. In this case, uk-th player in Ss-th coalition wouldmake |Ss| decisions (uk-th player has an |Ss| possibilities to join any ofthe neighbor coalitions). Consequently, the total number of playersâdecisions is Qworst = U |Ss|.â If players did not make any decisions. Since players make no decision,1545.6. Numerical Resultsthe overhead, in this case, is only Qbest = U (due to the initial player-coalition associations as in step 1).In practical, the number of playersâ decisions is between the above two cases,i.e., Qbest â¤ Q â¤ Qworst. Hence, if L average decisions are made by players,then Q = NL decisions that perform split-and-merge rules in Algorithm8. Therefore, combining all the overhead signaling components, the totaloverhead in each transmission is U(2U + L). Such signaling cost will addonly a few bytes, which are negligible in size compared to the entire packetâssize. Furthermore, to update the Has and Wants sets of UDs, only theindices of packets need to be exchanged between the UDs, not their contents.Hence, we ignore the overhead signaling factor because it is first constant(independent on the completion time and decoding delay) and that its sizeis negligible.5.6 Numerical ResultsThis section evaluates the performance of our proposed coalition forma-tion game (denoted by CFG partially-connected D2D) to demonstrate itscapability of reducing the completion time compared to the baseline schemes.We first give the simulation setup and the implemented schemes. Then, thecompletion time and game performances are comprehensively evaluated. Weconsider a partially connected D2D network where every UD is connected tosome other UDs within its coverage zone based on the connectivity index C.The considered model is shown in Figure 5.1 in the system model section.The connectivity index C is defined as the ratio of the average number ofneighboring UDs to the total number of UDs U . Further, the UDs in theconsidered model are uniformly re-positioned after each transmission in a500mÃ500m cell. The system setting in this work follows the setup stud-ied in [64], [67]. As mentioned in the system model, each UD has alreadyacquired some packets and wants some other packets from the set P. Suchinitial Has and Wants sets Huk and Wuk , âuk â N of UDs is independentlydrawn based on their average erasure probability. The short-range D2D1555.6. Numerical Resultslinks are more reliable than the CBS-UD communications [62], [63]. Hence,unless specified, we assume that the player-to-player erasure probability Ïis half the CBS-to-UD erasure  in all simulations, i.e., Ï = 0.5. Our sim-ulations were implemented using Matlab on a Windows 10 laptop 2.5 GHzIntel Core i7 processor and 8 GB 1600 MHz DDR3 RAM. For the sake ofcomparison, we implement the following schemes.â The fully-connected D2D scheme: In this scheme, a single UDwho has the largest number of received packets transmits an IDNCpacket at each transmission slot.â PMP: The CBS in this scheme is responsible for the transmissions.It provides all the requested packets to all the UDs. This scheme wasproposed in [115].â The one coalition formation game: This scheme is denoted byOCF partially-connected D2D. Only one coalition is formed in thisscheme, and accordingly, a single UD transmits an IDNC packet ateach transmission. The transmitting UD is selected based on its num-ber of received packets as well as on the maximum number of UDs inits coverage zone.â The FRAN partially-connected D2D scheme: In this scheme, afog central unit is responsible for determining the set of transmittingUDs and their corresponding packet combinations. This scheme wasproposed in [67].5.6.1 Completion Time Performance AnalysisThe completion time measures the total number of transmissions thatthe network needs until all UDs receive all their requested packets. Thus,all simulated schemes are executed until all UDs receive all their requestedpackets. The presented average values of the completion time are computedover a certain number of iterations. To study the completion time perfor-mance of the proposed solution by changing the number of players, packets,connectivity index, and the packetâs erasure probability.1565.6. Numerical Results20 30 40 50 60 70 80 90 100Number of Players N10152025303540455055Average Completion TimeFully-connected D2DOCF partially-connected D2DPoint to Multi-PointFRAN partially-connected D2DCFG partially-connected D2DAverage Completion TimeFigure 5.4: Average completion time versus the number of players U .In Figure 5.4, we depict the average completion time versus the num-ber of players U for a network composed of M = 30 packets,  = 0.25,Ï = 0.12, and connectivity index C = 0.4. It is observed from Figure 5.4that the proposed CFG partially-connected D2D algorithm outperforms thePMP, fully-connected D2D, and OCF partially-connected D2D schemes forall simulated numbers of players. This is because of the simultaneous IDNCpacket transmissions from cooperating players at the same time. In par-ticular, the fully-connected D2D system only considers the size of the Hasset as a metric to select a single UD for transmission at each time slot, i.e.,unâ = maxunâUHun . The OCF partially-connected D2D scheme focuses on themaximum number of connected UDs to be formed as well as on the size of theHas set of the transmitting UD. On the other hand, although the transmit-ter in the PMP scheme can encode all the IDNC combinations and schedulea certain number of UDs, the PMP scheme sacrifices the utility of the simul-taneous transmissions by considering only one transmission. Our proposedalgorithm strikes a balance between these aspects by jointly considering thenumber of scheduled UDs and the Has set size of each transmitting UD.Despite the gain achieved by the FRAN partially-connected D2D solution1575.6. Numerical Results10 15 20 25 30 35 40 45 50Number of Packets M010203040506070Average Completion TimeFully-connected D2DOCF partially-connected D2DPoint to Multi-PointFRAN partially-connected D2DCFG partially-connected D2DAverage Completion TimeFigure 5.5: Average completion time versus the number of packets M .with the presence of a fog that executes the whole process, our decentral-ized solution reaches the same performance. Clearly, due to the philosophyof D2D simultaneous transmissions that considers in the centralized FRANand our proposed schemes, their performances are roughly the same.We observe from Figure 5.4 that, for a small number of players, thePMP system is close to both the CFG partially-connected D2D and FRANpartially-connected D2D schemes. This is because, for a small amount ofplayers (U â¤ 60), the certainty that the whole frame M is distributed be-tween players in the initial transmissions is low, thus decreasing the prob-ability of delivering potential IDNC packets to UDs. This makes the over-all completion time performance of the partial D2D scenarios close to thePMP scheme. As the number of players increases (U â¥ 80), the bigger thecertainty that the union of their Has sets is equal to M . This results indelivering more potential D2D IDNC packets, thus increasing the gap be-tween the PMP performance and both the FRAN partially-connected D2Dand proposed schemes.In Figure 5.5, we illustrate the average completion time as a function ofthe number of packets M for a network composed of U = 30 UDs,  = 0.25,1585.6. Numerical ResultsÏ = 0.12, and connectivity index C = 0.4. The figure shows that the pro-posed scheme outperforms the fully connected, one coalition game, and PMPschemes. For a few packets, the IDNC combinations are limited, which af-fects the ability of the proposed scheme to generate coded packets thatsatisfy several scheduled UDs. With increasing the number of packets, thenumber of transmissions needed for the completion of the aforementionedschemes is remarkably increasing. Therefore, as the number of packets in-creases, the proposed scheme outperforms largely the fully connected andone coalition game schemes. We see from Figure 5.5 that the completiontime of all schemes linearly increases with the number of packets. This isexpected as the number of packets increases, a high number of transmis-sions is required towards the complete delivery of packets. This results inincreasing the average completion time.In Figure 5.6, we plot the average completion time as a function ofthe average player-player erasure probability Ï for a network composed ofU = 60, M = 30,  = 2Ï, and C = 0.4. Similar to what we have discussedin Figure 5.4 and Figure 5.5, the average completion time of the partialD2D schemes is noticeable compared to the fully-connected D2D and OCFpartially-connected D2D schemes, as shown in Figure 5.6. We clearly seethat the completion time of the partial D2D schemes is better than the PMPone because of their multiple UDsâ transmissions at each time slot. More-over, as the player-to-player erasure probability increases, the BS-playererasure probability increases two-fold ( = 2Ï), thus slightly affecting theperformance of the PMP scheme. The partial D2D settings, however, ben-efit from short D2D links, which provide much better UDs reachability andIDNC packet successful delivery compared to the PMP setting.In Figure 5.7, we investigate the average completion time as a functionof the connectivity index C for a network composed of U = 60, M = 30, = 0.25, and Ï = 0.12. It can clearly be seen that for a low connectivityindex (C â¤ 0.4), the proposed CFG partially-connected D2D approach no-ticeably outperforms the fully-connected D2D and OCF partially-connectedD2D approaches. In such poorly connected networks (C â¤ 0.4), multi-ple simultaneous playersâ transmissions are exploited in partially D2D algo-1595.6. Numerical Results0.05 0.1 0.15 0.2 0.25Average Player-to-Player Erasure Probability 020406080100120Average Completion TimeFully-connected D2DOCF partially-connected D2DPoint to Multi-PointFRAN partially-connected D2DCFG partially-connected D2DAverage Completion TimeFigure 5.6: Average completion time versus the average player-player erasureprobability Ï.rithms. However, as the connectivity index increases (C â¥ 0.6), the numberof formed disjoint coalitions in our proposed solution is drastically reduced,thus reducing the number of transmitting UDs. This results in a perfor-mance agreement with the fully-connected D2D scheme. Being independentof the coverage zones of the transmitting UDs and the delay created by thoseUDs, the PMP scheme is not affected by the changes to C. Thus, the PMPscheme has a constant average completion time.To conclude this section, we study the influence of the setting Ï = 0.5 onthe completion time performance of our proposed scheme. In Table 5.1, wesummarize the completion time performance for different values of Ï. Theconsidered network setup has 30 UDs, 20 packets,  = 0.5, and C = 0.1.From Table 5.1, we note that the completion time of our proposed solutionstill outperforms the PMP scheme for Ï = 0.7 and approximately reachesthe same performance as for the PMP scheme for Ï = 0.9. This is due to thesimultaneous transmissions and cooperative decisions by the transmittingUDs, which show the potential of the proposed CFG solution in minimizingthe completion time of UDs.1605.6. Numerical Results0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1Connectivity Index C050100150200250Average Completion TimeFully-connected D2DOCF partially-connected D2DPoint to Multi-PointFRAN partially-connected D2DCFG partially-connected D2DAverage Completion TimeFigure 5.7: Average completion time versus the connectivity index C.20 40 60 80 100 120 140 160Number of Players N0510152025Average Number of CoalitionsCFG Partially-Connected D2D-C=0.1CFG Partially-Connected D2D-C=0.3CFG Partially-Connected D2D-C=0.6Average Number of CoalitionsFigure 5.8: Average number of coalitions versus the number of players U .5.6.2 Proposed CFG Performance AnalysisTo quantify the analysis of the proposed formation coalition solution, weplot in Figure 5.8 the average number of coalitions as a function of the num-ber of players U for a network composed of M = 30, a different connectivityindex (C = 0.6, C = 0.3, and C = 0.1), and Ï = 0.12. Figure 5.8 showsthat the average coalition size increases with the increase in the number of1615.6. Numerical Resultsplayers. This is because, as N increases, the number of cooperating playersincreases, thus increasing the average size of the formed coalitions. We canconclude from Figure 5.8 that the resulting coalition structure Ψfin from Al-gorithm 8 is composed of a small number of relatively large coalitions whenC = 0.6. When C = 0.1, this number of formed coalitions increases, andthe resulting coalition structure Ψfin is composed of a large number of smallcoalitionsâ sizes.In Table 5.2, we evaluate the complexity of the proposed coalition gamesolution as a function of the algorithmic running time. In particular, Ta-ble 5.2 lists the consumed time of MATLAB to execute all schemes in dif-ferent network setups since starting the algorithms until all players receivetheir wanted packets. The considered small network setup has 30 players, 20packets,  = 0.5, Ï = 0.25, and C = 0.1. The considered large network setuphas 100 players, 70 packets,  = 0.5, Ï = 0.25, and C = 0.1. It can clearly beseen from the table that the proposed CFG-partially D2D scheme needs lowconsumed time than all other solutions for both network setups. Althoughthe completion time achieved by the CFG partially-connected D2D schemeis roughly the same as the centralized FRAN partially-connected D2D, thecomputing time required by our developed scheme is slightly higher thanthat required by the FRAN partially-connected D2D. This is because ourproposed scheme needs time to converge before generating the output. Thecentralized FRAN scheme has low execution time due to the presence of thefog entity.Finally, to evaluate the convergence rate analysis of the proposed scheme,the average number of merge-and-split rules before Algorithm 8 converges tothe final coalition structure is listed in Table 5.3. To achieve the stable coali-tion with our proposed CFG scheme, network setup 1 requires, on average16 iterations, and network setup 2 needs, on average 22 iterations. Theseresults show that our proposed distributed algorithm is robust to differentnetwork setups. In summary, these results show that our proposed algo-rithm allows UDs to quickly form converged and stable coalition structures,which confirms the theoretical findings in Section 5.4.1625.6. Numerical ResultsTable5.1:TheinfluenceofchangingÏonthecompletiontimeperformanceoftheproposedschemeSolutionÏ=0.6Ï=0.7Ï=0.9Ï=PointtoMulti-Point30.290030.280030.310030.4800CFGpartially-connectedD2D20.180023.470230.450033.9300Table5.2:AverageRunningTimesofthedifferentschemesSolutionTime(s)-SmallnetworkTime(s)-Largenet-workFRANpartially-connectedD2D0.56189315.98450PointtoMulti-Point1.9945001103.020716Fully-connectedD2D0.756420128.772580OCFpartially-connectedD2D0.78357528.726515CFGpartially-connectedD2D0.73673721.725739Table5.3:AverageNumberofCoalitionsandSplit/mergerulesoftheproposedschemeinthefirstiterationNetworkSetupNumberofCoalitionsSplit-and-mergerulesSetup1:N=100andC=0.116.348.12Setup2:N=160andC=0.123.6712.761635.7. Chapter Summery5.7 Chapter SummeryIn this chapter, we have developed a distributed game-theoretical frame-work for a partially connected D2D network using coalition game and IDNCoptimization. As such, the distribution of contents among UDs is mini-mized. A comprehensive completion time and game performance evaluationhave been carried out for the proposed distributed solution. In particu-lar, our performance evaluation results comprehensively demonstrated thatthe proposed distributed solution offers almost the same completion timeperformance similar to the centralized F-RAN D2D network.164Chapter 6ConclusionsIn this chapter, we provide the concluding remarks on the accomplishedworks in this thesis. We also discuss some potential future research topics.This thesis exploited the potential of NC for an effective allocation ofradio resources in cache-enabled 5G mobile networks. State-of-the-art liter-ature usually focuses on allocating a single user to each RRB, which needslarge numbers of RRBs to satisfy the tremendous increase in the numberof users. The developed NC schemes in this thesis overcome this issue bymixing usersâ contents and simultaneously allocating different users to thesame RRB. To this end, we developed NC schemes to efficiently deliver re-quested contents to users while satisfying userâ QoS in terms of throughputand completion time. The concluding remarks on these developed schemesin each chapter is provided in the next section.6.1 Concluding RemarksSome concluding remarks on the accomplished works of this thesis arepresented as follows.1. In Chapter 2, we introduced a cross-layer framework in downlink C-RAN to optimize throughput by streaming a set of popular files tousers. For any arbitrary transmission, we considered optimizing the re-ceived throughput, subject to usersâ side information, the cached/storedfiles at each RRH, NC constraints, and the channel qualities. We haveproposed two schemes, namely, joint and iterative schemes. Specifi-cally, in the joint scheme, we used a novel graph theoretical representa-tion to solve the joint coordinated scheduling and power control prob-lem, while in the iterative scheme, we solved the problem iteratively.1656.1. Concluding RemarksNumerical results showed that both proposed schemes offer improvedthroughput performances compared to the existing solutions. Numer-ical results provided the following observation. When a large numberof users is used, the RA-IDNC schemes significantly outperform theuncoded scheme. This is due to the fact that uncoded scheme alwaysserves one user per RRB regardless of the networkâs size, which limitsthe overall throughput gain. On the other hand, the number of servedusers in the RA-IDNC scheme increases with the increase in the num-ber of users in the system due to NC. Thus, the overall throughputgain of the RA-IDNC scheme is increased.2. In Chapter 3, we studied the joint design of CBS and edge processingfor F-RAN setting in which the eRRHs are equipped not only withthe functionalities of standard RRHs in C-RAN, but also with localcache. For any arbitrary fixed pre-fetching strategy, we considered theoptimization of the immediate file delivery phase with the goal of max-imizing the CBS offloading while guaranteeing userâs QoS, subject tothe eRRHs cache contents, the required minimum rate, power control,and network coding constraints. By using a graph theory technique,we proposed joint and iterative efficient approaches that use cross-layer NC and coordinated scheduling graphs, respectively. Presentednumerical results revealed that as the rate threshold increases, thethroughput improvement increases as well. This is because as the ratethreshold increases, certain number of users is targeted and the trans-mission rate of each RRB in each eRRH becomes high. As a result,number of users is left to be targeted by the CBS, which degradesits consumed time. Consequently, compared to the QoS un-aware al-gorithm, our proposed schemes have a certain degradation in CBSconsumed time.3. In Chapter 4, we developed frameworks that exploit the cached con-tents at eRRHs, their transmission rates, and previously received con-tents by different users to deliver the requesting contents to users witha minimum completion time in D2D-aided F-RAN. Simulation results1666.1. Concluding Remarksshown that our proposed schemes can effectively minimize the framedelivery time as compared to the conventional schemes. Such an im-proved performance has been achieved due to the joint and coordi-nated schemes that: (i) judiciously schedule users, adopt the trans-mission rate of each eRRH and optimize the transmission power ofeach eRRH, and (ii) select potential users for transmitting coded filesover D2D links.4. In Chapter 5, we developed a distributed game-theoretical frameworkfor a partially connected D2D network using coalition game and IDNCoptimization. As such, the delivery of contents to UDs is minimized. Inparticular, our proposed model is formulated as a coalition formationgame with non-transferable utility, and a fully distributed coalitionformation algorithm is proposed. The proposed distributed algorithmis converged to a Nash-stable coalition structure using split-and-mergerules while accounting for the altruistic playerâs preferences. With sucha distributed solution, each UD has to maintain a partial feedback ma-trix only for the UDs in its coverage zone instead of the global feedbackmatrix required in the fully connected D2D networks. Some observa-tions from the accomplished works in Chapter 5 are given as follows.First, the OCF partially-connected D2D scheme focuses on the max-imum number of connected UDs to be formed as well as on the sizeof the Has set of the transmitting UD. On the other hand, althoughthe transmitter in the PMP scheme can encode all the IDNC combina-tions and schedule a certain number of UDs, the PMP scheme sacrificesthe utility of the simultaneous transmissions by considering only onetransmission. Our proposed algorithm strikes a balance between theseaspects by jointly considering the number of scheduled UDs and theHas set size of each transmitting UD. Second, despite the gain achievedby the FRAN partially-connected D2D solution with the presence of afog that executes the whole process, our decentralized solution reachesthe same performance. This is due to the fact that both schemes followhe same philosophy of D2D simultaneous transmissions which results1676.2. Suggested Future Workin similar completion time performances. Third, although the com-pletion time achieved by the CFG partially-connected D2D scheme isroughly the same as the centralized FRAN partially-connected D2D,the computing time required by our developed scheme is slightly higherthan that required by the FRAN partially-connected D2D. This is dueto the fact that our proposed scheme needs time to converge beforegenerating the output. The centralized FRAN scheme has low execu-tion time due to the presence of the fog entity.6.2 Suggested Future WorkThis thesis investigates NC schemes for effective resource allocation incache-enabled 5G systems. Still, there are some interesting research topicsfor efficient resource allocation utilizations using NC need to be investigated.In what follows, we summarize some potential future extensions of the re-search conducted in this thesis.Low complexity power allocation for network-coded scheduling inCloud-RANsIn Chapter 2, we have developed a joint cross-layer NC method for maxi-mizing the cross-layer throughput in C-RAN setting. The proposed methodprovides significant performance gain as compared to existing schemes. How-ever, its implementation complexity highly increases with the increase inthe number of NC combinations, RRHs, and RRBs, especially for densenetworks. Notably, the proposed method requires generating multiple RRBsubgraphs whose union gives the CRAN-CLNC graph. One possible ex-tension is that we develop a low-complexity solution that involves the con-struction of a single RRB subgraph. To do that, we can take advantage ofthe realistic assumption that channels can typically be approximated by aconstant within each RRHâs frame to propose a simple solution consists of asingle RRB subgraph. Indeed, for a scheduling epoch in a short duration oftime, all RRBs in the same RRHâs frame do not change [110]. In particular,we consider slow-varying channels, meaning that if the RRB represents a1686.2. Suggested Future Workfrequency block, the channel is non-frequency selective. While if the RRBrepresents a time slot, the duration of the transmission frame is within thechannel coherence time. This will make the channel gain of users are con-stant in a short period of RRHâs frame. To further reduce the complexity ofthe future proposed approach, one can consider generating only potential setof NC combinations that aims to serve users with the maximum throughput.Cross-layer network codes for file delivery in cache-enabled D2DnetworksIn the recent literature, most works on file delivery problem with IDNCfocused on modeling the status of physical channels by file erasure probabil-ities and integrated such probability into aiding the coding decisions, e.g.,works listed in the survey paper [68]. Further, they considered minimumtransmission of all scheduled UDs. This results in prolonged transmissionduration and thus, consumes the time resources of network. On the con-trary, a more practically relevant scheme is to involve the dynamic natureof wireless channels in the coding decisions. This allows the transmittingUDs to intelligently select their transmission rates and IDNC files. In thisdirection, the authors of [70] proposed to incorporate the transmission ratesin the NC decisions in D2D network. As such, all files are delivered toall users with a minimum completion time. The main drawback is thatonly one UD is allowed to deliver files in each transmission slot. Thus theyignored the interference caused by different transmitting UDs to the sched-uled UDs. Actually, in D2D networks, UDs are spatially separated in aregion. This creates an opportunity to intelligently select multiple trans-mitting UDs that schedule a large number of other UDs. Therefore, asan interesting future work, one can study a realistic scenario that considermultiple transmitting UDs selection and optimization of the employed trans-mission rates using power control on each transmitting UD. To this end, weaim to develop a novel optimization framework taking network coding andrate/power optimization into account. This framework will be referred toD2D cross-layer network coding (D2D-CLNC). In the proposed D2D-CLNCframework, network-coded transmissions from potential UDs are developed1696.2. Suggested Future Workto deliver all files to all requesting UDs in the least amount of time. Themain consideration of this interesting future work can be summarized asfollows.â We show that the completion time minimization problem over powercontrol, transmitting UDs and their file combination selections is com-putationally intractable due to the interdependent among variablessuch as the UDsâ acquired and requested files, channel qualities andtransmitting UDs.â We derive a lower bound on the completion time for each UD. Usingthese lower bounds, we iteratively propose a heuristic algorithm thatselects a set of transmitting UDs only if the interference caused by thetransmissions of the newly selected UDs does not significantly degradethe transmission rates and completion time performance. In otherwords, the main idea of the heuristic algorithm is iteratively includingmore transmitting UDs and allocating transmission powers subject tothe reduction in the completion time.Rate-aware network codes for distributed content sharing incache-enabled D2D networkIn Chapter 5, we have developed a distributed and decentralized gametheoretical framework for a partially connected D2D network such that weminimize the distribution of contents among UDs. The developed frameworkfocused only on the upper layer view of the network, where network coding isperformed at the network layer, and a memory-less erasure channel abstractsthe physical-layer. The main drawback of the proposed framework is that itdid not consider the interference of transmissions caused by other UDs to theset of transmitting UDs. Consequently, UDs at the intersection region of anytransmitting UDs will experience collisions and no packets will be decoded.Further, we only consider D2D communications to deliver all files to all UDs.Even with proactive caching of popular files in the file-holder (FH) UDs, theimmediate file delivery to file-requester (FR) UDs may necessitate the helpof the edge-servers (ESs) in serving the FR UDs that have not been servedby the FH UDs.1706.2. Suggested Future WorkMotivated by the aforementioned limitation, developing a rate-awareNC framework that involves immediate transmissions from both ESs andFH UDs. To this end, our goal is to develop a novel distributed file shar-ing mechanism, by leveraging rate-aware network codes and coalition gametheory, to efficiently deliver the requested files within the lowest possible net-work delay to all the file-requesters (FRs) in a distributed caching network.Therefore, a smart scheduling of file delivery from the FH users and (pos-sibly) the ESs is required to: i) offload the ESs (i.e., minimize the amountof ESsâ resources consumed for helping the FH users), and ii) guaranteethe required QoS of the UEs. The main consideration of this work can besummarized as follows.â We first model the file combination that should be transmitted fromboth the ES and FH users to their corresponding served FR users.Then, the duration of transmission over an edge channel, D2D chan-nel, and the file fetching delay are defined. Given these delays, we for-mulate completion time minimization problem in cache-enabled D2Dnetwork.â We develop a coalition formation/coalition switch (CF/CS) algorithmthat allows the UDs to switch to any coalition for increasing theirutility. The switch-operations among coalitions may take long-time toconverge. As a result, we aim to develop a low-complexity algorithm.171Bibliography[1] Cisco visual networking index: global mobile data traffic forecast update,2017-2022, White Paper, Feb., 2019. â pages 1, 23[2] A. Nordrum, âThe internet of fewer things [news],â IEEE Spectrum, pp.12-13, Oct. 2016. â pages 1[3] J. G. Andrews et al., âWhat Will 5G Be?,â in IEEE Jou. on S. Areas inCommu., vol. 32, no. 6, pp. 1065-1082, Jun. 2014. â pages 1, 4, 23[4] M. Peng, Y. Sun, X. Li, Z. Mao, and C. Wang, âRecent advances incloud radio access networks: System architectures, key techniques, andopen issues,â IEEE Commun. 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Younis, âA survey on clustering algorithms forwireless sensor networks,â Computer Commun., vol. 30, pp. 2826-2841,2007. â pages 154191Appendix AProof of Theorem 2.1To prove Theorem 2.1, we first need to show that for any feasible scheduleS, there exists a unique clique C in CRAN-CLNC graph which resultingfrom Algorithm 1 and a solution to problem (2.5). Then, for each resultingclique C in CRAN-CLNC graph based on Algorithm 1, there exist a uniquefeasible schedule S. In other words, we prove that there is a one-to-onemapping between the set of cliques of a maximum size of Z that Algorithm1 can generate and the set of the feasible schedules. Finally, the proof canbe concluded by showing that the contributed weight of the clique C is theobjective function (2.5) to be maximized.Let S = {{Sz1 , · · · , SzZ} = {{s1, s2, · · · , s|Ïb1z1 |}, · · · , {sB, · · · , s|ÏbBzZ |}}be a feasible schedule (i.e., S â Sfs).5 Since each RRB zm â Z across allRRHs contributes with only one feasible schedule, |S| = Z. Proving that Scan be represented by a maximal clique in the CRAN-CLNC graph equiva-lents to show that S can be decomposed into Z schedules each representinga vertex in a local power subgraph. Afterwards, we show that the verticessatisfy GC condition that explained in Section 2.3.Define Szm as a specific schedule that represents the set of associationsfor which RRBs is indexed by zm. This schedule can be mathematicallyexpressed as Szm = {s â S|zm(s) = zm}. It is important to note that allassociations in S represent coded combinations in the first place (refer toSection 2.2.2 for more details). By the assumption that Szm â S is a feasibleschedule, thus it satisfies LC2. Therefore, Szm satisfy LC1 and LC2 andrepresents a vertex in the local power subgraph Gzm . Now, we show that thevertices across all subgraphs are connected by GC. The general condition5This proof considers only the coded case as the uncoded case can follow the samesteps that used in [109].192Appendix A. Proof of Theorem 2.1GC of the CRAN-CLNC graph insists that each user cannot be targetedby distinct RRHs, which represents the system network CC1. Hence, allvertices in the CRAN-CLNC graph are connected as long as the associatedusers are distinct. Since each RRBâs subgraph contributes by one uniquevertex, the union of all these connected vertices given GC is a unique clique.Therefore, C = {vz1 , vz2 , · · · , vzZ} is a maximal clique of size Z in theCRAN-CLNC graph. The feasible schedule S is decomposed into a set ofSzm , zm â Z in which each Szm consists of unique associations. Clearly, theclique C representing the schedule S is unique. In the following, we provethe converse.Define C as the set of all possible maximal cliques of degree Z in theCRAN-CLNC graph. Let C = {vz1 , vz2 , · · · , vzZ} â C be a maximal clique.From Section 3.2, it can be noted that each vzm â Gzm represents at leastB associations (i.e., uncoded scenario) or at most U associations. By theconfiguration of the vertices vzm â Gzm , we have vzm â Szm,fs. Thus, verticesin any subgraph satisfy LC1 and LC2 conditions. Since each subgraph isconfigured for each RRB, then by extension C satisfies GC condition. Next,we analyze the vertices included in the clique C. In particular, we aimto show that there exists a one-to-one mapping between vertices and thesubgraphs Gzm , zm â Z. In other terms, each subgraph contributes by onlyone unique vertex to C, and two different vertices belong to two differentsubgraphs. These unique configurations of the vertices in the subgraph Gzmleads to the uniqueness of the schedules. From the above analysis and thegeneral connectivity condition GC for any two different subgraphs, clearly,C satisfy CC1. Consequently, the resulting policy of Algorithm 1, i.e., Crepresents a feasible schedule. Thus, a one-to-one mapping between themexists.To finalize the proof, we now prove that the weight of the maximal cliqueis the objective function in (2.5) to be maximized. Let C = {vz1 , · · · , vzZ} ={{s1, s2, · · · , s|Ïb1z1 |}, · · · , {sB, · · · , s|ÏbBzZ |}} = S, vzm â Gzm . Let a vertexvzm â Vzm is associated with Szm = {s1, · · · , s|Szm |} â Szm,fs, where Szmrepresents the total targeted users ofâbnâB|Ïbnzm(Îºbnzm)|. The weight of the193Appendix A. Proof of Theorem 2.1maximal clique can be written asw(C) =âvzmâCw(vzm) =âzmâZâSzmâSzm,fsw(Szm) =âzmâZâSzmâSzm,fsâsâSzmminui(s)âÏbn(s)zm(s)log2(1 + SINRui(s)bn(s)zm(s)(P))(A.1)Therefore, the problem of maximizing the throughput (2.5) in C-RANsetting is equivalent to the maximum weight clique problem among the max-imal cliques in the CRAN-CLNC graph.194Table B.1: All possible IDNC combinations SIDNCi si = (κi, Ïi)1 ((f1 â f2), (u1, u2))2 ((f1), (u1))3 ((f1 â f3), (u1, u3))4 ((f2), (u2))5 ((f2 â f3), (u2, u3))6 ((f3), (u3))7 ((f1 â f2 â f3), (u1, u2, u3))Appendix BIllustration of Algorithm 1We illustrate here how to use Algorithm 1 to design the CRAN-CLNCgraph shown in Figure 2.3 of the C-RAN model presented in Example 1. InExample 1, a simple C-RAN composed of 2 RRHs, 1 RRB, 3 users, and 3files. A step-by-step illustration is given as follows.First step: We generate the set of all possible associations between usersand their requested files, i.e., S = {(u1, f1), (u2, f2), (u3, f3)}. Then, basedon the instant decodability conditions C1 and C2 that explained in Sec-tion 2.3, we generate all IDNC file combinations SIDNC as summarized inTable B.1.Second step: We generate feasible schedules Si â Sz1,fs, âi = 1, · · · , |Sz1,fs|,such that each schedule S consists of many associations s, in which theysatisfy CC1. Thus, Si is represented by a vertex vi in the power controlsubgraph as described in Section 2.3. Table B.2 summarizes all these feasibleschedules Sz1,fs.Third step: We solve the power problem for each vertex vi as explainedin Section 2.3. Then, we use the optimal power distribution P to calculatethe weight of that vertex vi as in (2.10). This weight reflects the total contri-195Appendix B. Illustration of Algorithm 1Table B.2: All feasible schedules Sz1,fsi Si = {s1, · · · , s|Si|} i Si = {s1, · · · , s|Si|}1 {b1z1s1Rb1z1 , b2z1s6Rb2z1} 9 {b2z1s1Rb2z1 , b1z1s6Rb1z1}2 {b1z1s5Rb1z1 , b2z1s2Rb2z1} 10 {b2z1s7Rb2z1}3 {b1z1s7Rb1z1} 11 {b1z1s2Rb1z1 , b2z1s4Rb2z1}4 {b2z1s2Rb2z1 , b1z1s6Rb1z1} 12 {b1z1s6Rb1z1 , b2z1s4Rb2z1}5 {b1z1s6Rb1z1 , b2z1s1Rb2z1} 13 {b1z1s4Rb1z1 , b2z1s2Rb2z1}6 {b1z1s4Rb1z1 , b2z1s3Rb2z1} 14 {b2z1s6Rb2z1 , b1z1s2Rb1z1}7 {b1z1s3Rb1z1 , b2z1s4Rb2z1} 15 {b2z1s6Rb2z1 , b1z1s4Rb1z1}8 {b2z1s5Rb2z1 , b1z1s6Rb1z1} 16 {b1z1s6Rb1z1 , b2z1s2Rb2z1}bution of the vertex to the network. These vertices and their correspondingweights are illustrated in Table B.3. A vertex vi in Table B.3 contains aset of associations each one labeled by the subscripts of RRH bn, RRB zm,user ui, file fk, achievable capacity Râbn,zm, and PL P âbnzm . For example, theassociation 1111Râ11P â11 represents the subscripts of b1-th RRH, z1-th RRB,u1-th user and its f1-th requested file, adopted transmission rate Râb1z1, andpower level P âb1z1 . The first vertex has two associated users to RRB z1 inRRH b1 and one associated user to RRB z1 in RRH b2. Thus, the cor-responding weight is 2 â Râ11 + Râ21 bits/s. The CRAN-CLNC graph thatcontains all configured vertices is shown in Figure B.1. Since the C-RANmodel that presented in Example 1 contains only one RRB, the constructedCRAN-CLNC graph in Figure B.1 contains only one power control subgraphand does not contain any edge connection.Fourth step: We execute the maximum-weight clique algorithm in theCRAN-CLNC graph to find the best clique that provides an efficient solu-tion. It is important to note that the proposed solution does guarantee theuncoded [109] solution. For example, if the best schedule that maximizesthe received throughput assigns a single user to each RRB/RRH, then theproposed algorithm would provide such schedules, i.e., red color circles inFigure B.1.196Appendix B. Illustration of Algorithm 1CRAN-CLNC Graph2133Râ21Pâ212122Râ21Pâ211111Râ11Pâ111111Râ11Pâ111122Râ11Pâ111133râ11Pâ111133Râ11Pâ111122Râ11Pâ112111Râ21Pâ212111Râ21Pâ212122Râ21Pâ212133Râ21Pâ212111Râ21Pâ211133R11P111122Râ11Pâ111111Râ11Pâ111122Râ11Pâ112133Râ21Pâ212111Râ21Pâ212122Râ21Pâ211133Râ11Pâ111111Râ11Pâ111133Râ11Pâ112122Râ21Pâ211111Râ11Pâ112122Râ21Pâ211133Râ11Pâ112122Râ21Pâ211122Râ11Pâ112111Râ21Pâ211122Râ11Pâ112133Râ21Pâ211133Râ11Pâ112111Râ21Pâ211111Râ11Pâ112133Râ21Pâ211122Râ11Pâ112111Râ21Pâ212133Râ21Pâ211133Râ11Pâ112122Râ21Pâ212111Râ21Pâ21Figure B.1: CRAN-CLNC graph of Example 1 that presented in Figure 2.3based on Algorithm 1.Table B.3: The generated vertices and their corresponding weightsi vi wi1 {1111Râ11P â11, 1122Râ11P â11, 2133Râ21P â21} 2 âRâ11 +Râ212 {1122Râ11P â11, 1133Râ11P â11, 2111Râ21P â21} 2 âRâ11 +Râ213 {1111Râ11P â11, 1122Râ11P â11, 1133Râ11P â11} 3 âRâ114 {2111Râ21P â21, 1122Râ11P â11, 1133Râ11P â11} Râ21 + 2 âRâ115 {1133Râ11P â11, 2122Râ21P â21, 2111Râ21P â21} Râ11 + 2 âRâ216 {1122Râ11P â11, 2111Râ21P â21, 2133Râ21P â21} Râ11 + 2 âRâ217 {1111Râ11P â11, 1133Râ11P â11, 2122Râ21P â21} 2 âRâ11 +Râ218 {2122Râ21P â21, 2133Râ21P â21, 1111Râ11P â11} 2 âRâ21 +Râ119 {2111Râ21P â21, 2122Râ21P â21, 1133Râ11P â11} 2 âRâ21 +Râ1110 {2111Râ21P â21, 2122Râ21P â21, 2133Râ21P â21} 3 âRâ2111 {1111Râ11P â11, 2122Râ21P â21} Râ11 +Râ2112 {1133Râ11P â11, 2122Râ21P â21} Râ11 +Râ2113 {1122Râ11P â11, 2111Râ21P â21} Râ11 +Râ2114 {1111Râ11P â11, 2133Râ21P â21} Râ11 +Râ2115 {1122Râ11P â11, 2133Râ21P â21} Râ11 +Râ2116 {1133Râ11P â11, 2111Râ21P â21} Râ11 +Râ21197Appendix CIllustration of Algorithm 4To illustrate Algorithm 4, a simple example is presented in this section,where a network consists of 2 eRRHs caching subsets of a library of 5 popularfiles that are all in possession of the CBS as shown in the left side of FigureC.1. Two eRRHs are assumed to collectively know the whole library. Eachuser requests one file, which has a fixed size of 1 Mbits.First, Algorithm 4 generates the set of all possible associations in thetwo eRRHs. i.e., Sb1 = {u1f1, u2f2, u4f4} and Sb2 = {u1f1, u3f3, u5f5},respectively. Then, it generates all ONC file combinations SIDNC,b1 andSIDNC,b2 of the two eRRHs as summarized in Table C.1. Afterwards, itgenerates all feasible schedules S â Sfs, where each feasible schedule Si isrepresented by a vertex (circle) vi in the RRB subgraphs based on LC1 andLC2 that are described in Section 3.4. Table C.2 summarizes all feasibleschedules S. The power optimization problem (2.10) is then applied for eachfeasible schedules S in Table C.2. Given the optimal power distribution P,a vertex v has a secondary weight w(v) as defined in (3.3). Each vertexhas a primary weight as defined in (3.4). The generated vertices and theirweights are illustrated in Table C.3, in which each vertex contains a set ofassociations each one labeled by bzufrp, where b, z, u, f , r, and p representthe indices of eRRHs, RRBs, users, files, achievable capacities, and PLs,respectively. The constructed FRAN-CLNC graph is shown in Figure C.1.Second, given all vertices and their corresponding weights that were con-structed previously, the maximum-weight independent set algorithm is runto find the maximal independent set that provides the best solution. Sincewe only consider one RRB per eRRHâs frame, the vertices of the resultedFRAN-CLNC graph are adjacent, thus a maximum-weight independent setcontains only one vertex, which reflects a partial contribution of that RRB to198Appendix C. Illustration of Algorithm 4Table C.1: All Possible File Combinations SIDNC,b1 and SIDNC,b2i eRRH b1 s1i (κ, Ï) eRRH b2 s2i (κ, Ï)1 ((f1), (u1)) ((f1), (u1))2 ((f1 â f4), (u1, u4)) ((f1 â f3), (u1, u3))3 ((f2), (u2)) ((f3), (u3))4 ((f2 â f4), (u2, u4)) ((f5), (u5))5 ((f4), (u4))Table C.2: All feasible Schedules Sfsi Si i Si1 {11s11R, 21c23R} 9 {11s14R, 21c21R}2 {11s11R, 21c24R} 10 {11s14R, 21c22R}3 {11s12R, 21s23R} 11 {11s14R, 21c23R}4 {11s12R, 21s24R} 12 {11s14R, 21c24R}5 {11s13R, 21s21R} 13 {11s15R, 21c21R}6 {11s13R, 21s22R} 14 {11s15R, 21c22R}7 {11s13R, 21s23R} 15 {11s15R, 21c23R}8 {11s13R, 21s24R} 16 {11s15R, 21c24R}FRAN-CLNC Graphv3v9v4v6v15v12v11v10v14v1v7v2v16v5v13v8ONC Graphu1, f1u2, f2u3, f3u4, f4u5, f5Color Graphu3, f3u5, f5f3 f4f3 f4f4f1f2f1f4u1u2u3u4u5eRRH1eRRH2f4f2f1f3 f5f1f3 f4 f5f2f1CBSSide-informationFigure C.1: F-RAN system containing 5 users, 2 eRRHs, 1 RRB in eacheRRHâs frame, and their side information is given on the left part of thefigure. This figure also shows the ONC, FRAN-CLNC, and color graphs ofexample 3, respectively.199Appendix C. Illustration of Algorithm 4the network. From Table C.3, it is clear that the user association {u1, u2, u4}has the maximum-primary weight of 1.3333 seconds. This association repre-sents the vertex v9 in the FRAN-CLNC graph in Figure C.1. Therefore, themaximum-weight independent set algorithm selects this vertex, which givesthe maximum possible throughput. Then, Phase II is performed. The algo-rithm removes the vertices associated to {u1, u2, u4} from the ONC graphand runs the greedy coloring scheme. Since the requested files of the un-served users (u3 and u5) cannot be combined, each vertex has a differentcolor as shown in the right part of Figure C.1, thus the CBS would servethese users in two different orthogonal channels.200Appendix C. Illustration of Algorithm 4TableC.3:Therepresentedverticesandtheircorrespondingweightsiv iwisecondaryweight(bps)wiprimaryweight(s)1{1111râ 11pâ 11,2133râ 21pâ 21}râ 11+râ 210.252{1111râ 11pâ 11,2155râ 21pâ 21}râ 11+râ 210.53{1111râ 11pâ 11,1144râ 11pâ 11,2133râ 21pâ 21}2ârâ 11+râ 211.24{1111râ 11pâ 11,1144râ 11pâ 11,2155râ 21pâ 21}2ârâ 11+râ 211.255{1122râ 11pâ 11,2111râ 21pâ 21}râ 11+râ 210.58336{1122râ 11pâ 11,2111râ 11pâ 11,2133râ 21pâ 21}râ 11+2ârâ 210.78337{1122râ 11pâ 11,2133râ 21pâ 21}râ 11+râ 210.53338{1122râ 11pâ 11,2155râ 21pâ 21}râ 11+râ 210.58339{1122râ 11pâ 11,1144râ 11pâ 11,2111râ 21pâ 21}2ârâ 11+râ 211.333310{1122râ 11pâ 11,1144râ 11pâ 11,2111râ 21pâ 21,2133râ 21pâ 21}2ârâ 11+2ârâ 211.2511{1122râ 11pâ 11,1144râ 11pâ 11,2133râ 21pâ 21}2ârâ 11+râ 211.212{1122râ 11pâ 11,1144râ 11pâ 11,2155râ 21pâ 21}2ârâ 11+râ 211.2513{1144râ 11pâ 11,2111râ 21pâ 21}râ 11+râ 21114{1144râ 11pâ 11,2111râ 21pâ 21,2133râ 21pâ 21}râ 11+2ârâ 211.215{1144râ 11pâ 11,2133râ 21pâ 21}râ 11+râ 211.216{1144râ 11pâ 11,2155râ 21pâ 21}râ 11+râ 211.25201
Thesis/Dissertation
eng
Electrical Engineering
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Network codes for eï¬ective resource allocation in cache-enabled 5G mobile networks
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