Design and analysis of lattice-based communication schemes : a study of constructions A and D
department or school: Applied Science, Faculty of
department or school: Engineering, School of (Okanagan)
data provider: DSpace
degree campus: UBCO
creator: Sadeghi, Maryam
issued: 2025-09-08T21:21:21Z
issued: 2025
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: Lattice codes are central to modern communication theory, unifying error correction, efficient transmission, and secure encoding. Among them, Constructions A and D are especially effective in achieving coding and quantization gains over additive white Gaussian noise (AWGN) and block fading (BF) channels. This dissertation examines the design, analysis, and application of algebraic lattice constructions to enhance reliability and performance in these channels. The first part of the work focuses on Construction A lattices built over the ring of imaginary quadratic integers, tailored for AWGN channels. A simplified and rigorous proof is presented for the existence of lattices that are simultaneously good for both coding and mean squared error (MSE) quantization. This construction exploits the arithmetic of imaginary quadratic fields and leverages discrete dithering to streamline the proof technique. The analysis provides foundational insights into the structure and behavior of algebraic lattices, demonstrating their potential for high-performance communication. The second part introduces a novel framework for Construction D lattices suited for block fading channels, where signal quality varies across transmission blocks. For the first time, these lattices are defined using a combination of nested linear codes and prime ideals in number fields. A layered coding framework is adopted, in which a semi-systematic generator matrix is derived to enable structured encoding. The corresponding decoding algorithm combines maximum-likelihood decoding in the early layers with successive cancellation in the deeper layers. This hybrid strategy ensures full diversity and maintains linear complexity with respect to the lattice dimension. Extensive simulations confirm the superior frame error rate (FER) performance of these lattices over their Construction A counterparts, particularly in high-diversity scenarios. The results also reveal that while multi-layer designs offer flexibility, …
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/92272
note: Design and Analysis of Lattice-BasedCommunication Schemes: A Study ofConstructions A and DbyMaryam SadeghiB.Sc., Shiraz University, Iran, 2009M.Sc., AmirKabir University of Technology (Polytechnic), Iran, 2013M.Sc., The University of British Columbia, 2018A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE COLLEGE OF GRADUATE STUDIES(Electrical Engineering)THE UNIVERSITY OF BRITISH COLUMBIA(Okanagan)September 2025© Maryam Sadeghi, 2025The following individuals certify that they have read, and recommendto the College of Graduate Studies for acceptance, a dissertation entitled:Design and Analysis of Lattice-Based Communication Schemes:A Study of Constructions A and Dsubmitted byMaryam Sadeghi in partial fulfilment of the requirements ofthe degree of Doctor of PhilosophyChen Feng, School of EngineeringSupervisorAnas Chaaban, School of EnineeringSupervisory Committee MemberZheng Liu, School of EngineeringSupervisory Committee MemberUniversity ExaminerShawn Wang, Department of Computer Science, Mathematics, Physics, and StatisticsExternal ExaminerDaniel Panario, School of Mathematics and Statistics- Carleton UniversityiiAbstractLattice codes are central to modern communication theory, unifying er-ror correction, efficient transmission, and secure encoding. Among them,Constructions A and D are especially effective in achieving coding and quan-tization gains over additive white Gaussian noise (AWGN) and block fading(BF) channels. This dissertation examines the design, analysis, and applica-tion of algebraic lattice constructions to enhance reliability and performancein these channels.The first part of the work focuses on Construction A lattices built overthe ring of imaginary quadratic integers, tailored for AWGN channels. Asimplified and rigorous proof is presented for the existence of lattices that aresimultaneously good for both coding and mean squared error (MSE) quan-tization. This construction exploits the ar…
has type: Thesis/Dissertation
date issued: 2025-11
is shown at: 10.14288/1.0450076
language: eng
degree discipline: Electrical Engineering
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: Attribution-NonCommercial-NoDerivatives 4.0 International
rights URI: http://creativecommons.org/licenses/by-nc-nd/4.0/
scholar level: Graduate
contributor: Feng, Chen
type: Text
identifier URI: http://hdl.handle.net/2429/92272