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UBC Theses and Dissertations

Linear information theory and its application to the coded caching problem Tootooni Mofrad, Amirhossein


We investigate the peculiar properties of information theory when all random variables involved are linear functions of a given source endowed with the structure of a Z/2Z-vector space. We describe the coded caching problem and review the progress made in particular cases of the problem. We devise a new caching scheme for a special instance of the problem and extend some approaches in the coded caching literature to the linear case such that we can use our results in linear algebra to drive new lower bounds. We show one example within coded caching, with the linearity assumption, where our results in information theory lead to stronger bounds. Our results infer certain "qualitative" aspects of caching schemes, using the information they must contain, rather than giving a complete analysis of such schemes.

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