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Abstract: We consider lossy compression of a binary symmetric source by means of alow-density generator-matrix code. We derive two lower bounds on the ratedistortion function which are valid for any low-density generator-matrix codewith a given node degree distribution Lx on the set of generators and for anyencoding algorithm. These bounds show that, due to the sparseness of the code,the performance is strictly bounded away from the Shannon rate-distortionfunction. In this sense, our bounds represent a natural generalization ofGallager-s bound on the maximum rate at which low-density parity-check codescan be used for reliable transmission. Our bounds are similar in spirit to thetechnique recently developed by Dimakis, Wainwright, and Ramchandran, but theyapply to individual codes.



Autor: Shrinivas Kudekar, Ruediger Urbanke

Fuente: https://arxiv.org/







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