Construction of Slepian-Wolf Source Code and Broadcast Channel Code Based on Hash Property

Abstract

The aim of this paper is to prove theorems for the Slepian-Wolf source coding and the broadcast channel coding (independent messages and no common message) based on the the notion of a stronger version of the hash property for an ensemble of functions. Since an ensemble of sparse matrices has a strong hash property, codes using sparse matrices can realize the achievable rate region. Furthermore, extensions to the multiple source coding and multiple output broadcast channel coding are investigated.

arXiv commentThe proofs of Lemmas 4 and 9 are revised. Some proofs are simplified. Some typos are fixed. A part of this paper has been published in Proceedings of 2010 IEEE International Symposium on Information Theory (ISIT2010) and Proceedings of 7th Asia-Europe Workshop "CONCEPTS in INFORMATION THEORY" (AEW7), 2011, 39 pages

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• Multi-Terminal Codes Using Constrained-Random-Number Generators