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.

The 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

References in corpus (3)

• Ripple Texturing of Suspended Graphene Atomic Membranes
• Lecture Notes on Network Information Theory
• An outer bound for 2-receiver discrete memoryless broadcast channels

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• Achievability proof via output statistics of random binning
• Construction of a Channel Code from an Arbitrary Source Code with Decoder Side Information
• Construction of Multiple Access Channel Codes Based on Hash Property
• Multi-Terminal Codes Using Constrained-Random-Number Generators