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

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 introduced.