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

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