Hash property and Wyner-Ziv source coding by using sparse matrices and maximum-likelihood coding

The aim of this paper is to prove the achievability of the Wyner-Ziv source coding problem by using sparse matrices and maximal-likelihood (ML) coding. To this end, the notion of a hash property for an ensemble of functions is introduced. For example, an ensemble of q-ary sparse matrices satisfies the hash property. Based on this property, it is proved that the rate of codes using sparse matrices and maximal-likelihood (ML) coding can achieve the optimal rate.