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

@article{Muramatsu2008HashPA,
  title={Hash property and Wyner-Ziv source coding by using sparse matrices and maximum-likelihood coding},
  author={Jun Muramatsu and Shigeki Miyake},
  journal={2008 IEEE International Symposium on Information Theory},
  year={2008},
  pages={424-428}
}
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. 

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