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The aim of this paper is to prove the achievability of the general (asymmetric) channel coding problem based on the hash property. Since an ensemble of q-ary sparse matrices (the maximum column weight grows logarithmically in the block length) satisfies the hash property, it is proved that the rate of codes using sparse matrices can achieve the channel capacity.
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...
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