A Construction of Lossy Source Code Using LDPC Matrices


IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E91-A   No.6   pp.1488-1501
Publication Date: 2008/06/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e91-a.6.1488
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
LDPC matrices,  lossy source coding,  rate-distortion theory,  

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Research into applying LDPC code theory, which is used for channel coding, to source coding has received a lot of attention in several research fields such as distributed source coding. In this paper, a source coding problem with a fidelity criterion is considered. Matsunaga et al. and Martinian et al. constructed a lossy code under the conditions of a binary alphabet, a uniform distribution, and a Hamming measure of fidelity criterion. We extend their results and construct a lossy code under the extended conditions of a binary alphabet, a distribution that is not necessarily uniform, and a fidelity measure that is bounded and additive and show that the code can achieve the optimal rate, rate-distortion function. By applying a formula for the random walk on lattice to the analysis of LDPC matrices on Zq, where q is a prime number, we show that results similar to those for the binary alphabet condition hold for Zq, the multiple alphabet condition.