A Construction of Lossy Source Code Using LDPC Matrices

Abstract

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 Z_q, where q is a prime number, we show that results similar to those for the binary alphabet condition hold for Z_q, the multiple alphabet condition.