Encoding of Spatially Coupled LDGM Codes for Lossy Source Compression

Abstract

It has been shown that a class of spatially coupled low-density generator-matrix (SC-LDGM) code ensembles displays distortion saturation for the lossy binary symmetric source coding problem with the belief propagation guided decimation (BPGD) algorithm, i.e., the BPGD distortion approaches the optimal expected distortion of the underlying ensemble asymptotically in code length. We investigate the distortion performance of a practical class of protograph-based SC-LDGM code ensembles and demonstrate distortion saturation numerically. Moreover, taking advantage of the convolutional structure of the SC-LDGM codes, we propose an efficient windowed encoding (WE) algorithm with two decimation techniques for lowering the WE complexity that maintain distortion performance close to the rate-distortion bound.