Lossy Source Coding via Spatially Coupled LDGM Ensembles

TL;DR

This paper introduces a spatially coupled LDGM coding scheme for lossy source compression, demonstrating that a belief-propagation guided-decimation algorithm can approach the optimal distortion and potentially reach the Shannon rate-distortion bound.

Contribution

It proposes a novel spatially coupled LDGM ensemble and a belief-propagation guided-decimation algorithm that achieves near-optimal lossy compression performance.

Findings

The algorithm approaches the optimal distortion of spatially coupled ensembles.

Optimal distortions of coupled and individual ensembles are the same.

Spatial coupling can help reach the rate-distortion bound with low complexity algorithms.

Abstract

We study a new encoding scheme for lossy source compression based on spatially coupled low-density generator-matrix codes. We develop a belief-propagation guided-decimation algorithm, and show that this algorithm allows to approach the optimal distortion of spatially coupled ensembles. Moreover, using the survey propagation formalism, we also observe that the optimal distortions of the spatially coupled and individual code ensembles are the same. Since regular low-density generator-matrix codes are known to achieve the Shannon rate-distortion bound under optimal encoding as the degrees grow, our results suggest that spatial coupling can be used to reach the rate-distortion bound, under a {\it low complexity} belief-propagation guided-decimation algorithm. This problem is analogous to the MAX-XORSAT problem in computer science.