Lower Bounds on the Rate-Distortion Function of LDGM Codes

TL;DR

This paper develops a generic technique to derive lower bounds on the rate-distortion functions of LDGM codes, highlighting the impact of bounded degrees on their lossy source coding performance.

Contribution

It introduces a novel method for bounding the rate-distortion function of binary linear codes, especially LDGM codes with bounded degrees, extending classical channel coding bounds.

Findings

Explicit lower bounds for check-regular LDGM ensembles

Bounds as a function of code degrees

Insights into the limitations of LDGM codes for lossy compression

Abstract

A recent line of work has focused on the use of low-density generator matrix (LDGM) codes for lossy source coding. In this paper, wedevelop a generic technique for deriving lower bounds on the rate-distortion functions of binary linear codes, with particular interest on the effect of bounded degrees. The underlying ideas can be viewing as the source coding analog of the classical result of Gallager, providing bounds for channel coding over the binary symmetric channel using bounded degree LDPC codes. We illustrate this method for different random ensembles of LDGM codes, including the check-regular ensemble and bit-check-regular ensembles, by deriving explicit lower bounds on their rate-distortion performance as a function of the degrees.