Binary quantization using Belief Propagation with decimation over factor graphs of LDGM codes

TL;DR

This paper introduces Bias Propagation, a simplified and faster Belief Propagation-based algorithm for binary quantization using LDGM codes, achieving near-optimal performance and challenging previous assumptions about the complexity of such tasks.

Contribution

The paper presents Bias Propagation, a novel, efficient Belief Propagation algorithm for binary quantization with LDGM codes, outperforming prior methods in simplicity and speed.

Findings

BiP achieves near-optimal rate-distortion performance.

BiP is 10-100 times faster than previous algorithms.

Suitable irregular LDGM codes enhance BiP performance.

Abstract

We propose a new algorithm for binary quantization based on the Belief Propagation algorithm with decimation over factor graphs of Low Density Generator Matrix (LDGM) codes. This algorithm, which we call Bias Propagation (BiP), can be considered as a special case of the Survey Propagation algorithm proposed for binary quantization by Wainwright et al. [8]. It achieves the same near-optimal rate-distortion performance with a substantially simpler framework and 10-100 times faster implementation. We thus challenge the widespread belief that binary quantization based on sparse linear codes cannot be solved by simple Belief Propagation algorithms. Finally, we give examples of suitably irregular LDGM codes that work with the BiP algorithm and show their performance.