Statistical mechanical aspects of joint source-channel coding

TL;DR

This paper explores the statistical mechanics of joint source-channel coding using MN-Gallager codes over Galois fields, analyzing thresholds, correlations, and efficiency improvements over traditional methods.

Contribution

It introduces a new coding scheme based on dynamical block posterior probabilities and analyzes its performance and thresholds in relation to correlations and field size.

Findings

Threshold extrapolation for infinite messages

Degradation of threshold with increased correlations

Enhanced performance with larger Galois fields

Abstract

An MN-Gallager Code over Galois fields, $q$, based on the Dynamical Block Posterior probabilities (DBP) for messages with a given set of autocorrelations is presented with the following main results: (a) for a binary symmetric channel the threshold, $f_c$, is extrapolated for infinite messages using the scaling relation for the median convergence time, $t_{med} \propto 1/(f_c-f)$; (b) a degradation in the threshold is observed as the correlations are enhanced; (c) for a given set of autocorrelations the performance is enhanced as $q$ is increased; (d) the efficiency of the DBP joint source-channel coding is slightly better than the standard gzip compression method; (e) for a given entropy, the performance of the DBP algorithm is a function of the decay of the correlation function over large distances.