Joint source-channel coding via statistical mechanics: thermal equilibrium between the source and the channel

TL;DR

This paper applies statistical physics concepts to joint source-channel coding, revealing a thermal equilibrium analogy that simplifies mutual information calculation and extends to multiuser communication scenarios.

Contribution

It introduces a novel thermodynamic framework for analyzing joint source-channel coding, connecting entropy and mutual information through physical equilibrium principles.

Findings

Posterior distribution dominated by source sequences in the random coding regime

Thermodynamical entropies relate to Shannon entropies of source and channel

Derived a simple formula for mutual information based on thermal equilibrium

Abstract

We examine the classical joint source--channel coding problem from the viewpoint of statistical physics and demonstrate that in the random coding regime, the posterior probability distribution of the source given the channel output is dominated by source sequences, which exhibit a behavior that is highly parallel to that of thermal equilibrium between two systems of particles that exchange energy, where one system corresponds to the source and the other corresponds to the channel. The thermodynamical entopies of the dual physical problem are analogous to conditional and unconditional Shannon entropies of the source, and so, their balance in thermal equilibrium yields a simple formula for the mutual information between the source and the channel output, that is induced by the typical code in an ensemble of joint source--channel codes under certain conditions. We also demonstrate how our results can be used in applications, like the wiretap channel, and how can it be extended to multiuser scenarios, like that of the multiple access channel.