Joint Source Channel Coding Via Statistical Mechanics: Thermal Equilibrium Between the Source and the Channel

DOI10.1109/TIT.2009.2032738zbMATH Open1367.94212arXiv0810.2164OpenAlexW2118493497MaRDI QIDQ4974085

Publication date: 8 August 2017

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/0810.2164

Mathematics Subject Classification ID

Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20) Source coding (94A29)