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We examine the classical joint source--channel coding problem from theviewpoint of statistical physics and demonstrate that in the random codingregime, the posterior probability distribution of the source given the channeloutput is dominated by source sequences, which exhibit a behavior that ishighly parallel to that of thermal equilibrium between two systems of particlesthat exchange energy, where one system corresponds to the source and the othercorresponds to the channel. The thermodynamical entopies of the dual physicalproblem are analogous to conditional and unconditional Shannon entropies of thesource, and so, their balance in thermal equilibrium yields a simple formulafor the mutual information between the source and the channel output, that isinduced by the typical code in an ensemble of joint source--channel codes undercertain conditions. We also demonstrate how our results can be used inapplications, like the wiretap channel, and how can it be extended to multiuserscenarios, like that of the multiple access channel.

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