Information Theory and Reliable Communication
Information Theory and Reliable Communication
Information Theory: Coding Theorems for Discrete Memoryless Systems
Information Theory: Coding Theorems for Discrete Memoryless Systems
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Information, Physics, and Computation
Information, Physics, and Computation
Mutual information and minimum mean-square error in Gaussian channels
IEEE Transactions on Information Theory
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
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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 entropies 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. This formula, as well as the statistical-mechanical perspective that leads to it, form the main contribution of this paper. 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.