Mean field theory of communication

We discuss a Gaussian vector channel with random channel matrix, as a mathematical model for various wireless communication systems including multiple-input multiple-output (MIMO) and code-division multiple-access (CDMA) channels, and how statistical-physics approaches can be applied to analyze the Gaussian vector channel. We then present a mean-field description of the Gaussian vector channel in terms of a joint distribution of any single element of originally sent channel input and its estimate via posterior probability, which is a refinement of the “decoupling” result reported by Guo and Verdú for a set of statistically equivalent elements of channel input, the number of which is extensive