Communication Near The Channel Capacity With An Absence Of Compression: Statistical Mechanical Approach

An MN-Gallager Code over Galois fields, q, based on the Dynamical Block Posterior probabilities (DBP) for messages with a given set of autocorrelations is presented. The novel idea of the decoder is the dynamical updating of the prior block probabilities which are derived from the transfer matrix solution of the effective 1D Ising Hamiltonian and from the posterior probabilities of the neighboring blocks. This bridge between statistical physics and information theory leads to an efficient algorithm for joint source-channel coding.