Statistical mechanical aspects of joint source-channel coding

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 with the following main results: a) for a binary symmetric channel the threshold, f_c, is extrapolated for infinite messages using the scaling relation for the median convergence time, t_med ∝ 1/(f_c f); b) a degradation in the threshold is observed as the correlations are enhanced; c) for a given set of autocorrelations the performance is enhanced as q is increased; d) the efficiency of the DBF joint source-channel coding is slightly better than the standard gzip compression method; e) for a given entropy, the performance of the DBF algorithm is a function of the decay of the correlation function over large distances.