  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, $t_{med} \propto 1/(f_c-f)$;
(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 DBP joint source-channel coding
is slightly better than the standard gzip compression method; (e) for a given
entropy, the performance of the DBP algorithm is a function of the decay of the
correlation function over large distances.
