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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_{\ab{c}}, is extrapolated for infinite messages using the
scaling relation for the median convergence time, t_{\ab{med}}
\propto 1/(f_{\ab{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
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