  An efficient joint source-channel (s/c) decoder based on the side information
of the source and on the MN-Gallager algorithm over Galois fields is presented.
The dynamical block priors (DBP) are derived either from a statistical
mechanical approach via calculation of the entropy for the correlated
sequences, or from the Markovian transition matrix. The Markovian joint s/c
decoder has many advantages over the statistical mechanical approach. In
particular, there is no need for the construction and the diagonalization of a
qXq matrix and for a solution to saddle point equations in q dimensions. Using
parametric estimation, an efficient joint s/c decoder with the lack of side
information is discussed. Besides the variant joint s/c decoders presented, we
also show that the available sets of autocorrelations consist of a convex
volume, and its structure can be found using the Simplex algorithm.
