  Belief Propagation (BP) decoding of LDPC codes is extended to the case of
Joint Source-Channel coding. The uncompressed source is treated as a Markov
process, characterized by a transition matrix, T, which is utilized as side
information for the Joint scheme. The method is based on the ability to
calculate a Dynamical Block Prior (DBP), for each decoded symbol separately,
and re-estimate this prior after every iteration of the BP decoder. We
demonstrate the implementation of this method using MacKay and Neel's LDPC
algorithm over GF(q), and present simulation results indicating that the
proposed scheme is comparable with Separation scheme, even when advanced
compression algorithms (such as AC, PPM) are used. The extension to 2D (and
higher) arrays of symbols is straight-forward. The possibility of using the
proposed scheme without side information is briefly sketched.
