An Efficient MN-Algorithm for Joint Source-Channel Coding
  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. 
Haggai Kfir, Eyal Shpilman, Ido Kanter