Joint source-channel turbo decoding of VLC-coded Markov sources

We analyse the dependencies between the variables involved in the source and channel coding chain. This chain is composed of 1/ a Markov source of symbols, followed by 2/ a variable length source coder, and 3/ a channel coder. The output process is analysed in the framework of Bayesian networks, which provide both an intuitive representation of the structure of dependencies, and a way of deriving joint (soft) decoding algorithms. Joint decoding relying on the hidden Markov model (HMM) of the global coding chain is intractable, except in trivial cases, due to the high dimensionality of the state space. We advocate instead an iterative procedure inspired from serial turbo codes, in which the three models of the coding chain are used in alternance. This idea of using separately each factor of a big product model inside an iterative procedure usually requires the presence of an interleaver between successive components. We show that only one interleaver is necessary here, placed between the source coder and the channel coder. As a sub-product, we also derive a soft VLC decoder with good (and adjustable) synchronization properties.