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A multiple description scalar quantization (MDSQ) based coding system can be regarded as a source coder (quantizer) followed by a channel coder, i.e. the combination of index and codeword assignment. The redundancy, or the correlation between the descriptions, is controlled by the number of diagonals covered by the index assignment. In this paper, we analyse dependencies between the variables involved in the MDSQ coding chain and design an estimation strategy making use of part of the global model of dependencies at each time. Inference of the hidden states of the connected models is done by applying belief propagation principles on the resulting Bayesian network. We try to evidence the most appropriate form of redundancy one should introduce in the context of variable length code compressed streams in order to fight against de-synchronizations when impaired by channel noise.