Lossless transmission of correlated sources over a multiple access channel with side information

In this paper, we consider lossless transmission of arbitrarily correlated sources over a multiple access channel. Characterization of the achievable rates in the most general setting is one of the longstanding open problems of information theory. We consider a special case of this problem where the receiver has access to correlated side information given which the sources are independent. We prove a source channel separation theorem for this system, that is, we show that there is no loss in performance in first applying distributed source coding where each encoder compresses its source conditioned on the side information at the receiver, and then applying an optimal multiple access channel code with independent codebooks. We also give necessary and sufficient conditions for source and channel separability in the above problem if there is perfect two-sided feedback from the receiver to the transmitters. These two communication scenarios constitute examples of few non-trivial multi-user scenarios for which separation holds.