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The problem of joint source-channel coding in transmitting independent sources over interference channels with correlated receiver side information is studied. When each receiver has side information correlated with its own desired source, it is shown that source-channel separation is optimal. When each receiver has side information correlated with the interfering source, sufficient conditions for reliable transmission are provided based on a joint source-channel coding scheme using the superposition encoding and partial decoding idea of Han and Kobayashi. When the receiver side information is a deterministic function of the interfering source, source-channel separation is again shown to be optimal. In addition to these source-channel coding problems, a new channel model that generalizes the classical interference channel is introduced: the interference channel with message side information. Achievable rate regions are given and a single letter characterization of the capacity region for a special class of Z-interference channels is provided. Using this capacity result and the optimality of source-channel separation, we demonstrate that our sufficient conditions for reliable transmission when each receiver has side information correlated with the interfering source are also necessary for some special cases. As a by-product, the capacity region of a class of Z-channels with degraded message sets is also provided.