Lossy Transmission of Correlated Sources over a Multiple Access Channel: Necessary Conditions and Separation Results

Lossy communication of correlated sources over a multiple access channel is studied. First, lossy communication is investigated in the presence of correlated decoder side information. An achievable joint source-channel coding scheme is presented, and the conditions under which separate source and channel coding is optimal are explored. It is shown that separation is optimal when the encoders and the decoder have access to a common observation conditioned on which the two sources are independent. Separation is shown to be optimal also when only the encoders have access to such a common observation whose lossless recovery is required at the decoder. Moreover, the optimality of separation is shown for sources with a common part, and sources with reconstruction constraints. Next, these results obtained for the system in presence of side information are utilized to provide a set of necessary conditions for the transmission of correlated sources over a multiple access channel without side information. The identified necessary conditions are specialized to the case of bivariate Gaussian sources over a Gaussian multiple access channel, and are shown to be tighter than known results in the literature in certain cases. Our results indicate that side information can have a significant impact on the optimality of sourcechannel separation in lossy transmission, in addition to being instrumental in identifying necessary conditions for the transmission of correlated sources when no side information is present.