  Lossy coding of correlated sources over a multiple access channel (MAC) is
studied. First, a joint source-channel coding scheme is presented when the
decoder has correlated side information. Next, the optimality of separate
source and channel coding, that emerges from the availability of a common
observation at the encoders, or side information at the encoders and the
decoder, is investigated. It is shown that separation is optimal when the
encoders have access to a common observation whose lossless recovery is
required at the decoder, and the two sources are independent conditioned on
this common observation. Optimality of separation is also proved when the
encoder and the decoder have access to shared side information conditioned on
which the two sources are independent. These separation results obtained in the
presence of side information are then utilized to provide a set of necessary
conditions for the transmission of correlated sources over a MAC without side
information. Finally, by specializing the obtained necessary conditions to the
transmission of binary and Gaussian sources over a MAC, it is shown that they
can potentially be tighter than the existing results in the literature,
providing a novel converse for this fundamental problem.
