Source-Channel Coding Theorems for the Multiple-Access Relay Channel

We study reliable transmission of arbitrarily correlated sources over multiple-access relay channels (MARCs) and multiple-access broadcast relay channels (MABRCs). In MARCs only the destination is interested in reconstructing the sources, while in MABRCs, both the relay and the destination want to reconstruct them. In addition to arbitrary correlation among the source signals at the users, both the relay and the destination have side information correlated with the source signals. Our objective is to determine whether a given pair of sources can be losslessly transmitted to the destination for a given number of channel symbols per source sample, defined as the source-channel rate. Sufficient conditions for reliable communication based on operational separation, as well as necessary conditions on the achievable source-channel rates are characterized. Since operational separation is generally not optimal for MARCs and MABRCs, sufficient conditions for reliable communication using joint source-channel coding schemes based on a combination of the correlation preserving mapping technique with Slepian-Wolf source coding are also derived. For correlated sources transmitted over fading Gaussian MARCs and MABRCs, we present conditions under which separation (i.e., separate and stand-alone source and channel codes) is optimal. This is the first time optimality of separation is proved for MARCs and MABRCs.