On source transmission over some classes of relay channels

We study the reliable transmission of correlated sources over the relay channel. One of the sources is available at the sender while the other one is known to the relay. The receiver wishes to reconstruct both sources. We find necessary and sufficient conditions for optimal separation of source and channel codes. The coding scheme is based on the combination of the Slepian-Wolf source coding and Partial Decode-and-Forward (PDF) strategy. In this scheme, the relay partially decodes the message transmitted by the sender. We also consider the semi-deterministic relay channel where the output at the relay is a deterministic function of inputs from the sender and the relay. For the transmission of a single source over the semi-deterministic relay channel with correlated side information at the relay, the proposed conditions coincide. We also find necessary and sufficient conditions for the transmission of sources over the degraded relay channel where the output at the receiver is a degraded version of the output at the relay.