Joint Source-Channel Decoding for Transmitting Correlated Sources over Broadcast Networks

We consider a set of S independent encoders that must transmit a set of correlated sources through a network of noisy, independent, broadcast channels to T receivers. For the general problem of sending correlated sources through broadcast networks, it is known that the source-channel separation theorem breaks down and the achievable rate region as well as the proper method of coding are unknown. For our scenario, however, we not only establish the optimal rate region, but we show that a type of source-channel separation is possible at the transmitter, provided joint source-channel decoding is used at the receiver. Furthermore, we show that while joint source-channel encoding is unnecessary, not using joint source-channel decoding is suboptimal. Finally, when the optimal input distribution from transmitter i to receiver j is independent of j, our result has a max-flow/min-cut interpretation. Specifically, in this case our result implies that if it is possible to send the sources to each receiver separately while ignoring the others, then it is possible to send to all receivers simultaneously