Lossless joint source-channel coding across broadcast channels with decoder side information

Lossless transmission of a source across a broadcast channel, where the decoders have side information about the source (unknown to the encoder), is discussed. Adopting separate source and channel coding strategies translates to sending hierarchical information, or degraded message sets, as is more commonly known, through the channel. Joint source-channel coding, on the other hand, allows for a simpler strategy, which turns out to be optimal. As a result, a complete single-letter characterization of achievable rates is successfully derived. This characterization surprisingly depends solely on the source and the channel marginal distributions. Finally, it is shown by an example that joint source-channel coding can be advantageous over the coding strategy which utilizes optimal source and channel codes separately.