Secure communication of correlated sources over broadcast channels

Broadcast channels with correlated sources are considered from a joint source-channel coding perspective, where each receiver is kept in ignorance of the source intended for the other receiver. This setting can be seen as a generalization of Han-Costa's broadcast channel with correlated sources under additional secrecy constraints on both receivers. General outer and inner bounds for this reliable and secure communication are determined. The joint source-channel coding is proved to be optimal for two special cases, including the sources satisfying a certain Markov property sent over semi-deterministic broadcast channels, and arbitrary correlated sources sent over less-noisy broadcast channels.