A source-channel separation theorem with application to the source broadcast problem

A source-channel separation theorem is established for a certain joint source-channel problem. It is shown that this separation theorem can be used in conjunction with a simple reduction argument to establish a general converse result for the source broadcast problem. Somewhat surprisingly, this converse result, albeit based on the source-channel separation theorem, can be used to prove the optimality of non-separation based schemes (e.g., hybrid coding schemes) and determine the performance limits in certain scenarios where the separation architecture is suboptimal.