To code, or not to code: Lossy source-channel communication revisited

What makes a source-channel communication system optimal? It is shown that in order to achieve an optimal cost-distortion tradeoff, the source and the channel have to be matched in a. probabilistic sense. The match (or lack of it) involves the source distribution, the distortion measure, the channel conditional distribution, and the channel input cost function. Closed-form necessary and sufficient expressions relating the above entities are given. This generalizes both the separation-based approach as well as the two well-known examples of optimal uncoded communication. The condition of probabilistic matching is extended to certain nonergodic and multiuser scenarios. This leads to a result on optimal single-source broadcast communication.