Functional Duality Between Distributed Source Coding with One Distortion Criterion and Semi-Deterministic Broadcast Channel Coding in the Case of Correlated Messages

In this letter, functional duality between Distributed Source Coding with One Distortion Criterion (DSC-ODC) and correlated messages and Semi-Deterministic Broadcast Channel Coding (SD-BCC) with correlated messages is considered. It is shown that under certain conditions, for a given DSC-ODC problem with correlated messages, a functional dual SD-BCC problem with correlated messages can be obtained, and vice versa. In particular, the correlation structure of the messages in the two dual problems are the same. The source distortion measure and the channel cost measure for this duality are also specified.