Functional Duality Between Distributed Reconstruction Source Coding and Multiple-Access Channel Coding in the Case of Correlated Messages

In this letter, functional duality between Distributed Reconstruction Source Coding (DRSC) with correlated messages and Multiple-Access Channel Coding (MACC) with correlated messages is considered. It is shown that under certain conditions, for a given DRSC problem with correlated messages, a functional dual MACC problem with correlated messages can be obtained, and vice versa. In particular, it is shown that the correlation structures 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.