In this letter, distributed source coding with one distortion criterion and correlated messages is considered. This problem can be regarded as “Berger-Yeung problem with correlated messages”. It corresponds to the source coding part of the graph-based framework for transmission of a pair of correlated sources over the multiple-access channel where one is lossless and the other is lossy. As a result, the achievable rate-distortion region for this problem is provided. A rigorous proof of both achievability and converse part is also given.

In this letter, functional duality between distributed source coding (DSC) with correlated messages and broadcast channel coding (BCC) with correlated messages is considered. It is shown that under certain conditions, for a given DSC problem with correlated messages, a functional dual BCC problem with correlated messages can be obtained, and vice versa. That is, the optimal encoder-decoder mappings for one problem become the optimal decoder-encoder mappings for the dual problem. Furthermore, the correlation structure of the messages in the two dual problems and the source distortion and channel cost measure for this duality are specified.

The transmission of correlated messages over strong interference channels is examined. The result is the proposal of a single-letter characterization of the sum-rate capacity of strong interference channels with correlated messages. It is shown that if the messages are independent, the sum-rate capacity is equal to that of [1] obtained by Costa and El Gamal. However, it can be larger than that of [1] if the messages are correlated. It is also shown that, in terms of the sum-rate, the achievable rate region in [2] is indeed the sum-rate capacity.

Transmission of correlated messages over interference channels with strong interference is considered. As a result, an achievable rate region is presented. It is shown that if the messages are correlated, the achievable rate region can be larger than the capacity region given by Costa and El Gamal. As an example, the Gaussian interference channel is considered.