Correlation between channel state and information source with empirical coordination constraint

Correlation between channel state and source symbol is under investigation for a joint source-channel coding problem. We investigate simultaneously the lossless transmission of information and the empirical coordination of channel inputs with the symbols of source and states. Empirical coordination is achievable if the sequences of source symbols, channel states, channel inputs and channel outputs are jointly typical for a target joint probability distribution. We characterize the joint distributions that are achievable under lossless decoding constraint. The performance of the coordination is evaluated by an objective function. For example, we determine the minimal distortion between symbols of source and channel inputs for lossless decoding. We show that the correlation source/channel state improves the feasibility of the transmission.