  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.
