Communications over a state dependent channel, when the channel state and message are dependent.

This paper studies communication over a discrete channel with state, where the (possibly non-ergodic) state of the channel is arbitrarily correlated with the message, and this state is provided causally to both encoder and decoder. Matching necessary and sufficient conditions for reliable variable length-channel codes are found. In particular, it is shown that in order to transmit a given message, the empirical capacity of the channel must be greater than the marginal entropy of the message conditioned on the total observed channel states.