Communication With Noncausal Message-Dependent Bi-Terminal Help

The capacity of a state-dependent discrete memoryless channel is derived for the setting where a message-cognizant rate-limited helper observes the state sequence noncausally and provides its description to both encoder and decoder. Said capacity is not increased if the channel outputs are fed back to the encoder via a noiseless feedback link. The analogous capacity is derived for the Gaussian channel, where the state corresponds to the additive noise. In this setting the feedback link—while not increasing capacity—eliminates the need for the helper’s cognition of the transmitted message. Moreover, in this setting, the results on capacity also hold for the cutoff rate and the listsize capacity.