On Computing the Feedback Capacity of Channels and the Feed-Forward Rate-Distortion Function of Sources

The problem of computing the capacity-cost function of channels with feedback and the rate-distortion function of sources with feed-forward is considered. Sufficient conditions are derived on : a) the structure of the cost function for a chosen joint distribution to achieve the optimal feedback capacity-cost function, b) the structure of the distortion function for a chosen joint distribution to achieve the optimal feed-forward rate-distortion function. These structural results are useful since it is infeasible in general to directly compute the optimizations. Examples are provided to show how the results can help compute the performance limits with feedback and feed-forward.