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

We study the problem of computing the rate-distortion function for sources with feed-forward and the capacity for channels with feedback. The formulas (involving directed information) for the optimal rate-distortion function with feed-forward and channel capacity with feedback are multi- letter expressions and cannot be computed easily in general. In this work, we derive conditions under which these can be computed for a large class of sources/channels with memory and distortion/cost measures. Illustrative examples are also provided.