In this work, study two problems- source coding with feed-forward and channel coding with feedback. A source coding model with feed-forward is a system with a noiseless,feed-forward link where the decoder has knowledge of some previous source samples while reconstructing the present sample. We present the rate-distortion function for an arbitrary source with feed-forward in terms of directed information[Massey]. Next, we give a new interpretation of directed information  which helps us understand why it arises in the capacity with feedback and rate-distortion function with feed-forward.

We then address the problem of evaluating the expressions for the rate-distortion function and capacity. The formulas for the optimal feed-forward rate-distortion function feedback capacity are multi-letter expressions and cannot be computed easily in general. We give conditions under which these can be evaluated for a large class of sources(channels) with memory and distortion (cost) measures and provide examples.