Source coding with feed-forward

In this work, we consider a source coding model with feedforward. We analyze a system with a noiseless feedforward link where the decoder has knowledge of all previous source samples while reconstructing the present sample. The rate-distortion function for an arbitrary source with feedforward is derived in terms of directed information, a variant of mutual information. The special cases of discrete memoryless sources and Gaussian sources with feedforward are further examined. We also derive a random coding error exponent which is used to bound the probability of decoding error for a source code (with feedforward) of finite block length. The results are then extended to feedforward with an arbitrary delay larger than the block length.