Source Coding With Feed-Forward: Rate-Distortion Theorems and Error Exponents for a General Source

In this work, we consider a source coding model with feed-forward. We analyze a system with a noiseless, feed-forward 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 feed-forward is derived in terms of directed information, a variant of mutual information. We further investigate the nature of the rate-distortion function with feed-forward for two common types of sources- discrete memoryless sources and Gaussian sources. We then characterize the error exponent for a general source with feed-forward. The results are then extended to feed-forward with an arbitrary delay larger than the block length.