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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 memory-less 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. Index Terms--Directed Information, random coding, real-time reconstruction, side information, source coding with feed-forward.

The two-channel multiple descriptions problem for an independent and identically distributed (i.i.d.) source, with feed-forward to one or both side-decoders is considered. A single-letter achievable rate-region is derived; it enlarges the best known rate-region for multiple descriptions without feed-forward. The proof of the result uses a block-Markov superposition source coding strategy. In point-to-point source coding, feed-forward does not decrease the rate-distortion function of an i.i.d. source. In contrast, an example is provided to show that the derived region can be strictly larger than the optimal multiple description rate-distortion region without feed-forward. [ABSTRACT FROM AUTHOR]