Rate-distortion function when side-information may be present at the decoder

A discrete memoryless source {X_k} is to be coded into a binary stream of rate R bits/symbol such that {X_k} can be recovered with minimum possible distortion. The system is to be optimized for best performance with two decoders, one of which has access to side-information about the source. For given levels of average distortion for these two decoders, the minimum achievable rate R (in the usual Shannon theory sense) is given as a per-letter minimization of information theoretic quantities. The problem is solved for two cases: where the encoder is and is not informed of the side-information