Constrained Wyner-Ziv source coding

We generalize the Wyner-Ziv source coding problem with side-information at the decoder to the case where the encoder is required to be able to compute the decoder's reconstruction sequence with some fidelity. This requirement limits the extent to which the reconstruction sequence can depend on the side-information, which is not available to the encoder. For finite-alphabet memoryless sources and single-letter distortion measures we compute the minimal description rate as a function of the joint law of the source and side-information and of the allowed distortions at the encoder and decoder. We also treat memoryless Gaussian sources with mean squared-error distortion measures.