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.