On the Heegard-Berger/Kaspi problem with decoder cooperation

We consider decoder cooperation in the Heegard-Berger/Kaspi problem. The encoder sends a common description of a source to two decoders, one of which has side information. Cooperation between the two decoders is of the form of a limited capacity link from the informed decoder to the uninformed decoder. Inner and outer bounds are obtained to the rate distortion region for this problem. The bounds are shown to coincide for the case where the better informed decoder wants to recover X losslessly and also for certain distortion regimes in the quadratic Gaussian case. The rate distortion tradeoff is completely characterized for the case when the encoder also has access to the side information. Finally, we look at the case when the two decoders want to losslessly reconstruct functions of X and characterize the achievable rate region.