On the Role of Encoder Side-Information in Source Coding for Multiple Decoders

We consider a lossy source coding problem where the description of a source is going to be used by two decoders, each having access to information correlated with the source. This side-information is also present at the encoder. We give inner and outer bounds to the set of achievable rate and distortion triples. For the special case of Gaussian sources with degraded side-information and squared error distortions, the two bounds coincide and we obtain the true rate-distortion region. As a further specialization, we obtain the rate-distortion region of the Gaussian version of a problem previously solved by Kaspi for discrete memoryless sources. Using this result, we quantify how much revealing the side-information to the encoder helps in such a Gaussian setup.