The Kaspi Rate-Distortion Problem with Encoder Side-Information: Gaussian Case

We consider the problem of compressing a Gaussian source for two decoders, one of which has access to side-information. Kaspi has solved this problem for discrete memoryless sources for the two cases with and without encoder side-information. We focus on the case in which the encoder has access to side-information and we explicitly solve the optimization problem for Gaussian sources and squared error distortion measures. The achievability part of the proof provides an intuitive insight based on the idea of using innovations for the conditional rate-distortion problem. We compare our result to the case in which the encoder is not informed. Heegard and Berger have solved this problem for Gaussian sources. The comparison shows that in this multiple-decoder setup, side-information at the encoder improves the rate-distortion curve even in the Gaussian case.