Successive Coding of Correlated Sources

The rate-distortion (RD) problem for two-layer coding of a pair (X,Y) of correlated sources is considered. The first layer information enables reconstruction of X within a certain distortion DX, while reception of both layers additionally enables reconstruction of Y within distortion DY. Although this problem is a special case of the successive refinement problem, the computation of the RD region for this scenario is nontrivial. Using a general class of outer bounds (analogous to Shannon lower bound in the classical RD theory) to the successive refinement rate-distortion region, the successive coding RD region for the case where (X,Y) is a jointly Gaussian pair and the distortion measure is squared-error is explicitly characterized.