Gaussian multiple descriptions with common and constrained reconstruction constraints

The problem of multiple descriptions for a Gaussian source is considered, in which all the decoders have access to correlated Gaussian side-information. Two variations of this problem are studied. First, the rate-distortion tradeoff is characterized under the assumption of a common reconstruction constraint, in which the estimate produced at each of the decoders is also exactly recoverable at the encoder. Secondly, a generalization of this setup is studied in which possibly different distortions are tolerable between the estimates at the encoder and the respective estimates at each of the decoders.