Vector Gaussian Heegard-Berger Problem With Common Reconstructions

In this paper, the vector Gaussian Heegard-Berger problem with common reconstruction constraints is considered. We characterize the rate-distortion function of this instance, when decoders' error covariance distortion constraints are both diagonal positive matrices. In particular, the Timo-Chan-Grant coding scheme is shown to be optimal, via using the source enhancement argument.