Rate-distortion function for a Heegard-Berger problem with two sources and degraded reconstruction sets

In this work, we investigate an instance of the Heegard-Berger problem with two sources and arbitrarily correlated side information at two decoders, in which the reconstruction sets at the decoders are degraded. Specifically, two sources are to be encoded in a manner that one of the two is reproduced losslessly by both decoders, and the other is reproduced to within some prescribed distortion level at one of the two decoders. We establish the optimal rate-distortion function for this model. The investigation of the result in some special cases also sheds light on the utility of joint compression of the two sources.