Lossless source coding for a Heegard-Berger problem with two sources and degraded reconstruction sets

This work investigates the problem of lossless compression of two arbitrarily correlated memoryless sources in an instance of Heegard-Berger problem with degraded reconstruction sets. Specifically, one of the sources is to be reproduced losslessly by two separate decoders, and the other one is to be reproduced losslessly by only one of the two decoders. The decoders observe side information sequences that are arbitrarily correlated among them, and with the sources. We establish a single-letter characterization of the optimal compression rate of this model. We also discuss several examples, and highlight the utility of an appropriate joint compression of the two sources for it to be optimal.