On the Continuity of Achievable Rate Regions for Source Coding over Networks

The continuity property of achievable rate regions for source coding over networks is considered. We show rate- distortion regions are continuous with respect to distortion vectors. Then we focus on the continuity of lossless rate regions with respect to source distribution: First, the proof of continuity for general networks with independent sources is given; then, for the case of dependent sources, continuity is proven both in examples where one-letter characterizations are known and in examples where one-letter characterizations are not known; the proofs in the latter case rely on the concavity of the rate regions for those networks.