On the Concavity of Rate Regions for Lossless Source Coding in Networks

For a family of network source coding problems, we prove that the lossless rate region is concave in the distribution of sources. While the proof of concavity is straightforward for the few examples where a single-letter characterization of the lossless source coding region is known, it is more difficult for the vast majority of networks where the lossless source coding region remains unsolved. The class of networks that we investigate includes both solved and unsolved examples. We further conjecture that the same property applies more widely and sketch an avenue for investigating that conjecture.