Distributed function computation over a rooted directed tree

This paper establishes the capacity region for a class of source coding function computation setups, where sources of information are available at the nodes of a tree and where a function of these sources must be computed at its root. The capacity region holds for any function as long as the sources' joint distribution satisfies a certain Markov criterion. This criterion is met, in particular, when the sources are independent. This result recovers the capacity regions of several function computation setups. These include the point-to-point communication setting with arbitrary sources, the noiseless multiple access network with conditionally independent sources, and the cascade network with Markovian sources.