Distributed function computation in asymmetric communication scenarios

We consider the distributed function computation problem where the sink computes some function of the data split among N correlated informants, in asymmetric communication scenarios. The distributed function computation problem is addressed as a generalization of distributed source coding (DSC) problem. We are interested in computing the minimum number of informant bits required, in the worst-case, to allow the sink to exactly compute the function. We provide a constructive solution for this in terms of an interactive communication protocol and prove its optimality. The proposed protocol also allows us to compute the worst-case achievable rate-region for the computation of any function. We introduce two equivalence classes of functions: lossy and lossless and show that, in general, the lossy functions can be computed with fewer informant bits than the DSC problem, while computation of the lossless functions requires as many informant bits as the DSC problem.