Capacity of a two-way function multicast channel

We explore the role of interaction for the problem of reliable computation over two-way multicast networks. Specifically we consider a four-node network in which two nodes wish to compute a modulo-sum of two independent Bernoulli sources generated from the other two, and a similar task is done in the other direction. The main contribution of this work lies in the characterization of the computation capacity region for a deterministic model of the network via a novel transmission scheme. One consequence of this result is that not only we can get an interaction gain over the one-way non-feedback computation capacities, we can sometime get all the way to perfect-feedback computation capacities simultaneously in both directions. This result draws a parallel with the recent result developed in the context of two-way interference channels [1].