Two-Way Function Computation

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, but also we can get all the way to perfect-feedback
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computation capacities simultaneously in both directions for some channel regimes. This result draws a parallel with the recent result developed in the context of two-way interference channels.This is an idealistic case where feedback links are perfect with infinite capacities and are given for free. We left the exact definition in Section II.