Two-way Function Computation

TL;DR

This paper characterizes the computation capacity region in a two-way multicast network, demonstrating interaction gains and conditions for achieving perfect-feedback capacities, advancing understanding of interactive computation in network settings.

Contribution

It provides a novel transmission scheme to characterize the capacity region for a deterministic two-way network, highlighting interaction benefits and feedback capacity achievement.

Findings

Interaction can improve computation capacity over one-way limits.

Simultaneous perfect-feedback capacities are achievable in both directions.

A new transmission scheme enables capacity characterization for the network.

Abstract

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 sometimes 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.