Infinite-message Interactive Function Computation in Collocated Networks

TL;DR

This paper characterizes the minimum sum-rate for infinite-message interactive function computation in collocated networks, providing bounds, optimality tests, and an iterative evaluation algorithm.

Contribution

It introduces a convex-geometric characterization of the infinite-message sum-rate and proposes an iterative algorithm for its evaluation.

Findings

Derived lower bounds for the sum-rate functional

Developed an optimality test for achievable sum-rates

Demonstrated the approach with a three-source example

Abstract

An interactive function computation problem in a collocated network is studied in a distributed block source coding framework. With the goal of computing a desired function at the sink, the source nodes exchange messages through a sequence of error-free broadcasts. The infinite-message minimum sum-rate is viewed as a functional of the joint source pmf and is characterized as the least element in a partially ordered family of functionals having certain convex-geometric properties. This characterization leads to a family of lower bounds for the infinite-message minimum sum-rate and a simple optimality test for any achievable infinite-message sum-rate. An iterative algorithm for evaluating the infinite-message minimum sum-rate functional is proposed and is demonstrated through an example of computing the minimum function of three sources.