Information-Theoretic Bounds for Multiround Function Computation in Collocated Networks

TL;DR

This paper establishes information-theoretic bounds for multiround function computation in collocated networks, revealing the fundamental limits and scaling laws of communication efficiency for various symmetric functions.

Contribution

It provides a computable characterization of the rate region for function computation and introduces improved bounds on the minimum sum-rate, especially for symmetric functions.

Findings

Derived a single-letter information measure characterization of feasible rate regions.

Showed that computing symmetric functions leaks additional information, affecting bounds.

Established orderwise improvements over cut-set bounds as network size increases.

Abstract

We study the limits of communication efficiency for function computation in collocated networks within the framework of multi-terminal block source coding theory. With the goal of computing a desired function of sources at a sink, nodes interact with each other through a sequence of error-free, network-wide broadcasts of finite-rate messages. For any function of independent sources, we derive a computable characterization of the set of all feasible message coding rates - the rate region - in terms of single-letter information measures. We show that when computing symmetric functions of binary sources, the sink will inevitably learn certain additional information which is not demanded in computing the function. This conceptual understanding leads to new improved bounds for the minimum sum-rate. The new bounds are shown to be orderwise better than those based on cut-sets as the network scales. The scaling law of the minimum sum-rate is explored for different classes of symmetric functions and source parameters.