A Classification of Functions in Multiterminal Distributed Computing

TL;DR

This paper develops a general method to analyze when distributed function computation can be simplified to Slepian-Wolf coding, improving understanding of function classification in multiterminal distributed computing.

Contribution

It introduces a unified approach to derive converse bounds and refines the conditions for the dichotomy theorem in multiterminal distributed computing.

Findings

Recovered sufficiency conditions for Slepian-Wolf optimality.

Derived improved sufficient conditions for i.i.d. sources.

Established matching necessary and sufficient conditions for smooth sources.

Abstract

In the distributed function computation problem, dichotomy theorems, initiated by Han-Kobayashi, seek to classify functions by whether the rate regions for function computation improve on the Slepian-Wolf regions or not. In this paper, we develop a general approach to derive converse bounds on the distributed function computation problem. By using this approach, we recover the sufficiency part, i.e. the conditions such that the Slepian-Wolf regions become optimal, of the known dichotomy theorems in the two-terminal distributed computing. Furthermore, we derive an improved sufficient condition on the dichotomy theorem in the multiterminal distributed computing for the class of i.i.d. sources with positivity condition. Finally, we derive the matching sufficient and necessary condition on the dichotomy theorem in the multiterminal distributed computing for the class of smooth sources.