On Cooperation in Multi-Terminal Computation and Rate Distortion

TL;DR

This paper explores how cooperation between transmitters affects the efficiency of computing functions of correlated sources, establishing bounds and demonstrating significant reductions in communication costs with minimal cooperation.

Contribution

It provides a general inner bound for the rate region in multi-terminal function computation with cooperation, showing tightness in key cases and illustrating the impact of cooperation on communication efficiency.

Findings

Cooperation can arbitrarily reduce total transmitted bits.

One bit of cooperation can significantly decrease information transmission.

Inner bounds are established and shown tight in several scenarios.

Abstract

A receiver wants to compute a function of two correlated sources separately observed by two transmitters. One of the transmitters may send a possibly private message to the other transmitter in a cooperation phase before both transmitters communicate to the receiver. For this network configuration this paper investigates both a function computation setup, wherein the receiver wants to compute a given function of the sources exactly, and a rate distortion setup, wherein the receiver wants to compute a given function within some distortion. For the function computation setup, a general inner bound to the rate region is established and shown to be tight in a number of cases: partially invertible functions, full cooperation between transmitters, one-round point-to-point communication, two-round point-to-point communication, and the cascade setup where the transmitters and the receiver are aligned. In particular it is shown that the ratio of the total number of transmitted bits without cooperation and the total number of transmitted bits with cooperation can be arbitrarily large. Furthermore, one bit of cooperation suffices to arbitrarily reduce the amount of information both transmitters need to convey to the receiver. For the rate distortion version, an inner bound to the rate region is exhibited which always includes, and sometimes strictly, the convex hull of Kaspi-Berger's related inner bounds. The strict inclusion is shown via two examples.