Every Bit Counts: Second-Order Analysis of Cooperation in the Multiple-Access Channel

TL;DR

This paper analyzes how limited cooperation via a facilitator improves the sum-rate in a multiple access channel, showing even minimal cooperation yields significant benefits in finite-blocklength regimes.

Contribution

It provides a finite-blocklength analysis of the MAC with a cooperation facilitator, quantifying the sum-rate gains for sub-linear cooperation rates.

Findings

A log(K) bit transmission yields a sum-rate benefit of order √(log(K)/n)

Even a single bit of cooperation offers a sum-rate benefit of order 1/√n

The results extend to a wide range of cooperation levels K

Abstract

The work at hand presents a finite-blocklength analysis of the multiple access channel (MAC) sum-rate under the cooperation facilitator (CF) model. The CF model, in which independent encoders coordinate through an intermediary node, is known to show significant rate benefits, even when the rate of cooperation is limited. We continue this line of study for cooperation rates which are sub-linear in the blocklength $n$. Roughly speaking, our results show that if the facilitator transmits $\log{K}$ bits, there is a sum-rate benefit of order $\sqrt{\log{K}/n}$. This result extends across a wide range of $K$: even a single bit of cooperation is shown to provide a sum-rate benefit of order $1/\sqrt{n}$.