Can Negligible Cooperation Increase Network Capacity? The Average-Error Case

TL;DR

This paper investigates how negligible cooperation via a cooperation facilitator affects the average-error sum-capacity in a multiple access channel, revealing continuity properties that differ from the maximal-error case.

Contribution

It demonstrates that the average-error sum-capacity remains continuous as CF output link capacities approach zero, contrasting with the discontinuity observed in the maximal-error sum-capacity.

Findings

Average-error sum-capacity is continuous at zero CF output link capacity.

Infinite derivative of average-error sum-capacity is not due to discontinuity.

Contrast with maximal-error sum-capacity behavior.

Abstract

In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as sum-rate. This work studies encoder cooperation in the setting of a discrete multiple access channel with two encoders and a single decoder. A node in the network that is connected to both encoders via rate-limited links, referred to as the cooperation facilitator (CF), enables the cooperation strategy. Previously, the authors presented a class of multiple access channels where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero. The authors also demonstrated that for some channels, the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work shows that the the average-error sum-capacity is continuous when CF output link capacities converge to zero; that is, the infinite derivative of the average-error sum-capacity is not a result of its discontinuity as in the maximal-error case.