Negligible Cooperation: Contrasting the Maximal- and Average-Error Cases

TL;DR

This paper compares the effects of encoder cooperation via a cooperation facilitator on the maximal- and average-error sum-capacities in a multiple access channel, revealing that small cooperation can significantly improve maximal-error capacity but not average-error capacity.

Contribution

It demonstrates that minimal cooperation can substantially enhance maximal-error sum-capacity, whereas even increasing cooperation yields negligible gains in average-error sum-capacity.

Findings

Small bits of cooperation significantly improve maximal-error capacity.

Large or growing cooperation does not notably increase average-error capacity.

Contrasts the impact of cooperation on maximal- and average-error regimes.

Abstract

In communication networks, cooperative strategies are coding schemes where network nodes work together to improve network performance metrics such as the total rate delivered across the network. This work studies encoder cooperation in the setting of a discrete multiple access channel (MAC) with two encoders and a single decoder. A network node, here called the cooperation facilitator (CF), that is connected to both encoders via rate-limited links, enables the cooperation strategy. Previous work by the authors presents two classes of MACs: (i) one class where the average-error sum-capacity has an infinite derivative in the limit where CF output link capacities approach zero, and (ii) a second class of MACs where the maximal-error sum-capacity is not continuous at the point where the output link capacities of the CF equal zero. This work contrasts the power of the CF in the maximal- and average-error cases, showing that a constant number of bits communicated over the CF output link can yield a positive gain in the maximal-error sum-capacity, while a far greater number of bits, even numbers that grow sublinearly in the blocklength, can never yield a non-negligible gain in the average-error sum-capacity.