The Unbounded Benefit of Encoder Cooperation for the $k$-user MAC

TL;DR

This paper shows that in certain $k$-user MACs, even minimal cooperation can lead to unbounded capacity gains, highlighting the significant potential of encoder cooperation in network communication.

Contribution

It introduces a class of $k$-user MACs where the ratio of capacity gain to cooperation rate becomes infinite as cooperation diminishes, a novel theoretical insight.

Findings

Existence of MACs with unbounded benefit-to-cost ratio

Binary erasure MAC for $k=2$ exemplifies this phenomenon

Gaussian MACs for any $k extgreater{}1$ also demonstrate this property

Abstract

Cooperation strategies allow communication devices to work together to improve network capacity. Consider a network consisting of a $k$-user multiple access channel (MAC) and a node that is connected to all $k$ encoders via rate-limited bidirectional links, referred to as the "cooperation facilitator" (CF). Define the cooperation benefit as the sum-capacity gain resulting from the communication between the encoders and the CF and the cooperation rate as the total rate the CF shares with the encoders. This work demonstrates the existence of a class of $k$-user MACs where the ratio of the cooperation benefit to cooperation rate tends to infinity as the cooperation rate tends to zero. Examples of channels in this class include the binary erasure MAC for $k=2$ and the $k$-user Gaussian MAC for any $k\geq 2$.