Can Negligihle Cooperation Increase Capacity? The Average-Error Case

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. Index TermsContinuity, cooperation facilitator, edge removal problem, maximal-error capacity region, multiple access channel.

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

“…In the above theorem, dividing both sides of (3) by h and letting h → 0 + results in the next corollary. 2 Corollary IV.1. For any MAC in C * and any…”

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

“…We study the CF model for 2-user MACs under the average error criterion. In this setting, the maximal sum-rate is a continuous function of R OUT at R OUT = 0 [6], [7], implying a first-order upper-bound on the benefit of cooperation for rates that are sub-linear. However, sub-linear CF cooperation may still increase sum-rate, albeit through second-order terms.…”