The Unbounded Benefit of Encoder Cooperation for the k-User MAC

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 ≥ 2. Index TermsConferencing encoders, cooperation facilitator, cost constraints, edge removal problem, multiple access channel, multivariate covering lemma, network information theory.

The benefit of encoder cooperation in the presence of state information

“…In cooperative strategies, various network nodes work together towards a common goal. Previous work [1] shows that under a model of cooperation that incorporates a "cooperation facilitator" (CF)-a node that receives ratelimited information from the encoders of a multiple access channel (MAC) and sends rate-limited information back-even a very low rate cooperation between the MAC encoders can vastly increase the total rate that can be delivered through the MAC. In fact, if we measure cost as the number of bits the CF shares with the encoders and the benefit as the gain in sum-capacity, then for some MACs, the cost-benefit curve has infinite slope in the limit of low cost.…”

“…In fact, if we measure cost as the number of bits the CF shares with the encoders and the benefit as the gain in sum-capacity, then for some MACs, the cost-benefit curve has infinite slope in the limit of low cost. This paper extends the exploration of cooperation beyond the networks of [1] to examine the cost-benefit tradeoff of cooperation in networks where state information is present at some nodes.…”

“…On the other hand, when the state sequence M. Langberg is with the State University of New York at Buffalo, Buffalo, NY 14260 USA (email: mikel@buffalo.edu). 1 models a signal that the transmitter sends to another receiver, then the state sequence is available non-causally at the transmitter [6].…”

“…Here we study cooperation under the CF model. In this model, encoders cooperate indirectly as in [1], rather than directly, as in [8]. The CF enables both message and state cooperation; this proves crucial to the cooperation gain obtained through a CF, which we next describe in more detail.…”

“…In earlier work [1], we exhibit single-letter conditions on the channel transition matrix of the MAC which guarantee an infinite slope in sum-capacity as a function of the capacities of the CF output edges; the additive Gaussian MAC [10, p. 544] is an important example of a scenario where the infinite slope phenomenon occurs. In this work, we characterize channels for which the cooperation gain has an infinite slope in the presence of state information (Section IV); interestingly, this includes channels for which the infinite slope phenomenon did not arise in the absence of state information.…”