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.

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

“…Similarly, in [4], [7], an analog to Lemma 2 is shown for asymptotic blocklength. Specifically, it is shown that the existence of distributions p X1 p X2 ∈ P and p X1 X2 over X 1 × X 2 such that (a) the support of p X1 X2 is included in that of p X1 p X2 , and (b)…”

“…In [4], an analog to Theorem 3 is proven for the asymptotic blocklength regime. Namely, in our notation, [4] proves that for any > 0 and δ > 0, if we set K = 2 Ω(n) then there exist n such that,…”

“…, so for sufficiently large n, (5)-( 6) are easily satisfied. It remains to prove (4). Let p e be the probability in (4).…”

“…Although Theorem 3 and Lemma 2 (and their proof techniques) are similar in nature to those of [4], [7], the analysis presented here is refined in that it captures higher order behavior in blocklength n and further optimized to address the challenges in studying values of K that are sub-exponential in the blocklength n.…”

“…The CF distinguishes the amount of information that must be understood to facilitate cooperation (i.e., the rate R IN to the CF) from the amount of information employed in the coordination (i.e., the rate R OUT from the CF). Key results using the CF model show that for many MACs, no matter what the (non-zero) fixed rate C IN , the curve describing the maximal sum-rate as a function of R OUT has infinite slope at R OUT = 0 [4]. That is, very little coordination through a CF can change the MAC capacity considerably.…”