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

The work at hand presents a finite-blocklength analysis of the multiple access channel (MAC) sum-rate under the cooperation facilitator (CF) model. The CF model, in which independent encoders coordinate through an intermediary node, is known to show significant rate benefits, even when the rate of cooperation is limited. We continue this line of study for cooperation rates which are sub-linear in the blocklength n. Roughly speaking, our results show that if the facilitator transmits log K bits, then there is a sum-rate benefit of order √log K/n compared to the best-known achievable rate. This result extends across a wide range of K: even a single bit of cooperation is shown to provide a sum-rate benefit of order 1/√n.