Uncoordinated rate selection: Approaching the capacity of Gaussian MAC without coordination

The achievable rate region of a K-user Gaussian multiple access channel (GMAC) is well known. Several schemes have been proposed to achieve some points in this region with minimal encoding and decoding complexities such as successive interference cancelation and successive integer forcing. But these schemes require coordination among the nodes or with the base station for choosing the rates of transmission. In this paper, we propose an uncoordinated scheme in which each node picks the rate randomly according to a predetermined probability distribution, independently of the other nodes. We show that in the asymptotic limit as K → ∞, the sumrate achieved by this uncoordinated scheme is only Θ(log logK) away from the sum capacity of GMAC. When an energy constraint is considered instead of a power constraint, we show that our scheme is optimal.