Output Distributions of Capacity-Achieving Codes for Gaussian Multiple Access Channels

This letter considers communication over the Gaussian multiple access channel (MAC) with multiple sources. A sequence of length-n codes for the Gaussian MAC is said to be capacity-achieving if the codes achieve the sum-rate capacity. It is shown that for any sequence of capacity-achieving codes, the normalized relative entropy between the output distribution resulted from the interaction between the length-n code and the Gaussian MAC, denoted by p Y n , and the n-fold product of the capacity-achieving output distribution p Y *, denoted by p Y * n , converges to zero as the blocklength grows, i.e., 1/n D(p Y n ||p Y * n ) → 0. Applications of the convergence result are also discussed.