On the sum-capacity of Gaussian MAC with peak constraint

This paper addresses a two-user Gaussian Multiple Access Channel (MAC) under peak constraints at the transmitters. It is shown that generating the code-books of both users according to discrete distributions achieves the largest sum-rate in the network. In other words, sum-capacity achieving input distributions for this channel are discrete with a finite number of mass points. We also demonstrate uniqueness of the input distributions which achieve rates at any of the corner points of the capacity region of the channel.