Optimality of FDMA in Gaussian Multiple-Access Channels with Non-zero SNR Margin and Gap

This paper investigates the effect of non-zero SNR margin and coding gap on the maximum sum rate and achievable rate region of the Gaussian Multiple-Access Channel (MAC). Frequency-division multiple-access (FDMA) is shown to be the only sum-rate-maximizing scheme for a scalar Gaussian MAC when the margin/gap is not zero. Furthermore, successive decoding is shown to be strictly sub-optimal from a sum rate perspective. With fixed probability-of-error, single-user codes with finite gap are sufficient to achieve the maximum sum rate. The achievable rate region of the scalar Gaussian MAC with non-zero margin/gap is also characterized. Unlike the capacity region of a scalar MAC, the optimal achievable rate region with non-zero margin/gap is not a pentagon. Finally it is shown that when there is non-zero margin/gap, the optimality of the FDMA scheme can be generalized to a Gaussian MAC with inter-symbol interference (ISI).