On the second-order cost of TDMA for Gaussian multiple access

Time division multiple access (TDMA) is widely considered to be a practical multi-access communication scheme that can achieve the highest possible sum-rate with appropriate power allocation. Exploring a Gaussian multiple access channel, we show that this result does not carry over to second-order coding rates. In particular, as the number of users grows, the cost of using TDMA is significant relative to the largest known achievable second-order sum-rate for the Gaussian MAC. The latter sum-rate is established by a random coding argument with non-i.i.d. spherical inputs, which is conveniently analyzed via a central limit theorem (CLT) for functions.