Achievable Second-Order Asymptotics for MAC and RAC With Additive Non-Gaussian Noise

We first study the two-user additive noise multiple access channel (MAC) where the noise distribution is arbitrary. For such a MAC, we use spherical codebooks and either joint nearest neighbor (JNN) or successive interference cancellation (SIC) decoding. Under both decoding methods, we derive second-order achievable rate regions and compare the finite blocklength performance between JNN and SIC decoding. Our results indicate that although the first-order rate regions of JNN and SIC decoding are identical, JNN decoding has better second-order asymptotic performance. When specialized to the Gaussian noise, we provide an alternative achievability proof to the result by MolavianJazi and Laneman (T-IT, 2015). Furthermore, we generalize our results to the random access channel (RAC) where neither the transmitters nor the receiver knows the user activity pattern. We use spherical-type codebooks and a rateless transmission scheme combining JNN/SIC decoding and derive second-order achievability bounds. Comparing second-order achievability results of JNN and SIC decoding in a RAC, we show that JNN decoding achieves a strictly larger first-order asymptotic rate. When specialized to Gaussian noise, our second-order asymptotic results recover the corresponding results of Yavas, Kostina, and Effros (T-IT, 2021) up to second-order.