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

We derive a second-order achievability bound for the two-user multiple access channel with additive non-Gaussian noise. In our setting, both users use spherical codebooks and the decoder uses the nearest neighbor decoding. Our result generalizes the dispersion analysis for point-to-point mismatched channel coding by Scarlett, Tan and Durisi (TIT 2017) to the multiple user setting. When specialized to the Gaussian noise, our proof provides an alternative second-order achievability analysis of MolavianJazi and Laneman (TIT, 2015). Furthermore, we generalize our results to the random access channel with additive non-Gaussian noise, where the number of active users in each time slot are unknown, and derive a second-order achievability bound. When specialized to the Gaussian noise, our second-order asymptotic results are consistent with the Gaussian noise case recently derived by Yavas, Kostina and Effros (TIT, 2021).