Second-order Asymptotics for Asymmetric Broadcast Channel with non-Gaussian Noise

We study the two-user asymmetric broadcast channel with additive non-Gaussian noise and derive a second-order achievability rate region when separate error probabilities constraints are imposed on users. Specifically, we use spherical codebooks for both users. The weak user with worse channel quality applies nearest neighbor decoding while treating the signal of the other user as interference. For the strong use with better channel quality, we consider two decoding schemes: successive interference cancellation (SIC) decoding and joint nearest neighbor (JNN) decoding. Counter-intuitively, the achievable second-order rate regions under both SIC and JNN decoding are identical although JNN decoding usually yields better performance in other multiterminal problems with Gaussian noise. Our achievability results also hold for the symmetric broadcast channel where each user decodes one message.