Achievable Rate Regions for the Gaussian Broadcast Channel with Fixed Blocklength and Per User Reliability

This paper considers second-order achievable rate regions for two-user, single antenna, static Gaussian Broadcast channels with individual user error constraints. Even though the channel is stochastically degraded, we surprisingly show that the “usual” infinite blocklength superposition order in which the user with the higher Signal to Noise Ratio (SNR) is superimposed on top of the lower SNR user, does not necessarily lead to the largest second-order achievable rates. This suggests that a careful consideration of user requirements, in addition to channel conditions, is required in designing broadcasting schemes with a fixed blocklength and per-user reliability requirements. This form of superposition coding combined with rate splitting gives the largest known second order region, as it also includes “concatenate and code”, the transmission of a single message containing bits intended for both users as a special case.