A Finite Blocklength Analysis of Unequal Bit Protection for the AWGN Channel

In classical capacity analysis for point-to-point (P2P) channels, all transmitted data is equally protected. Transmitted data will be recovered if and only if transmitted at a rate below the channel's capacity. When a P2P channel is studied in the Finite Blocklength (FBL) regime the inclusion of a reliability term suggests the possibility of constructing codes that protect portions of the data differently. In this paper, we present an FBL achievable bound for the utilization of superposition (SUP) coding with successive interference cancellation (SIC) in the realization of Unequal Bit Protection (UBP) in transmission over a static, scalar additive white Gaussian noise (AWGN) channel. We also present a converse bound for the problem. Through our numerical analysis we show that in cases where data to be transmitted has known and differing reliability requirements, the use of superposition coding can increase the achievable sum rate of transmission of all classes of data protection over a uniform protection coding scheme and orthogonalization over time. However, the (SUP-SIC) achievable region and converse are not tight, and the FBL UBP capacity remains an open problem.