Variable-Length Stop-Feedback Codes With Finite Optimal Decoding Times for BI-AWGN Channels

Abstract

In this paper, we are interested in the performance of a variable-length stop-feedback (VLSF) code with m optimal decoding times for the binary-input additive white Gaussian noise (BI-AWGN) channel. We first develop tight approximations on the tail probability of length-n cumulative information density. Building on the work of Yavas et al., we formulate the problem of minimizing the upper bound on average blocklength subject to the error probability, minimum gap, and integer constraints. For this integer program, we show that for a given error constraint, a VLSF code that decodes after every symbol attains the maximum achievable rate. We also present a greedy algorithm that yields possibly suboptimal integer decoding times. By allowing a positive real-valued decoding time, we develop the gap-constrained sequential differential optimization (SDO) procedure. Numerical evaluation shows that the gap-constrained SDO can provide a good estimate on achievable rate of VLSF codes with m optimal decoding times and that a finite m suffices to attain Polyanskiy's bound for VLSF codes with m = ∞.