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 \emph{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 $m = \infty$.

翻译：在本文中,我们感兴趣的是,对于二进制添加添加添加的白色高斯噪音(BI-AWGN)频道,如何用美元最优的解码时间对二进制添加添加的白色高索尼噪音(BI-AWGN)频道使用以美元为最佳解码时间的可变长阻截回(VLSF)代码。我们首先在长-美元累积信息密度的尾概率(长度-美元累积信息密度)上制定紧近的近似值。根据Yavas \ emph{et al.}的工作,我们提出了在受差错概率、最小差距和整数限制的情况下,在平均区段长度内最大限度地减少上限值(VLSF)的问题。对于这个整数程序,我们显示对于一个给定的错误限制,一个在每一个符号达到最高可实现的速率之后解码的VLSF代码。我们还提出一种贪婪的算算法,可以产生低于最优化的整数的解码时间。我们还提出一种能用美元来达到软的拼码。