In the literature, it has been shown that the secrecy capacity of the additive white Gaussian noise (AWGN) wiretap channel with noise-free feedback equals the capacity of the same model without secrecy constraint, and the classical Schalkwijk-Kailath (SK) scheme achieves the secrecy capacity. In this paper, we show that in finite blocklength regime, the SK scheme is not optimal, and propose a modified SK scheme which may perform better than the classical one. Besides this, this paper establishes a finite blocklength converse for the AWGN wiretap channel with feedback, which can also be viewed as a converse for the same model without secrecy constraint. To the best of the authors' knowledge, this is the first paper to address such a problem, and the results of this paper are further explained via numerical examples.

翻译：现有文献表明，具有无噪声反馈的加性高斯白噪声（AWGN）窃听信道的保密容量等于无保密约束下同一模型的信道容量，且经典的Schalkwijk-Kailath（SK）方案能够达到该保密容量。本文证明在有限码长条件下，SK方案并非最优，并提出一种改进的SK方案，其性能可能优于经典方案。此外，本文建立了具有反馈的AWGN窃听信道的有限码长逆定理，该结论亦可视为无保密约束下同一模型的逆定理。据作者所知，本文是首篇探讨该问题的论文，并通过数值算例进一步阐释了相关结果。