In a classical wiretap channel setting, Alice communicates with Bob through a main communication channel, while her transmission also reaches an eavesdropper Eve through a wiretap channel. In this paper, we consider a general class of polar secrecy codes for wiretap channels and study their finite-length performance. In particular, bounds on the normalized mutual information security (MIS) leakage, a fundamental measure of secrecy in information-theoretic security frameworks, are presented for polar secrecy codes. The bounds are utilized to characterize the finite-length scaling behavior of polar secrecy codes, where scaling here refers to the non-asymptotic behavior of both the gap to the secrecy capacity as well as the MIS leakage. Furthermore, the bounds are shown to facilitate characterizing numerical bounds on the secrecy guarantees of polar secrecy codes in finite block lengths of practical relevance, where directly calculating the MIS leakage is in general infeasible.

翻译：在经典窃听信道场景中，Alice通过主通信信道与Bob通信，同时其传输也会通过窃听信道被窃听者Eve接收。本文研究适用于窃听信道的一类广义极化保密码，并分析其有限长度性能。具体而言，我们针对极化保密码提出了归一化互信息安全（MIS）泄露量的界，该指标是信息论安全框架中保密性的基本度量。这些界被用于刻画极化保密码的有限长度标度特性，此处的标度特性指代保密容量差距与MIS泄露量两者的非渐近行为。进一步地，我们证明这些界有助于表征极化保密码在实际相关的有限块长下的保密性数值界，而在该场景下直接计算MIS泄露量通常不可行。