We study the performance of polarizing codes over a degraded symmetric wiretap channel under a total variation distance (TVD) secrecy constraint. We show that the leakage can be bounded by the sum of the TVDs of the bit-channels corresponding to the confidential and frozen bits. In the asymptotic regime, this gives a new criterion to design wiretap codes with vanishing TVD leakage. In finite blocklength, it allows us to compute lower bounds for the secrecy rate of different families of polarizing wiretap codes over a binary erasure wiretap channel.

翻译：我们研究了退化对称窃听信道中，在全变差距离（TVD）保密约束下极化码的性能。我们证明，窃听泄漏量可由对应保密比特与冻结比特的比特信道的全变差之和来界定。在渐近条件下，这为设计具有零全变差泄漏的窃听码提供了新准则；在有限块长下，则允许我们计算二进制擦除窃听信道上不同极化窃听码族的保密率下界。