We revisit the binary adversarial wiretap channel (AWTC) of type II in which an active adversary can read a fraction $r$ and flip a fraction $p$ of codeword bits. The semantic-secrecy capacity of the AWTC II is partially known, where the best-known lower bound is non-constructive, proven via a random coding argument that uses a large number (that is exponential in blocklength $n$) of random bits to seed the random code. In this paper, we establish a new derandomization result in which we match the best-known lower bound of $1-H_2(p)-r$ where $H_2(\cdot)$ is the binary entropy function via a random code that uses a small seed of only $O(n^2)$ bits. Our random code construction is a novel application of pseudolinear codes -- a class of non-linear codes that have $k$-wise independent codewords when picked at random where $k$ is a design parameter. As the key technical tool in our analysis, we provide a soft-covering lemma in the flavor of Goldfeld, Cuff and Permuter (Trans. Inf. Theory 2016) that holds for random codes with $k$-wise independent codewords.

翻译：我们重新审视了II型二进制对抗窃听信道，其中主动攻击者可以读取码字中比例为$r$的比特并翻转比例为$p$的比特。该类信道的语义安全容量部分已知，目前最佳下界是非构造性的，通过随机编码论证获得，该论证使用了指数级（随码长$n$指数增长）的随机比特来生成随机码。本文建立了一个新的去随机化结果，通过仅使用$O(n^2)$比特小种子的随机码，匹配了最佳已知下界$1-H_2(p)-r$，其中$H_2(\cdot)$是二元熵函数。我们的随机码构造是伪线性码的新颖应用——这是一类非线性码，随机选取时其码字具有$k$阶独立性质，其中$k$为设计参数。作为分析中的关键技术工具，我们提供了Goldfeld、Cuff和Permuter（《信息论汇刊》2016）风格的软覆盖引理，该引理适用于具有$k$阶独立码字的随机码。