We consider error-correction coding schemes for adversarial wiretap channels (AWTCs) in which the channel can a) read a fraction of the codeword bits up to a bound $r$ and b) flip a fraction of the bits up to a bound $p$. The channel can freely choose the locations of the bit reads and bit flips via a process with unbounded computational power. Codes for the AWTC are of broad interest in the area of information security, as they can provide data resiliency in settings where an attacker has limited access to a storage or transmission medium. We investigate a family of non-linear codes known as pseudolinear codes, which were first proposed by Guruswami and Indyk (FOCS 2001) for constructing list-decodable codes independent of the AWTC setting. Unlike general non-linear codes, pseudolinear codes admit efficient encoders and have succinct representations. We focus on unique decoding and show that random pseudolinear codes can achieve rates up to the binary symmetric channel (BSC) capacity $1-H_2(p)$ for any $p,r$ in the less noisy region: $p<1/2$ and $r<1-H_2(p)$ where $H_2(\cdot)$ is the binary entropy function. Thus, pseudolinear codes are the first known optimal-rate binary code family for the less noisy AWTC that admit efficient encoders. The above result can be viewed as a derandomization result of random general codes in the AWTC setting, which in turn opens new avenues for applying derandomization techniques to randomized constructions of AWTC codes. Our proof applies a novel concentration inequality for sums of random variables with limited independence which may be of interest as an analysis tool more generally.

翻译：我们研究对抗性窃听信道（AWTC）的纠错编码方案，该信道能够：a) 读取码字中不超过$r$比例的比特位置；b) 翻转不超过$p$比例的比特位置。信道可通过无限计算能力的进程自由选择比特读取和翻转的位置。AWTC编码在信息安全领域具有广泛意义，可在攻击者对存储或传输介质具有有限访问权限的场景中提供数据弹性。本文研究一类称为伪线性码的非线性编码族，该编码由Guruswami和Indyk（FOCS 2001）首次提出，用于构建独立于AWTC场景的列表可译码。与一般非线性码不同，伪线性码支持高效编码器并具有简洁表示。我们聚焦于唯一译码，证明随机伪线性码在较无噪声区域：$p<1/2$且$r<1-H_2(p)$（其中$H_2(\cdot)$为二进制熵函数）中，可达高达二进制对称信道（BSC）容量$1-H_2(p)$的码率。因此，伪线性码是首个已知的、支持高效编码器且对较无噪声AWTC达到最优码率的二进制码族。上述结果可视为AWTC场景中随机一般码的去随机化结论，进而为将去随机化技术应用于AWTC码的随机化构造开辟了新途径。我们的证明应用了针对有限独立性随机变量和的新型浓度不等式，该不等式本身可能具有更广泛的分析工具价值。