In this paper, we use a linear programming (LP) optimization approach to evaluate the equivocation for a wiretap channel where the main channel is noiseless, and the wiretap channel is a binary symmetric channel (BSC). Using this technique, we present an analytical limit for the achievable secrecy rate in the finite blocklength regime that is tighter than traditional fundamental limits. We also propose a secrecy coding technique that outperforms random binning codes. When there is one overhead bit, this coding technique is optimum and achieves the analytical limit. For cases with additional bits of overhead, our coding scheme can achieve equivocation rates close to the new limit. Furthermore, we evaluate the patterns of the generator matrix and the parity-check matrix for linear codes and we present binning techniques for both linear and non-linear codes using two different approaches: recursive and non-recursive. To our knowledge, this is the first optimization solution for secrecy coding obtained through linear programming.

翻译：本文采用线性规划优化方法评估窃听信道的疑义度，其中主信道为无噪信道，窃听信道为二进制对称信道。基于该技术，我们提出了有限块长下可达保密率的新解析界，该界比传统基本界更为紧凑。同时设计了一种优于随机装箱编码的保密编码技术。当存在一个额外开销比特时，该编码技术达到最优并实现了解析界。对于更多开销比特的情形，所提编码方案可获得接近新界的疑义度。进一步地，我们评估了线性码生成矩阵与校验矩阵的结构特征，并采用递归与非递归两种途径分别给出了线性码与非线性码的装箱方法。据我们所知，这是首个通过线性规划求解保密编码优化问题的方案。