Shoushtari Morteza, Harrison Willie
Department of Electrical and Computer Engineering, Brigham Young University, Provo, UT 84602, USA.
Entropy (Basel). 2023 Oct 17;25(10):1456. doi: 10.3390/e25101456.
Nested linear coding is a widely used technique in wireless communication systems for improving both security and reliability. Some parameters, such as the relative generalized Hamming weight and the relative dimension/length profile, can be used to characterize the performance of nested linear codes. In addition, the rank properties of generator and parity-check matrices can also precisely characterize their security performance. Despite this, finding optimal nested linear secrecy codes remains a challenge in the finite-blocklength regime, often requiring brute-force search methods. This paper investigates the properties of nested linear codes, introduces a new representation of the relative generalized Hamming weight, and proposes a novel method for finding the best nested linear secrecy code for the binary erasure wiretap channel by working from the worst nested linear secrecy code in the dual space. We demonstrate that our algorithm significantly outperforms the brute-force technique in terms of speed and efficiency.
嵌套线性编码是无线通信系统中广泛使用的一种技术，用于提高安全性和可靠性。一些参数，如相对广义汉明重量和相对维度/长度分布，可以用来表征嵌套线性码的性能。此外，生成矩阵和校验矩阵的秩特性也可以精确地表征它们的安全性能。尽管如此，在有限码长情况下找到最优的嵌套线性保密码仍然是一个挑战，通常需要采用暴力搜索方法。本文研究了嵌套线性码的性质，引入了相对广义汉明重量的一种新表示，并提出了一种新颖的方法，通过从对偶空间中最差的嵌套线性保密码开始寻找用于二元擦除窃听信道的最佳嵌套线性保密码。我们证明，我们的算法在速度和效率方面明显优于暴力技术。
