物理层安全下二元随机线性码的伴随编码构造算法研究

Research on Construction of Binary Random Linear Code for Syndrome Coding in Physical Layer Security

在利用伴随编码提升系统安全性方面,现有研究多是从改善系统结构、增大信道差异性角度出发的,而如何从码本身的特性入手,进行物理层安全码的设计是迫切而必要的。本文提出了一类物理层安全中二元随机线性码的伴随编码算法。基于系统安全性的分析,推导了窃听方疑义度公式。基于伴随编码的基本思想,对码的一致校验矩阵进行构造,提出了一种基于最小距离优化的码构造算法,使得在扩展校验矩阵的同时,码的最小距离可以达到可取的最大值。仿真结果表明:与同码长、码率的最佳线性码(Best Known Code,BKC)以及最佳疑义度码(Best Equivocation Code,BEC)相比,所提算法构造的码具有更好的安全性,且在算法效率方面也明显优于BEC码。

In the aspects of increasing system security by syndrome coding,extant research aims at improving system structure and increasing channel difference. However,it is urgent and necessary to design a kind of secure code by using characteristics of the code itself. This paper proposed an algorithm of syndrome coding of binary random linear codes with physical layer security. Based on the analysis of system security,we deducted the formula of the wiretap＇s equivocation. Based on the basic idea of syndrome coding,we constructed the parity check matrix of the code and proposed a construction algorithm on consider of minimum distance optimization. The algorithm guarantees the minimum distance of the code reaching the biggest during the extension of parity check matrix. The simulation results show that compared with Best Known Code（BKC）and Best Equivocation Code（BEC） of same length and rate,the newly constructed code by this paper provides better security. It is also superior to BEC code from the aspect of efficiency of algorithm.