QC-LDPC Code Hopping Design for Physical Layer Information Security
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School of Communication Engineering, Army Engineering University of PLA, Nanjing 210007, China
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摘要:
低密度奇偶校验(Low density parity check, LDPC)跳码可以在物理层基于跳变的校验矩阵进行差错控制编译码。准循环低密度奇偶校验码(Quasi-cyclic low density parity check code, QC-LDPC)因其良好的纠错性能和易于工程实现的优点而得到广泛应用。本文提出了一种简单且易于工程实现的QC-LDPC跳码设计方法。首先采用有限域的两类子群设计跳变的基矩阵,再通过基模图码的外信息转移算法对基矩阵散列的校验矩阵进行掩模,使跳变矩阵具有统一架构和快速编码结构。仿真和分析表明,设计的QC-LDPC跳码具有超大的跳变码集和良好的纠错性能,码集中LDPC码数目可达1034个,随着码长增加,码集中的LDPC码数目呈指数倍增加,其平均性能可与诸多协议中的LDPC码相当,可用于提升通信系统的可靠性和安全性。
Abstract:
Low density parity check (LDPC) code hopping can improve the security and reliability of information transmission through error control coding based on the hopping check matrix at the physical layer. Quasi-cyclic low density parity check code (QC-LDPC) is widely used because of its good error correction performance and easy engineering implementation. This paper proposes a QC-LDPC code hopping design method. Firstly two kinds of subgroups in finite field are used to design the hop-basis matrix, and then the check matrix of the hashed basis matrix is masked by the protograph-based external information transfer (PEXIT), so that the hop matrix has a unified architecture and a fast coding structure, which is easy to implement in engineering. Simulation and analysis show that the designed QC-LDPC codehopping has a huge code hopping set and good error-correcting performance. The number of LDPC codes in a code hopping set can be up to 1034. With the increase of code length, the number of LDPC codes in a code hopping set increases exponentially, and the average performance of LDPC codes is comparable to that of many protocols. It can be used to improve the reliability and security of the communication system.
图1 传统加密编码图Fig.1 Code diagram for traditional encryption
图2 物理层联合编码加密Fig.2 Physical layer code encryption
图3 通信质量图Fig.3 Communication quality chart
图4 基模图示例Fig.4 Example protograph
图5 基模图扩展后得到的Tanner图示例Fig.5 Extend Tanner graph
图6 跳码设计流程图Fig.6 Flow chart of code hopping design
图7 跳码编码架构图Fig.7 Architecture diagram of code hopping coding
图8 跳码性能曲线图Fig.8 Code hopping performance
图9 单短阵性能对比图Fig.9 Comparison diagram of single matrix performance
图10 窃听方和合法通信方性能对比图Fig.10 Performance comparison between eavesdropper and legitimate communicator