卫星激光通信中基于Fibonacci数列与GCD序列的非规则QC-LDPC码构造方法

为提高卫星激光通信系统的可靠性，节约其硬件资源，提出一种基于斐波那契(Fibonacci)数列与最大公约数(GCD)序列的非规则准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity-Check, QC-LDPC)码构造方法。该方法通过由Fibonacci数列与GCD序列组合构造的循环移位矩阵扩展原模图基矩阵，从而得到校验矩阵。所构造的校验矩阵围长至少为6且码长码率可灵活选择，需存储元素少，利于硬件实现，较适用于卫星激光通信系统。仿真结果表明，采用该方法构造的非规则QC-LDPC码与相同码率码长的基于完备差集的非规则Type-I QC-LDPC码、基于消除陷阱集的有限长度非规则FL-QC-LDPC码、基于GCD可快速编译的非规则GL-QC-LDPC码以及基于矩阵扩展的非规则RC-LDPC码相比，其净编码增益均有一定提高。

A Construction Method of QC-LDPC Codes Based on Fibonacci Sequence and GCD Sequence for Satellite Laser Communications

A novel construction method of the irregular quasi-cyclic low-density parity-check (QC-LDPC) based on Fibonacci and greatest common divisor (GCD) is proposed to improve the reliability of the satellite laser communication systems and save the hardware resources of the satellite laser communication system. The construction method expands the protograph basic matrix by means of the cyclic shift matrix constructed by the combination of the Fibonacci sequence and GCD sequence to obtain the parity check matrix. The girth of the constructed parity check matrix is at least 6 and the code length and rate can flexibly be selected. It requires the less storage element, which is beneficial to the hardware implementation. Therefore, the novel construction method can better be suitable for satellite laser communication systems. The simulation results show that compared with the irregular type-I QC-LDPC code based on the complete difference sets, the finite-length irregular FL-QC-LDPC code based on the elimination of the trapping sets, the fast-compiled irregular GL-QC-LDPC code based on the GCD and the irregular RC-LDPC code based on the matrix expansion with the same code-rate and code-length, the net coding gain of the irregular QC-LDPC code constructed by this novel construction method can be improved to a certain extent.