基于原模图的8环QC-LDPC码构造方法

Construction Method of Girth-8 QC-LDPC Codes Based on theProtograph

摘要:

针对当前准循环低密度奇偶校验(Quasi-Cyclic Low-Density Parity-Check, QC-LDPC)码存在短环及纠错性能不够好的问题,基于原模图提出一种新颖的QC-LDPC码构造方法。该方法选择码长码率可灵活调整的原模图作为基矩阵,再结合具有特殊性质的卢卡斯数列和等差数列,通过原模图的低译码门限和数列的特殊性质,构造校验矩阵环长至少为8,且所需存储空间少,易于硬件实现。仿真结果表明：该方法构造的PLA-QC-LDPC(2400,1200)码与同等码长码率中基于卢卡斯数列和最大公约数(Greatest Common Divisor, GCD)序列的可快速编码的非规则LG-QC-LDPC码、基于素数和乘法表构造的PM-QC-LDPC码以及基于原模图和消除基本陷阱集的非规则PL-QC-LDPC码相比,净编码增益均有一定程度的提高。

Abstract:

In order to solve the problems of the short girth and the insufficient error-correction performance for quasi-cyclic low-density parity-check (QC-LDPC) codes, a novel construction method for QC-LDPC codes based on the protograph is proposed. In this method, the protograph whose code-length and code-rate can be flexibly adjusted is selected as the base matrix, and then the girth-8 of the parity check matrix can be constructed by means of combining with Lucas sequence and arithmetic progression with special properties as well as the low decoding threshold of the protograph and the special properties of the sequence, and the proposed method requires the less storage space and is easy to be implemented in hardware. The simulation results show that compared with the irregular LG-QC-LDPC code based on the Lucas sequence and the greatest common divisor (GCD) sequence, the PM-QC-LDPC code based on the prime number and the multiplication table, and the irregular PL-QC-LDPC code based on the protograph and the eliminating basic trapping sets with the same code-length and code-rate, the net coding gain of the PLA-QC-LDPC (2400, 1200) code constructed by the proposed method is improved to a certain extent.