基于QR码的广义LDPC码的设计与译码算法的研究

Design of generalized LDPC code based on QR code and research on decoding algorithm

广义低密度奇偶校验(generalized low-density parity-check,GLDPC)码可以降低原始低密度奇偶校验(low-density parity-check,LDPC)码的错误平层,但传统GLDPC码的构造方法会造成码率损失较大。鉴于此,采用平方剩余(quadratic residue,QR)码作为分量码,提出一种新颖的GLDPC码构造方法,并设计相应的译码算法。统计给定码字的陷阱集,并利用陷阱集挑选变量节点作为QR码的信息位;把QR码变量节点的校验位补全在原始LDPC码后,从而构造一种GLDPC码,设计出一种适合GLDPC码的两阶段译码算法。仿真结果表明,这种GLDPC码构造方法码率损失比较小,在BER为1×10^(-9)时,GLDPC码与原始LDPC码相比,得到了约0.3 dB的增益。

Generalized low-density parity-check(GLDPC)codes can reduce the error floor of original low-density parity-check(LDPC)codes.However,the traditional GLDPC code construction method will cause a large loss of code rate.Therefore,this paper uses the quadratic residue(QR)codes as the component code,and proposes a novel GLDPC code construction method.In addition,a corresponding decoding algorithm is designed.First,the trapping sets database is completed and is used to select variable nodes as the information bits of the QR code.Second,the QR code check bits is supplemented after the original LDPC code and a GLDPC code is constructed.Finally,a two-stage decoding algorithm is designed which is suitable for GLDPC codes.Simulation results show that the code rate loss of this GLDPC code construction method is relatively small.Compared with the original LDPC code,the GLDPC code can obtain a gain of about 0.3 dB when the BER is 1×10^(-9).