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Computer Engineering and Applications Journal

The Construction of Quasi-cyclic LDPC Codes and its Simulation Performance

Jingdong Zhong, Liang Zhao

Published Jan 1, 2006• 3 citations
OpenAlex

Abstract

论文研究了准循环LDPC码的构造方法,并对其译码性能进行了仿真.结果表明,准循环LDPC码在中短码时具有很强的纠错能力,性能接近目前与其长度相仿的最好的LDPC码,且编译码简单,易于实现,因而具有广阔的应用前景.

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设计的一条改进欧几里德几何学的几何学途径伪周期(质量管理) 有高率、低的错误地板的低密度的同等值检查(LDPC ) 代码被论述。构造 QC-LDPC 代码与高率比原来的代码有更低的错误地板。最小的重量 codeword 的分发被分析，并且最小的重量 codeword 的一个足够的存在条件被发现。很多 QC-LDPC 与更低的错误地板编码的模拟表演能被减少最小的重量 codewords 的数字设计令人满意这个足够的条件。
This paper presents a construction method of quasi-cyclic non-binary low density parity-check(NB-LDPC)code based on the finite field three-dimensional construction.After construction of base matrix based on the finite field,a cyclic matrix is constructed with the method of three-dimensional extension.Finally,non-binary parity check matrix with quasi-cyclic feature is constructed.Compared with the GF(29)-based RS(511,305)and NB-LDPC code constructed by the three-dimensional construction can increase 3.3dB net code gain(NCG)at the bit error rate(BER)of 10-7.Compared with the binary QC-LDPC codes constructed by the traditional way,the binary LDPC codes randomly constructed,the32-ary QC-LDPC codes constructed based on finite fields and the 64-ary cyclic LDPC codes constructed based on Euclidean geometry,the NB-LDPC code constructed by the three-dimensional construction can increase 0.56dB,0.56dB,0.03dB and 0.83dB NCGrespectively at the BERof 10-7.Through performance simulation of the NB-LDPC code constructed based on this three-dimensional construction,it shows that such an NB-LDPC code not only has quasi-cyclic feature,conducive to hardware implementation,but also shows better error correction performance in the short code length.
This paper constructs Partially Balanced Incomplete Block Designs (PBIBD) based on finite fields,and uses them to construct regular Low-Density Parity-Check(LDPC) codes.The constructed LDPC codes are free of 4-cycles and with high flexibility for the choosing of the code rate.Further,the paper even constructs QC-LDPC codes with girth at least 8,they can also be quasi-cyclic.Simulation results show that some of the codes can have slightly better performance than random regular LDPC codes over AWGN channel.