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中国邮电高校学报：英文版

Quasi-cyclic LDPC codes with high-rate and low error floor based on Euclidean geometries

LIUYluan-hua, ZHANGMei-ling, FANJiu-lun

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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。

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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 letter presents an approach to the construction of multiple-rate quasi-cyclic (QC) low-density parity-check (LDPC) codes based on hyperplanes (μ-flats) of two different dimensions in Euclidean geometries. The codes constructed with this method have the same code length, multiple-rate and large stopping sets while maintaining the same basic hardware architecture. The code performance is investigated in terms of the bit error rate (BER) and compared with those of the LDPC codes which are proposed in IEEE 802.16e standard. Simulation results show that our codes perform very well and have low error floors over the AWGN channel.
A new method for constructing quasi-cyclic (QC) low-density parity-check (LDPC) codes based on the structural properties of Euclidean geometries is presented. The proposed method changes the incidence vectors of some lines in the original Euclidean geometry method to construct much more parity check matrices and results in a large class of QC-LDPC codes with girth of at least 6. Simulations show that some codes in this class have better performance and lower error floor than the original Euclidean geometry codes.
Presented in this paper is a reduced-complexity iterative decoding scheme for quasi-cyclic (QC) LDPC codes. This decoding scheme is devised based on the section-wise cyclic structure of the parity-check matrix of a QC-LDPC code. Using this decoding scheme, the hardware implementation complexity of a QC-LDPC decoder can be significantly reduced without performance degradation. A high-rate QC-LDPC code that can achieve a very low error-rate without a visible error-floor is used to demonstrate the effectiveness of the proposed decoding scheme. Also presented in this paper are two other high-rate QC-LDPC codes and a method for constructing rate -1/2 QC-LDPC codes whose Tanner graphs have girth 8. All the codes constructed perform well with low error-floor using the proposed decoding scheme.
该文设计了一种特殊的高码率准循环低密度校验(QC-LDPC)码,其校验矩阵以单位矩阵的循环移位阵为基本单元,与随机构造的LDPC码相比可节省大量存储单元。利用该码校验矩阵的近似下三角特性,一种高效的递推编码方法被提出,它使得该码编码复杂度与码长成线性关系。另外,该文提出一种分析QC-LDPC码二分图中短长度环分布情况的方法,并且给出了相应的不含长为4环QC-LDPC码的构造方法。计算机仿真结果表明,新码不但编码简单,而且具有高纠错能力、低误码平层。