Deterministic Construction of QC-LDPC Codes for Any Column Weight with a Large Girth

doi:10.3969/j.issn.0372-2112.2016.08.006

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Deterministic Construction of QC-LDPC Codes for Any Column Weight with a Large Girth

更新时间：2025-07-08

- Deterministic Construction of QC-LDPC Codes for Any Column Weight with a Large Girth
- Acta Electronica Sinica Vol. 44, Issue 8, Pages: 1814-1819(2016)
- 作者机构：
  
  空军工程大学信息与导航学院,陕西,西安,710077
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61271250)
- DOI：10.3969/j.issn.0372-2112.2016.08.006
  CLC： TN911.22
- Published Online：25 August 2016，
  
  Published：2016
- 稿件说明：
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Deterministic Construction of QC-LDPC Codes for Any Column Weight with a Large Girth[J]. Acta Electronica Sinica, 2016, 44(8): 1814-1819.
DOI：

Deterministic Construction of QC-LDPC Codes for Any Column Weight with a Large Girth[J]. Acta Electronica Sinica, 2016, 44(8): 1814-1819. DOI： 10.3969/j.issn.0372-2112.2016.08.006.

摘要

针对准循环低密度奇偶校验（Quasi-Cyclic Low-Density Parity-Check，QC-LDPC）码中准循环基矩阵的移位系数确定问题，提出基于等差数列的确定方法.该方法构造的校验矩阵围长为8，列重可任意选取，移位系数由简单的数学表达式确定，编码复杂度与码长呈线性关系，节省了编解码存储空间.研究结果表明，列重和围长是影响码字性能的重要因素.在加性高斯白噪声（Additive White Gauss Noise，AWGN）信道和置信传播（Belief Propagation，BP）译码算法下，该方法构造的码字在短码时可以获得与IEEE 802.11n、802.16e码相一致的性能，在长码时误比特率性能接近DVB-S2码.同时表明该方法对码长和码率参数的设计具有较好的灵活性.

Abstract

To cope with the issue of determining cyclic shift coefficients of the quasi-cyclic sub-matrix in the Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes

a method was presented based on the arithmetic progression to compute the cyclic shift coefficients.By this method

a class of girth eight QC-LDPC codes for any column weight is obtained

and the cyclic shift coefficients can be expressed in simple analytic expressions to reduce required memory usage.Meanwhile

the encoding complexity is linearly proportional to code length due to the lower triangular parity matrix.The simulation result shows that column weight and girth have important influences on code performance.Furthermore

over an Additive White Gauss Noise (AWGN) channel and under the Belief Propagation (BP) decoding algorithm

the simulation results represent that bit error rate of the proposed QC-LDPC codes is no less than the LDPC codes in IEEE 802.11n and 802.16e with short code length

and is close to the LDPC codes in DVB-S2 with long code length.Moreover

the study result also confirms that the proposed algorithm has high flexibility with respect to the design of code length and rate.

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