一种类Raptor多速率QC-LDPC码的代数构造方法

doi:10.19665/j.issn1001-2400.2022.01.013

西安电子科技大学学报 ›› 2022, Vol. 49 ›› Issue (1): 134-141.doi: 10.19665/j.issn1001-2400.2022.01.013

一种类Raptor多速率QC-LDPC码的代数构造方法

李华安¹(),白宝明¹(),徐恒舟²(),陈超¹()

1.西安电子科技大学综合业务网理论及关键技术国家重点实验室,陕西西安 710071
2.周口师范学院网络工程学院,河南周口 466001

收稿日期:2021-01-19 出版日期:2022-02-20 发布日期:2022-04-27
通讯作者: 白宝明
作者简介:李华安(1989—),男,西安电子科技大学博士研究生,E-mail: liha16@stu.xidian.edu.cn;|徐恒舟(1987—),男,副教授,博士,E-mail: hzxu@zknu.edu.cn;|陈超(1981—),男,副教授,博士,E-mail: cchen@xidian.edu.cn
基金资助:
国家自然科学基金(61771364);国家自然科学基金(61801527);国家自然科学基金数学天元基金(12026231);国家自然科学基金数学天元基金(12026230);河南省科技攻关项目(212102310544);陕西省教育厅专项科研计划(20JK0918)

Algebraic method for constructing Raptor-like multi-rate QC-LDPC codes

LI Hua'an¹(),BAI Baoming¹(),XU Hengzhou²(),CHEN Chao¹()

1. State Key Laboratory of Integrated Service Networks,Xidian University,Xi'an 710071,China
2. School of Network Engineering,Zhoukou Normal University,Zhoukou 466001,China

Received:2021-01-19 Online:2022-02-20 Published:2022-04-27
Contact: Baoming BAI

摘要/Abstract

摘要：

变速率低密度校验码是一类可支持不同码率的码,在实际通信中具有非常重要的应用。常见的变速率低密度校验码主要有两种:码长固定的多速率低密度校验码以及信息位长度固定的速率兼容低密度校验码。结合代数和叠加构造方法,通过渐进改变移位尺寸,提出了一种类Raptor多速率准循环低密度校验码的构造方法。基于该方法,随着码率减小,所构造的低密度校验码的基矩阵/循环移位矩阵的大小增大,移位尺寸变小。为了获得固定码长和匹配不同信息位长度,还引入了信息位缩短和校验位打孔操作。所构造的码同时具有准循环结构和类Raptor结构,易于硬件实现编译码器和校验矩阵可直接编码,而且循环移位矩阵具有明显的代数结构,存储复杂度极低。数值仿真结果表明,与一些标准低密度校验码相比,所构造的码具有较好的整体性能。这为未来地面网络与近地卫星等通信系统的编码融合研究提供了一种候选方案。

关键词: 低密度校验码, 类Raptor, 多速率, 代数构造

Abstract:

Variable-rate low-density parity-check (LDPC) codes are one class of codes with various code rates and play an important role in most communication systems.Two representatives of such codes are multi-rate LDPC (MR-LDPC) codes with a constant codeword length and rate-compatible LDPC codes with a constant information length.Combining algebraic and superposition construction methods,this paper studies the design and construction of the Raptor-like multi-rate quasi-cyclic LDPC codes by progressively adjusting the lifting sizes for different code rates.Based on the proposed method,with the decrease in code rate,the sizes of the base matrix and exponent matrix of the constructed codes become large while the lifting sizes are reduced.Besides,to achieve a constant codeword length and various information lengths,both shortening of information bits and puncturing of parity bits are considered.Resulting codes simultaneously own quasi-cyclic and Raptor-like structures,so that the corresponding encoder/decoder can be easily implemented by hardware and the encoding can also be done directly based on the parity-check matrix.Moreover,exponent matrices of the constructed codes have a specific algebraic structure,and thus the storage complexity is very low.Numerical results show that,compared to some standard codes,e.g.,WiMAX LDPC codes,the constructed codes can obtain a better overall performance,which can provide a promising scheme for the coding method fusion design of the future ground network and other communication systems.

Key words: low-density parity-check codes, Raptor-like, multi-rate, algebraic construction

中图分类号:

TN911.22

李华安,白宝明,徐恒舟,陈超. 一种类Raptor多速率QC-LDPC码的代数构造方法[J]. 西安电子科技大学学报, 2022, 49(1): 134-141.

LI Hua'an,BAI Baoming,XU Hengzhou,CHEN Chao. Algebraic method for constructing Raptor-like multi-rate QC-LDPC codes[J]. Journal of Xidian University, 2022, 49(1): 134-141.

图/表 5

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一种类Raptor多速率QC-LDPC码的代数构造方法

Algebraic method for constructing Raptor-like multi-rate QC-LDPC codes

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码率	矩阵大小	移位尺寸	信息位缩短位数	校验位打孔位数
1/2	18×34	31	16	16
2/3	10×26	41	16	8
5/6	6×22	53	48	52