Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

Hai Zhu; Liqun Pu; Hengzhou Xu; Bo Zhang

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Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

机译：基于算术基础定理的准循环LDPC代码构建

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Quasi-cyclic (QC) LDPC codes play an important role in 5G communications and have been chosen as the standard codes for 5G enhanced mobile broadband (eMBB) data channel. In this paper, we study the construction of QC LDPC codes based on an arbitrary given expansion factor (or lifting degree). First, we analyze the cycle structure of QC LDPC codes and give the necessary and sufficient condition for the existence of short cycles. Based on the fundamental theorem of arithmetic in number theory, we divide the integer factorization into three cases and present three classes of QC LDPC codes accordingly. Furthermore, a general construction method of QC LDPC codes with girth of at least 6 is proposed. Numerical results show that the constructed QC LDPC codes perform well over the AWGN channel when decoded with the iterative algorithms.

机译：准循环（QC）LDPC码在5G通信中发挥着重要作用，已被选为5G增强移动宽带（eMBB）数据信道的标准码。本文研究了基于任意给定扩展因子（或提升度）的QC-LDPC码的构造。首先，我们分析了QC-LDPC码的循环结构，给出了短循环存在的充要条件。基于数论中的算术基本定理，我们将整数分解分为三种情况，并相应地给出了三类QC-LDPC码。此外，还提出了一种周长至少为6的QC-LDPC码的一般构造方法。数值结果表明，当使用迭代算法解码时，所构造的QC-LDPC码在AWGN信道上表现良好。

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《Wireless communications & mobile computing》 |2018年第1期|共9页
作者
Hai Zhu; Liqun Pu; Hengzhou Xu; Bo Zhang;
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School of Network Engineering Zhoukou Normal University;

School of Mathematics and Statistics Zhengzhou University;

School of Network Engineering Zhoukou Normal University;

School of Network Engineering Zhoukou Normal University;

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正文语种 eng
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1. Construction of Rate-Compatible (RC) Low-Density Parity-Check (LDPC) Convolutional Codes Based on RC-LDPC Block Codes [J] . MU Liwei, HAN Guojun, LIU Zhiyong 上海交通大学学报（英文版） . 2016,第006期
2. Combinatorial design-based quasi-cyclic LDPC codes with girth eight [J] . Sina Vafi, Narges Rezvani Majid 数字通信与网络（英文） . 2018,第004期
3. Quasi-cyclic LDPC codes with high-rate and low error floor based on Euclidean geometries [J] . LIU Yuan-hua, ZHANG Mei-ling, FAN Jiu-lun 中国邮电高校学报（英文版） . 2012,第002期
4. DESIGN OF QUASI-CYCLIC LDPC CODES BASED ON EUCLIDEAN GEOMETRIES [J] . Liu Yuanhua, Niu Xinliang, Wang Xinmei, 电子科学学刊（英文版） . 2010,第003期
5. Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic [J] . Zhu Hai, Pu Liqun, Xu Hengzhou, Wireless communications & mobile computing . 2018,第1期

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6. A New Construction Method for Large Girth Quasi-Cyclic LDPC Codes with Optimized Lower Bound using Chinese Remainder Theorem [J] . Bajpai Ambar, Srirutchataboon Gan, Kovintavewat Piya, Wireless personal communications: An Internaional Journal . 2016,第1期

机译：中国剩余定理的优化下界优化大围准循环LDPC码的新方法
7. Construction of quasi-cyclic LDPC codes based on a two-dimensional MDS code [J] . Communications Letters, IEEE . 2010,第5期

机译：基于二维MDS码的准循环LDPC码的构造
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机译：基于芦苇尺码的最小重量码字的准循环LDPC码的构造
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机译：高性能且可有效编码的非二进制准循环LDPC码的代数结构。
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机译：算术基本定理的模型
11. Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic [O] . Hai Zhu, Liqun Pu, Hengzhou Xu, 2018

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12. Construction of Protograph LDPC Codes with Linear Minimum Distance [R] . Divsalar, Dariush, Dolinar, Sam, Jones, Christopher 2006

机译：线性最小距离的protograph LDpC码的构造

Construction of Quasi-Cyclic LDPC Codes Based on Fundamental Theorem of Arithmetic

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