Explicit Constructions of Short QC-LDPC Codes Free of Small Cycles and with Large Column Weight

ZHANG Guo-hua; SUN Ai-jing; NI Meng-di; FANG Yi

doi:10.12263/DZXB.20230300

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Explicit Constructions of Short QC-LDPC Codes Free of Small Cycles and with Large Column Weight

PAPERS | 更新时间：2025-12-11

- Explicit Constructions of Short QC-LDPC Codes Free of Small Cycles and with Large Column Weight
- ACTA ELECTRONICA SINICA Vol. 52, Issue 6, Pages: 1862-1868(2024)
- 作者机构：
  
  1.西安邮电大学通信与信息工程学院，陕西西安 710121
  2.广东工业大学信息工程学院，广东广州 510000
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China(62322106;62071131);International Collaborative Research Programof Guangdong Science and Technology Department(2022A0505050070)
- DOI：10.12263/DZXB.20230300
  CLC： TN911.22;TN927
- Received：04 April 2023，
  
  Revised：2023-10-14，
  
  Published：25 June 2024
- 稿件说明：
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张国华,孙爱晶,倪孟迪,等.无小环大列重QC-LDPC短码的显式构造[J].电子学报,2024,52(06):1862-1868.

ZHANG Guo-hua, SUN Ai-jing, NI Meng-di, et al.Explicit Constructions of Short QC-LDPC Codes Free of Small Cycles and with Large Column Weight[J].Acta Electronica Sinica, 2024, 52(06): 1862-1868.
张国华,孙爱晶,倪孟迪,等.无小环大列重QC-LDPC短码的显式构造[J].电子学报,2024,52(06):1862-1868. DOI：10.12263/DZXB.20230300

ZHANG Guo-hua, SUN Ai-jing, NI Meng-di, et al.Explicit Constructions of Short QC-LDPC Codes Free of Small Cycles and with Large Column Weight[J].Acta Electronica Sinica, 2024, 52(06): 1862-1868. DOI：10.12263/DZXB.20230300

摘要

针对列重较大的无4环且无6环的准循环（Quasi-Cyclic，QC）低密度奇偶校验（Low-Density Parity-Check，LDPC）码，本文提出了三种新的显式构造方法.新方法的指数矩阵由两个整数序列完全定义，其中第一个序列是从0开始且公差为1的等差序列，第二个序列是由符合最大公约数约束的整数组成的特殊序列.对于现有显式方法只能提供较大循环块尺寸的多种行重类型，新显式构造方法在这些行重类型下均获得了相当小的循环块尺寸，从而将最小循环块尺寸降低到大约只有原来的一半.与近期提出的基于搜索的对称结构法相比，新的显式构造方法具有类似或更优的译码性能、极低的描述复杂度且不需要计算机搜索.

Abstract

Three new explicit constructions are proposed for quasi-cyclic (QC) low-density parity-check (LDPC) codes free of 4-cycles and 6-cycles with large column weights. The exponent matrices for these new methods are completely defined by two sequences of integers. The first sequence is an arithmetic sequence starting from zero with the common difference being one

and the second is a special sequence composed of integers satisfying the greatest-common-divisor(GCD) constraint. The new methods can produce rather small circulant sizes for many categories of row weights

while the existing explicit methods can only provide relatively large circulant sizes

thus the up-to-date smallest circulant sizes being nearly halved. Compared with the recently proposed symmetrical construction which relies upon extensive search

the new explicit constructions have similar or better decoding performance

possess extremely low description complexity and need no computer search.

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references

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