Novel Constructions of QC-LDPC Codes with Girth at Least Eight: An Explicit Framework

ZHANG Guo-hua; WANG Xin-mei

doi:10.3969/j.issn.0372-2112.2012.02.020

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Novel Constructions of QC-LDPC Codes with Girth at Least Eight: An Explicit Framework

更新时间：2025-07-16

- Novel Constructions of QC-LDPC Codes with Girth at Least Eight: An Explicit Framework
- Acta Electronica Sinica Vol. 40, Issue 2, Pages: 331-337(2012)
- 作者机构：
  
  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. 中国空间技术研究院西安分院,陕西,西安,710100
  3. 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
  4. 中国空间技术研究院西安分院,陕西,西安,710100
- 作者简介：
- 基金信息：
- DOI：10.3969/j.issn.0372-2112.2012.02.020
  CLC： TN911.22
- Published：2012
- 稿件说明：
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ZHANG Guo-hua, WANG Xin-mei. Novel Constructions of QC-LDPC Codes with Girth at Least Eight: An Explicit Framework[J]. Acta Electronica Sinica, 2012, 40(2): 331-337.
DOI：

ZHANG Guo-hua, WANG Xin-mei. Novel Constructions of QC-LDPC Codes with Girth at Least Eight: An Explicit Framework[J]. Acta Electronica Sinica, 2012, 40(2): 331-337. DOI： 10.3969/j.issn.0372-2112.2012.02.020.

摘要

构造围长较大的校验矩阵

是提高二进制和多进制QC-LDPC码译码性能的一种有效手段.本文提出一种不需要借助于任何计算机搜索步骤

能够直接构造出围长至少为8的QC-LDPC码的显式构造框架.该框架所构造的QC-LDPC码不仅满足围长至少为8的条件

而且还具有循环置换矩阵(CPM)尺寸可以连续变化的优点.该框架可以分为两个步骤:第一步是在无穷大CPM尺寸条件下利用确定性方法构造一个围长至少为8的校验矩阵;第二步是根据本文新发现的一个围长性质

从该校验矩阵的移位矩阵直接精确地计算出CPM尺寸连续变化的紧致下界.

Abstract

Enabling the parity-check matrices to have a large girth is an efficient method to improve the decoding performance for many binary and non-binary QC-LDPC codes.A new explicit framework to construct QC-LDPC codes with girth at least eight is proposed

without any computer search procedures.The QC-LDPC codes constructed by the framework not only have a girth at least eight

but also possess an advantage of consecutive cyclic permutation matrix (CPM) sizes.The framework includes two steps:first

a parity-check matrix is explicitly constructed with a girth at least eight under an infinite CPM size;second

the tight lower bound of consecutive CPM sizes is precisely calculated directly from the corresponding shift matrix of the parity-check matrix

by employing a new girth property discovered by this paper.

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