Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

中国科学通报：英文版

Tight lower bound of consecutive lengths for QC-LDPC codes with girth at least ten

Zhang, Guohua, Wang, JuHua, Li -, Xueyuan, Xinmei

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

为一任意(3， L ) 伪周期(质量管理) 有尺寸的低密度的同等值检查(LDPC ) 代码至少十，连续长度的紧密的更低的界限被介绍。为在界限上面的任意的长度，相应 LDPC 代码必然有一种尺寸至少十，并且为到界限的长度平等者，结果的代码不可避免地有比十小的一种尺寸。这个新结论能很好被用于一些重要问题，例如大尺寸 QC-LDPC 代码的存在的证明，大尺寸 QC-LDPC 的构造基于中国剩余物定理编码，以及 LDPC 的构造与保证错误修正能力编码。

Related papers

围长为12的QC-LDPC码连续码长的紧致下界

Guohua Zhang, Xinmei Wang

For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of large-girth QC-LDPC codes, the construction of large-girth QC-LDPC codes based on the Chinese remainder theorem, and the construction of LDPC codes with the guaranteed error correction capability.

Chinese Science Bulletin (Chinese Version)•Jun 1, 2011•0 citations

Tight lower bound of consecutive lengths for QC-LDPC codes with girth at least ten

Guohua Zhang, Juhua Wang, Xueyuan Li +1 more

For an arbitrary (3, L ) quasi-cyclic(QC) low-density parity-check (LDPC) code with girth at least ten, a tight lower bound of the consecutive lengths is presented. For an arbitrary length above the bound the corresponding LDPC code necessarily has a girth at least ten, and for the length equal to the bound, the resultant code inevitably has a girth smaller than ten. This new conclusion can be well applied to some important issues, such as the proofs of the existence of large girth QC-LDPC codes, the construction of large girth QC-LDPC codes based on the Chinese remainder theorem, as well as the construction of LDPC codes with the guaranteed error correction capability.

Chinese Science Bulletin•Apr 1, 2011•0 citations

A Class of High-Rate Low-Complexity QC-LDPC Codes

Long-jiang Jing, Jing-li Lin, Zhu Wei-le

该文设计了一种特殊的高码率准循环低密度校验(QC-LDPC)码,其校验矩阵以单位矩阵的循环移位阵为基本单元,与随机构造的LDPC码相比可节省大量存储单元。利用该码校验矩阵的近似下三角特性,一种高效的递推编码方法被提出,它使得该码编码复杂度与码长成线性关系。另外,该文提出一种分析QC-LDPC码二分图中短长度环分布情况的方法,并且给出了相应的不含长为4环QC-LDPC码的构造方法。计算机仿真结果表明,新码不但编码简单,而且具有高纠错能力、低误码平层。

JOURNAL OF ELECTRONICS INFORMATION TECHNOLOGY•Mar 17, 2011•0 citations

Tight lower bound of consecutive lengths for QC-LDPC codes with girth twelve

Guohua Zhang, Xinmei Wang

For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of large-girth QC-LDPC codes, the construction of large-girth QC-LDPC codes based on the Chinese remainder theorem, and the construction of LDPC codes with the guaranteed error correction capability.

arXiv:1204.4864•Apr 22, 2012•0 citations

围长至少为10 的QC-LDPC 码连续码长的紧致下界

国华 张, 新梅 王, 学远 李 +1 more

和 L, 则相应的 LDPC 码称为(R,L)LDPC 码; 若校验 矩阵是一个由循环置换矩阵构成的阵列, 则相应的 LDPC 码称为准循环(QC-)LDPC 码. 本文将围长至少 为 g 记为 girth-g + , 将围长恰好为 g 记为 girth-g.采用 各种思路, 人们目前已经开发出一些构造 girth-10 + (3, L)LDPC 码的方法.这些巧妙的思路包括: 容许斜率 对 [8] 、二次置换多项式 [9] 、平衡环路 [10] 、控制方程 [11] 、 网格 [12] 、三维循环网格 [13] 、邻接矩阵理论 [14] 和爬山算 法 [ 1 5 ] .

Chinese Science Bulletin (Chinese Version)•Aug 1, 2010•1 citation

Tight lower bound of consecutive lengths for QC-LDPC codes with girth twelve

Zhang Guo

For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of large-girth QC-LDPC codes, the construction of large-girth QC-LDPC codes based on the Chinese remainder theorem, and the construction of LDPC codes with the guaranteed error correction capability.

Chinese Science Bulletin•Jan 1, 2011•0 citations
为一任意(3， L ) 伪周期(质量管理) 有尺寸的低密度的同等值检查(LDPC ) 代码至少十，连续长度的紧密的更低的界限被介绍。为在界限上面的任意的长度，相应 LDPC 代码必然有一种尺寸至少十，并且为到界限的长度平等者，结果的代码不可避免地有比十小的一种尺寸。这个新结论能很好被用于一些重要问题，例如大尺寸 QC-LDPC 代码的存在的证明，大尺寸 QC-LDPC 的构造基于中国剩余物定理编码，以及 LDPC 的构造与保证错误修正能力编码。
For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of large-girth QC-LDPC codes, the construction of large-girth QC-LDPC codes based on the Chinese remainder theorem, and the construction of LDPC codes with the guaranteed error correction capability.
For an arbitrary (3, L ) quasi-cyclic(QC) low-density parity-check (LDPC) code with girth at least ten, a tight lower bound of the consecutive lengths is presented. For an arbitrary length above the bound the corresponding LDPC code necessarily has a girth at least ten, and for the length equal to the bound, the resultant code inevitably has a girth smaller than ten. This new conclusion can be well applied to some important issues, such as the proofs of the existence of large girth QC-LDPC codes, the construction of large girth QC-LDPC codes based on the Chinese remainder theorem, as well as the construction of LDPC codes with the guaranteed error correction capability.
该文设计了一种特殊的高码率准循环低密度校验(QC-LDPC)码,其校验矩阵以单位矩阵的循环移位阵为基本单元,与随机构造的LDPC码相比可节省大量存储单元。利用该码校验矩阵的近似下三角特性,一种高效的递推编码方法被提出,它使得该码编码复杂度与码长成线性关系。另外,该文提出一种分析QC-LDPC码二分图中短长度环分布情况的方法,并且给出了相应的不含长为4环QC-LDPC码的构造方法。计算机仿真结果表明,新码不但编码简单,而且具有高纠错能力、低误码平层。
For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of large-girth QC-LDPC codes, the construction of large-girth QC-LDPC codes based on the Chinese remainder theorem, and the construction of LDPC codes with the guaranteed error correction capability.
和 L, 则相应的 LDPC 码称为(R,L)LDPC 码; 若校验 矩阵是一个由循环置换矩阵构成的阵列, 则相应的 LDPC 码称为准循环(QC-)LDPC 码. 本文将围长至少 为 g 记为 girth-g + , 将围长恰好为 g 记为 girth-g.采用 各种思路, 人们目前已经开发出一些构造 girth-10 + (3, L)LDPC 码的方法.这些巧妙的思路包括: 容许斜率 对 [8] 、二次置换多项式 [9] 、平衡环路 [10] 、控制方程 [11] 、 网格 [12] 、三维循环网格 [13] 、邻接矩阵理论 [14] 和爬山算 法 [ 1 5 ] .
For an arbitrary (3,L) QC-LDPC code with a girth of twelve, a tight lower bound of the consecutive lengths is proposed. For an arbitrary length above the bound the resultant code necessarily has a girth of twelve, and for the length meeting the bound, the corresponding code inevitably has a girth smaller than twelve. The conclusion can play an important role in the proofs of the existence of large-girth QC-LDPC codes, the construction of large-girth QC-LDPC codes based on the Chinese remainder theorem, and the construction of LDPC codes with the guaranteed error correction capability.