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

IEEE Transactions on Communications

A necessary and sufficient condition for determining the girth of quasi-cyclic LDPC codes

Xiaofu Wu, Xiaohu You, Chunming Zhao

Published Jun 1, 2008• 29 citations
Publisher

Abstract

The parity-check matrix of a quasi-cyclic low- density parity-check (QC-LDPC) code can be compactly represented by a polynomial parity-check matrix. By using this compact representation, we derive a necessary and sufficient condition for determining the girth of QC-LDPC codes in a systematic way. The new condition avoids an explicit enumeration of cycles for determining the girth of codes, and thus can be well employed to generate QC-LDPC codes with large girth.

DOI
10.1109/tcomm.2008.060362

Related papers

Bounds on the Size of Parity-Check Matrices for Quasi-Cyclic Low-Density Parity-Check Codes

Kyung-Joong Kim, Jin-Ho Chung, Kyeongcheol Yang

In this paper, we investigate the cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation of a parity-check matrix for a QC-LDPC code, we analyze a necessary and sufficient condition for a cycle of a given length to exist. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. We also give a bound which is a sufficient condition for a QC-LDPC code of a given girth to be constructed by a greedy algorithm. The bounds derived here are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds in many classes of regular LDPC codes.

IEEE Transactions on Information Theory•Aug 28, 2013•15 citations

An Efficient Girth-Locating Algorithm for Quasi-Cyclic LDPC Codes

Xiaofu Wu, Xiaohu You, Chunming Zhao

The parity-check matrix of a quasi-cyclic code can be represented by a polynomial parity-check matrix with a significantly lower dimension. By using this compact representation, we can develop an efficient method for locating the girth of the quasi-cyclic code. The proposed girth-locating algorithm can be well employed to generate quasi-cyclic low-density parity-check codes with large girth

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2006•11 citations

Necessary conditions for quasi-cyclic LDPC codes to have a given girth

Kyung-Joong Kim, Jin-Ho Chung, Kyeongcheol Yang

Short cycles in the Tanner graph of a low-density parity-check (LDPC) code may cause a severe performance degradation. In this paper, we investigate the cycle properties of quasi-cyclic LDPC (QC-LDPC) codes. We first analyze a necessary and sufficient condition for a cycle of a given length to exist, by using the sequence representation of a parity-check matrix for a QC-LDPC code. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. Our necessary conditions are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds for many classes of regular QC-LDPC codes.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2013•0 citations

Girth of Tanner’s (3, 5) Quasi-Cyclic LDPC Codes

Sunghwan Kim, Jong‐Seon No, Habong Chung +1 more

In this paper, the cycles of Tanner’s (3, 5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4, 6, 8, and 10 in Tanner’s (3, 5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15-th root of unity of the prime field Fp. By checking the existence of solutions for these equations over Fp, the girths of Tanner’s (3, 5) QC LDPC codes are derived.

한국통신학회 학술대회 및 강연회•Apr 1, 2005•0 citations

Tanner $(J,L)$ Quasi-Cyclic LDPC Codes: Girth Analysis and Derived Codes

Hengzhou Xu, Huaan Li, Baoming Bai +2 more

Girth plays an important role in the design of low-density parity-check (LDPC) codes. Motivated by the works on the girth of some classes of Tanner quasi-cyclic (QC) LDPC codes, e.g., Tanner (3, 5), (3, 7), (3, 11), and (5, 7) codes, we, in this paper, study the girth of Tanner$(J,L)$QC-LDPC codes where$J$and$L$can be any two positive integers. According to the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10, we propose an algorithm to determine the girth of Tanner$(J,L)$QC-LDPC codes with finite code lengths. Through the analysis of the obtained girth values, we generalize the laws of the girth distributions of Tanner$(J,L)$QC-LDPC codes. Furthermore, based on the exponent matrices of Tanner$(J,L)$QC-LDPC codes with known girths, we employ the column selection method and/or the masking technique to construct binary/nonbinary LDPC codes. The numerical results show that the constructed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise channel.

IEEE Access•Dec 10, 2018•21 citations

On the girth of tanner (3, 5) quasi-cyclic LDPC codes

Sunghwan Kim, Jong‐Seon No, Habong Chung +1 more

In this correspondence, the cycles of Tanner (3,5) quasi-cyclic (QC) low-density parity-check (LDPC) codes are analyzed and their girth values are derived. The conditions for the existence of cycles of lengths 4,6,8, and 10 in Tanner (3,5) QC LDPC codes of length 5p are expressed in terms of polynomial equations in a 15th root of unity of the prime field F/sub p/. By checking the existence of solutions for these equations over F/sub p/, the girths of Tanner (3,5) QC LDPC codes are derived.

IEEE Transactions on Information Theory•Apr 1, 2006•33 citations
The parity-check matrix of a quasi-cyclic low- density parity-check (QC-LDPC) code can be compactly represented by a polynomial parity-check matrix. By using this compact representation, we derive a necessary and sufficient condition for determining the girth of QC-LDPC codes in a systematic way. The new condition avoids an explicit enumeration of cycles for determining the girth of codes, and thus can be well employed to generate QC-LDPC codes with large girth.
In this paper, we investigate the cycle properties of quasi-cyclic low-density parity-check (QC-LDPC) codes. Using the sequence representation of a parity-check matrix for a QC-LDPC code, we analyze a necessary and sufficient condition for a cycle of a given length to exist. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. We also give a bound which is a sufficient condition for a QC-LDPC code of a given girth to be constructed by a greedy algorithm. The bounds derived here are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds in many classes of regular LDPC codes.
Short cycles in the Tanner graph of a low-density parity-check (LDPC) code may cause a severe performance degradation. In this paper, we investigate the cycle properties of quasi-cyclic LDPC (QC-LDPC) codes. We first analyze a necessary and sufficient condition for a cycle of a given length to exist, by using the sequence representation of a parity-check matrix for a QC-LDPC code. We then derive bounds which are necessary conditions for a QC-LDPC code to have a given girth in terms of its parameters. Our necessary conditions are applicable to any regular or irregular QC-LDPC codes as well as they improve the existing bounds for many classes of regular QC-LDPC codes.
Tanner (J,L)(J,L)(J,L) Quasi-Cyclic LDPC Codes: Girth Analysis and Derived Codes
Girth plays an important role in the design of low-density parity-check (LDPC) codes. Motivated by the works on the girth of some classes of Tanner quasi-cyclic (QC) LDPC codes, e.g., Tanner (3, 5), (3, 7), (3, 11), and (5, 7) codes, we, in this paper, study the girth of Tanner(J,L)(J,L)(J,L)QC-LDPC codes whereJJJandLLLcan be any two positive integers. According to the sufficient and necessary conditions for the existence of cycles of lengths 4, 6, 8, and 10, we propose an algorithm to determine the girth of Tanner(J,L)(J,L)(J,L)QC-LDPC codes with finite code lengths. Through the analysis of the obtained girth values, we generalize the laws of the girth distributions of Tanner(J,L)(J,L)(J,L)QC-LDPC codes. Furthermore, based on the exponent matrices of Tanner(J,L)(J,L)(J,L)QC-LDPC codes with known girths, we employ the column selection method and/or the masking technique to construct binary/nonbinary LDPC codes. The numerical results show that the constructed LDPC codes have good performance under iterative decoding over the additive white Gaussian noise channel.