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

Newly Designed Quasi-Cyclic Low Density Parity Check Codes

Abid Yahya, Othman Sidek, Fadzli Mohamed Nazri, Mohd Fadzli Mohd Salleh, Sardar Muhammad Ali

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

Abstract — This paper presents the construction of large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight which has cut down hardware implementation cost and complexity as compared to the connection of individual columns and rows. The construction of newly obtained codes gives a class of efficiently encodable quasi-cyclic LDPC codes.

Related papers

Row Division Method to Generate QC-LDPC Codes

Abid Yahya, Othman Sidek, Mohd Fadzli Mohd Salleh +1 more

To cut down the hardware implementation cost this paper presents an efficient method to construct large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight, which has the complexity as compared to the connection of individual columns and rows. The complexity of directing within groups estimates on the transposition employed to connect rows and columns between groups. The newly obtained codes are incorporated with diversity techniques and are employed as a forward error correction codes to cater for some anti-jamming (AJ) competences in the presence of partial band noise jamming (PBNJ). The robustness of two girth-twelve QC-LDPC codes is evidenced by comparing it with randomly constructed LDPC codes and QC-LDPC codes proposed in [14].

International Conference on Internet and Web Applications and Services•Jan 1, 2009•3 citations

Very Large Girth Column-weight two Quasi-cyclic LDPC Codes

Gabofetswe Malema, Michael John Liebelt

In this paper a modified bit-filling algorithm is used for constructing column-weight two quasi-cyclic low-density parity-check codes with large girths. Code rows are divided into groups. A column is connected to two rows from different groups, which are apart by at least a specified minimum length. Rows that meet the minimum length are searched sequentially. Group rows are connected to consecutive columns resulting in a cyclic structure in the code matrix. Larger codes can be obtained by using larger row groups. Compared to other methods, the algorithm provides an easy and fast way to construct codes of a wide range of rates, girths and lengths. Constructed codes show good bit error rate performance. They are also easily implementable in hardware compared to those obtained using the original bit filling algorithm

•Jan 1, 2006•1 citation

Design of good quasi-cyclic LDPC codes

Xu Dan

The existing design of quasi-cyclic(QC) low-density parity-check(LDPC) codes has not considered the problems of short length girths and the rows' dependency.The first problem leads to the BER performance of QC LDPC codes to be much poorer than that of randomly constructed LDPC codes,while the second problem leads to the difficulty of construction of generator matrices from parity-check matrices.To solve the first problem,the constraint conditions for designing the QC LDPC codes are proposed,and the dimension and shift factors of the circulant matrices of the given sparse parity-check matrix are adjusted according to the test results of both girth 4 and girth 6.To solve the second problem,an approach of irregular QC LDPC codes is proposed.The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.Though adopting bidiagonal submatrices in parity-check matrix can solve the rows' dependency problem,many code words with low weights will occur,which leads to the BER performance can not be better by increasing code lengths.Examples are provided for the proposed design of QC LDPC codes,and computer simulation results show that the proposed QC LDPC codes achieve good BER performance.

Systems engineering and electronics•Jan 1, 2009•1 citation

A new Quasi-Cyclic low density parity check codes

Abid Yahya, Othman Sidek, Mohd Fadzli Mohd Salleh +1 more

This paper proposes a new technique for constructing the Quasi-Cyclic low density parity check (QC-LDPC) codes based on row division method. The new codes offer more flexibility in term of girth, code rates and codeword length. In this method of code construction, the rows are used to form as the distance graph. Then they are transformed to a parity-check matrix in order to acquire the desired girth. The new QC-LDPC codes show good bit-error rate performance as compared to the renowned Mackay codes for given values of Eb/Noby 0.12 dB at BER of10-7.

IEEE Symposium on Industrial Electronics & Applications (ISIEA)•Oct 1, 2009•5 citations

QC-LDPC Codes with Girth Eight Based on Independent Row-Column Mapping Sequence

Lei Wang, Xing Zhang, Feng Yu +2 more

Quasi-cyclic low-density parity-check (QC-LDPC) codes are known to have algebraic structure, which suits hardware implementation. However, low girth makes their performances worse than random structured LDPC codes. Based on independent row-column mapping sequence, this work proposed a generalized method of constructing QC-LDPC codes with girth eight, which enlarges the class of girth eight QC-LDPC codes to a fairly general series. Simulation results show that the bit error rate of the constructed codes is close to that of progressive edge growth (PEG) based QC-LDPC codes under iterative decoding.

IEEE Communications Letters•Oct 10, 2013•6 citations

Flexible Construction of High-Girth QC-LDPC Codes

Gabofetswe Malema

This article presents a highly flexible method for constructing high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes. The proposed algorithm constructs a Tanner graph formed by connecting groups of rows (check nodes) and columns (variable nodes) of the constructed code. To obtain a sub-matrix structure, rows and columns are divided into groups of equal sizes. Rows and columns in a group are connected in their numerical (positional) order to obtain a cyclic structure. Connected rows and columns must satisfy the desired minimum cycle length. We present conditions that guarantee desired girths. The proposed algorithm is by far more flexible in constructing a wide range (rates and lengths) of regular and irregular QC-LDPC codes compared to existing methods. The algorithm, which has linear complexity with respect to the number of rows or columns, provides an easy and fast way to construct QC-LDPC codes. Constructed codes show good bit error rate performances.

International journal of computer science and applications•Aug 1, 2012•2 citations
Abstract — This paper presents the construction of large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight which has cut down hardware implementation cost and complexity as compared to the connection of individual columns and rows. The construction of newly obtained codes gives a class of efficiently encodable quasi-cyclic LDPC codes.
To cut down the hardware implementation cost this paper presents an efficient method to construct large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight, which has the complexity as compared to the connection of individual columns and rows. The complexity of directing within groups estimates on the transposition employed to connect rows and columns between groups. The newly obtained codes are incorporated with diversity techniques and are employed as a forward error correction codes to cater for some anti-jamming (AJ) competences in the presence of partial band noise jamming (PBNJ). The robustness of two girth-twelve QC-LDPC codes is evidenced by comparing it with randomly constructed LDPC codes and QC-LDPC codes proposed in [14].
In this paper a modified bit-filling algorithm is used for constructing column-weight two quasi-cyclic low-density parity-check codes with large girths. Code rows are divided into groups. A column is connected to two rows from different groups, which are apart by at least a specified minimum length. Rows that meet the minimum length are searched sequentially. Group rows are connected to consecutive columns resulting in a cyclic structure in the code matrix. Larger codes can be obtained by using larger row groups. Compared to other methods, the algorithm provides an easy and fast way to construct codes of a wide range of rates, girths and lengths. Constructed codes show good bit error rate performance. They are also easily implementable in hardware compared to those obtained using the original bit filling algorithm
The existing design of quasi-cyclic(QC) low-density parity-check(LDPC) codes has not considered the problems of short length girths and the rows' dependency.The first problem leads to the BER performance of QC LDPC codes to be much poorer than that of randomly constructed LDPC codes,while the second problem leads to the difficulty of construction of generator matrices from parity-check matrices.To solve the first problem,the constraint conditions for designing the QC LDPC codes are proposed,and the dimension and shift factors of the circulant matrices of the given sparse parity-check matrix are adjusted according to the test results of both girth 4 and girth 6.To solve the second problem,an approach of irregular QC LDPC codes is proposed.The proposed approach is to replace some sub-matrices by zero matrices and identity matrices at special positions in the given sparse parity-check matrix so as to get a nonsingular square matrix for the construction of the generator matrix.Though adopting bidiagonal submatrices in parity-check matrix can solve the rows' dependency problem,many code words with low weights will occur,which leads to the BER performance can not be better by increasing code lengths.Examples are provided for the proposed design of QC LDPC codes,and computer simulation results show that the proposed QC LDPC codes achieve good BER performance.
This paper proposes a new technique for constructing the Quasi-Cyclic low density parity check (QC-LDPC) codes based on row division method. The new codes offer more flexibility in term of girth, code rates and codeword length. In this method of code construction, the rows are used to form as the distance graph. Then they are transformed to a parity-check matrix in order to acquire the desired girth. The new QC-LDPC codes show good bit-error rate performance as compared to the renowned Mackay codes for given values of Eb/Noby 0.12 dB at BER of10-7.
Quasi-cyclic low-density parity-check (QC-LDPC) codes are known to have algebraic structure, which suits hardware implementation. However, low girth makes their performances worse than random structured LDPC codes. Based on independent row-column mapping sequence, this work proposed a generalized method of constructing QC-LDPC codes with girth eight, which enlarges the class of girth eight QC-LDPC codes to a fairly general series. Simulation results show that the bit error rate of the constructed codes is close to that of progressive edge growth (PEG) based QC-LDPC codes under iterative decoding.
This article presents a highly flexible method for constructing high-girth quasi-cyclic low-density parity-check (QC-LDPC) codes. The proposed algorithm constructs a Tanner graph formed by connecting groups of rows (check nodes) and columns (variable nodes) of the constructed code. To obtain a sub-matrix structure, rows and columns are divided into groups of equal sizes. Rows and columns in a group are connected in their numerical (positional) order to obtain a cyclic structure. Connected rows and columns must satisfy the desired minimum cycle length. We present conditions that guarantee desired girths. The proposed algorithm is by far more flexible in constructing a wide range (rates and lengths) of regular and irregular QC-LDPC codes compared to existing methods. The algorithm, which has linear complexity with respect to the number of rows or columns, provides an easy and fast way to construct QC-LDPC codes. Constructed codes show good bit error rate performances.