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 Information Theory

Quasi-cyclic LDPC codes for fast encoding

Seho Myung, Kyeongcheol Yang, Jaeyoel Kim

Published Jul 19, 2005• 278 citations
Publisher

Abstract

In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.

DOI
10.1109/tit.2005.851753

Related papers

On the Low Complexity Construction of Quasi-Cyclic Low-Density Parity-Check Codes by Progressive-Block Growth

Qiangy Yuan, Pinyi Ren, Yilin Feng +1 more

In this paper, we propose a novel method with low complexity for constructing quasi-cyclic LDPC codes. The algorithm chooses every circulant permutation matrix sequentially, and makes sure that the current circulant permutation matrix forms no cycles of length 4 and 6 with the existent matrices, finally a family of $(3,L)$ QC-LDPC codes with girth at least 8 is obtained. The main complexity of the algorithm is checking cycles of length 6, the number of which is no more than $L^2$. Simulation results show that, when block length is 1008 and using the iterative belief propagation decoding, the LDPC code constructed by the proposed algorithm out performs the random code about 0.1dB at the bit-error-rate of $ 10^{ - 5}$.

•Jan 1, 2009•1 citation

Efficiently Encodable Irregular QC-LDPC Codes Constructed from Self-Reciprocal Generator Polynomials of MDS Codes

Norifumi Kamiya

This letter presents a class of quasi-cyclic (QC) low-density parity-check (LDPC) codes which are efficiently encodable and have better memory efficiency than other randomly constructed QC-LDPC codes. The parity-check matrix of the codes is obtained from a block circulant matrix that is generated from a self-reciprocal generator polynomial of a maximum distance separable (MDS) code by replacing some of its block entries by all zero matrices. We show by simulations that the codes can achieve excellent error performance.

IEEE Communications Letters•Aug 27, 2010•6 citations

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

Random-permutation-matrix-based cyclically-coupled LDPC codes

Francis C. M. Lau, Fanlu Mo, Wai M. Tarn +1 more

Cyclically-coupled quasi-cyclic low-density parity-check (CC-QC-LDPC) codes are a new class of QC-LDPC codes which can achieve excellent error performance and relatively low hardware requirement. In this paper, we modify the CC-QC-LDPC code construction by using random permutation matrices instead of circulant permutation matrices, forming the “random-permutation-matrix-based CC-LDPC (RP-CC-LDPC) code”. The objective is to achieve a better error performance under the same code length. We simulate the bit error rate using FPGA simulations. We also compare the BER results and decoder complexity of the above codes with those of regular and irregular QC-LDPC codes under the same code length and code rate.

International Conference on Advanced Communication Technology•Jan 1, 2017•3 citations

Linear Permutation Polynomial Codes

Ryoichiro Yoshida, Kenta Kasai

Quasi-cyclic low-density parity-check (QC-LDPC) codes are one of the most important code classes of LDPC codes. They have two drawbacks: lack of randomness and limited girth lead to a degraded decoding performance in the waterfall and error floor regions, respectively. To tackle these problems, we present a new class of LDPC codes, named linear permutation polynomial (LPP) codes, whose parity-check matrix consists of permutation matrices based on LPPs. The girth of regular QC-LDPC codes is upper bounded by 12, while LPP codes break this limit. We demonstrate that LPP codes have error performance almost equivalent to random ones.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2019•3 citations

Construction of the cyclic block-type LDPC codes for low complexity hardware implementation

Kuang-Hao Lin, KyungHi Chang, Chien‐Lin Huang +1 more

In this paper, we construct the cyclic block-type low-density parity-check (CB-LDPC) codes for low complexity hardware implementation. The CB-LDPC code, which is a special class of quasi-cyclic LDPC (QC-LDPC), has an efficient encoding algorithm due to the simple structure of their parity-check matrices. A distribution of irregular parity-check matrix for the CB-LDPC is developed so that we can obtain an area-efficient decoder design, good error correction performance, and low complexity architecture implementation. The CB-LDPC code decoding uses the iterative min-sum algorithm (MSA) and the block parallel connection design to improve the hardware architecture complexity and area.

IEEE International Conference on Electronics, Circuits and Systems (ICECS)•Aug 1, 2008•2 citations
In this correspondence we present a special class of quasi-cyclic low-density parity-check (QC-LDPC) codes, called block-type LDPC (B-LDPC) codes, which have an efficient encoding algorithm due to the simple structure of their parity-check matrices. Since the parity-check matrix of a QC-LDPC code consists of circulant permutation matrices or the zero matrix, the required memory for storing it can be significantly reduced, as compared with randomly constructed LDPC codes. We show that the girth of a QC-LDPC code is upper-bounded by a certain number which is determined by the positions of circulant permutation matrices. The B-LDPC codes are constructed as irregular QC-LDPC codes with parity-check matrices of an almost lower triangular form so that they have an efficient encoding algorithm, good noise threshold, and low error floor. Their encoding complexity is linearly scaled regardless of the size of circulant permutation matrices.
In this paper, we propose a novel method with low complexity for constructing quasi-cyclic LDPC codes. The algorithm chooses every circulant permutation matrix sequentially, and makes sure that the current circulant permutation matrix forms no cycles of length 4 and 6 with the existent matrices, finally a family of (3,L)(3,L)(3,L) QC-LDPC codes with girth at least 8 is obtained. The main complexity of the algorithm is checking cycles of length 6, the number of which is no more than L2L^2L2. Simulation results show that, when block length is 1008 and using the iterative belief propagation decoding, the LDPC code constructed by the proposed algorithm out performs the random code about 0.1dB at the bit-error-rate of $ 10^{ - 5}$.
This letter presents a class of quasi-cyclic (QC) low-density parity-check (LDPC) codes which are efficiently encodable and have better memory efficiency than other randomly constructed QC-LDPC codes. The parity-check matrix of the codes is obtained from a block circulant matrix that is generated from a self-reciprocal generator polynomial of a maximum distance separable (MDS) code by replacing some of its block entries by all zero matrices. We show by simulations that the codes can achieve excellent error performance.
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.
Cyclically-coupled quasi-cyclic low-density parity-check (CC-QC-LDPC) codes are a new class of QC-LDPC codes which can achieve excellent error performance and relatively low hardware requirement. In this paper, we modify the CC-QC-LDPC code construction by using random permutation matrices instead of circulant permutation matrices, forming the “random-permutation-matrix-based CC-LDPC (RP-CC-LDPC) code”. The objective is to achieve a better error performance under the same code length. We simulate the bit error rate using FPGA simulations. We also compare the BER results and decoder complexity of the above codes with those of regular and irregular QC-LDPC codes under the same code length and code rate.
Quasi-cyclic low-density parity-check (QC-LDPC) codes are one of the most important code classes of LDPC codes. They have two drawbacks: lack of randomness and limited girth lead to a degraded decoding performance in the waterfall and error floor regions, respectively. To tackle these problems, we present a new class of LDPC codes, named linear permutation polynomial (LPP) codes, whose parity-check matrix consists of permutation matrices based on LPPs. The girth of regular QC-LDPC codes is upper bounded by 12, while LPP codes break this limit. We demonstrate that LPP codes have error performance almost equivalent to random ones.
In this paper, we construct the cyclic block-type low-density parity-check (CB-LDPC) codes for low complexity hardware implementation. The CB-LDPC code, which is a special class of quasi-cyclic LDPC (QC-LDPC), has an efficient encoding algorithm due to the simple structure of their parity-check matrices. A distribution of irregular parity-check matrix for the CB-LDPC is developed so that we can obtain an area-efficient decoder design, good error correction performance, and low complexity architecture implementation. The CB-LDPC code decoding uses the iterative min-sum algorithm (MSA) and the block parallel connection design to improve the hardware architecture complexity and area.