• Journal of Communications and Networks
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• v.14 no.4
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• pp.429-433
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• 2012

In this paper, we consider nonbinary quasi-cyclic low-density parity-check (QC-LDPC) codes and propose a method to design multiple rate codes with either fixed information bit length or block bit length, tailored to different scenarios in wireless applications. We show that the proposed codes achieve good performance over a broad range of code rates.

• Journal of Communications and Networks
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• v.16 no.3
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• pp.249-257
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• 2014

This paper presents methods to the construction of regular and irregular low-density parity-check (LDPC) codes based on Euclidean geometries over the Galois field. Codes constructed by these methods have quasi-cyclic (QC) structure and large girth. By decomposing hyperplanes in Euclidean geometry, the proposed irregular LDPC codes have flexible column/row weights. Therefore, the degree distributions of proposed irregular LDPC codes can be optimized by technologies like the curve fitting in the extrinsic information transfer (EXIT) charts. Simulation results show that the proposed codes perform very well with an iterative decoding over the AWGN channel.

• Journal of Communications and Networks
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• v.13 no.3
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• pp.205-210
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• 2011

This paper presents an approach to the construction of multiple-rate quasi-cyclic low-density parity-check (LDPC) codes. Parity-check matrices of the proposed codes consist of $q{\times}q$ square submatrices. The block rows and block columns of the parity-check matrix correspond to the hyperplanes (${\mu}$-fiats) and points in Euclidean geometries, respectively. By decomposing the ${\mu}$-fiats, we obtain LDPC codes of different code rates and a constant code length. The code performance is investigated in term of the bit error rate and compared with those of LDPC codes given in IEEE standards. Simulation results show that our codes perform very well and have low error floors over the additive white Gaussian noise channel.

• Journal of Communications and Networks
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• v.17 no.2
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• pp.157-161
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• 2015

A new block low-density parity-check (Block-LDPC) code based on quadratic permutation polynomials (QPPs) is proposed. The parity-check matrix of the Block-LDPC code is composed of a group of permutation submatrices that correspond to QPPs. The scheme provides a large range of implementable LDPC codes. Indeed, the most popular quasi-cyclic LDPC (QC-LDPC) codes are just a subset of this scheme. Simulation results indicate that the proposed scheme can offer similar error performance and implementation complexity as the popular QC-LDPC codes.

• Bulletin of the Korean Mathematical Society
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• v.55 no.6
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• pp.1627-1638
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• 2018

In this paper, we study an special type of cyclic codes called skew cyclic codes over the ring ${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$, where p is a prime number. This set of codes are the result of module (or ring) structure of the skew polynomial ring (${\mathbb{F}}_p+v{\mathbb{F}}_p+v^2{\mathbb{F}}_p$)[$x;{\theta}$] where $v^3=1$ and ${\theta}$ is an ${\mathbb{F}}_p$-automorphism such that ${\theta}(v)=v^2$. We show that when n is even, these codes are either principal or generated by two elements. The generator and parity check matrix are proposed. Some examples of linear codes with optimum Hamming distance are also provided.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.419-437
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• 2019

This paper investigates skew ${\Theta}-{\lambda}$-constacyclic codes over $R=F_0{\oplus}F_1{\oplus}{\cdots}{\oplus}F_{k-1}$, where $F{_i}^{\prime}s$ are finite fields. The structures of skew ${\lambda}$-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew ${\lambda}$-constacyclic codes of arbitrary length are studied under a new definition. We also show that a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over R or a quasi-cyclic code over R.

• Steel and Composite Structures
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• v.33 no.1
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• pp.19-36
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• 2019

Cyclic behaviour of composite (steel-concrete) plate shear walls (CPSW) with variable column flexural stiffness is experimentally and numerically investigated. The investigation included design, fabrication and testing of three pairs of one-bay one-storey CPSW specimens. The reference specimen pair was designed in way that its column flexural stiffness corresponds to the value required by the design codes, while within the other two specimen pairs column flexural stiffness was reduced by 18% and 36%, respectively. Specimens were subjected to quasi-static cyclic tests. Obtained results indicate that column flexural stiffness reduction in CPSW does not have negative impact on the overall behaviour allowing for satisfactory performance for up to 4% storey drift ratio while also enabling inelastic buckling of the infill steel plate. Additionally, in comparison to similar steel plate shear wall (SPSW) specimens, column "pull-in" deformations are less pronounced within CPSW specimens. Therefore, the results indicate that prescribed minimal column flexural stiffness value used for CPSW might be conservative, and can additionally be reduced when compared to the prescribed value for SPSWs. Furthermore, finite element (FE) pushover simulations were conducted using shell and solid elements. Such FE models can adequately simulate cyclic behaviour of CPSW and as such could be further used for numerical parametric analyses. It is necessary to mention that the implemented pushover FE models were not able to adequately reproduce column "pull-in" deformation and that further development of FE simulations is required where cyclic loading of the shear walls needs to be simulated.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.35 no.2B
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• pp.325-333
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• 2010

Most communication systems including Wibro use quasi-cyclic LDPC codes composed of circulants. However, it is very difficult to design quasi-cyclic(QC) LDPC codes with optimal degree distribution satisfying conditions on layered decoding and girth due to the restriction of the size of its base matrix. In this paper, we propose a good solution by introducing superposition matrices to QC LDPC codes. We derive the conditions on checking girth of QC LDPC codes with superposition matrices, and propose new decoder to support layered decoding both for original QC LDPC codes and their modifications with superposition matrices. Simulation results show considerable improvements to convergence speed and error-correcting performance of proposed scheme which adopts QC LDPC codes with superposition matrices.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.11
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• pp.92-100
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• 2009

In this paper, we analyze the hardware architecture of Low Density Parity Check (LDPC) decoder using Log Likelihood Ration-Belief Propagation (LLR-BP) decoding algorithm. Various design issues that affect the decoding performance and the hardware complexity are discussed and the tradeoffs between the hardware complexity and the performance are analyzed. The message data for passing error probability is quantized to 7 bits and among them the fractional part is 4 bits. To maintain the decoding performance, the integer and fractional parts for the intrinsic information is 2 bits and 4 bits respectively. We discuss the alternate implementation of $\Psi$(x) function using piecewise linear approximation. Also, we improve the hardware complexity and the decoding time by applying overlapped scheduling.

• ETRI Journal
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• v.45 no.3
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• pp.404-417
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• 2023

This paper proposed a novel method for constructing quasi-cyclic low-density parity-check (QC-LDPC) codes of medium to high code rates that can be applied in cloud data storage systems, requiring better error correction capabilities. The novelty of this method lies in the construction of sparse base matrices, using a girth greater than 4 that can then be expanded with a lift factor to produce high code rate QC-LDPC codes. Investigations revealed that the proposed large-sized QC-LDPC codes with high code rates displayed low encoding complexities and provided a low bit error rate (BER) of 10^-10 at 3.5 dB E_b/N₀ than conventional LDPC codes, which showed a BER of 10^-7 at 3 dB E_b/N₀. Subsequently, implementation of the proposed QC-LDPC code in a softwaredefined radio, using the NI USRP 2920 hardware platform, was conducted. As a result, a BER of 10^-6 at 4.2 dB E_b/N₀ was achieved. Then, the performance of the proposed codes based on their encoding-decoding speeds and storage overhead was investigated when applied to a cloud data storage (GCP). Our results revealed that the proposed codes required much less time for encoding and decoding (of data files having a 10 MB size) and produced less storage overhead than the conventional LDPC and Reed-Solomon codes.