Efficient encoding of QC-LDPC codes related to cyclic MDS codes

Kamiya, Norifumi; Sasaki, Eisaku

doi:10.1109/jsac.2009.090803

Cited by 18 publications

(11 citation statements)

References 18 publications

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“…In this paper, such an analysis is provided. This analysis generalizes and simplifies the rank analysis of a class of QC-LDPC codes constructed based on cyclic MDS (or RS) codes with two information symbols [11]. In Section IV, we present a large class of algebraic QC-LDPC codes constructed based on Latin squares over finite fields, called QC-LDPC codes on Latin squares.…”

Section: Introductionmentioning

confidence: 94%

Quasi-cyclic LDPC codes on Latin squares and the ranks of their parity-check matrices

Zhang

Huang

Lin

et al. 2010

2010 Information Theory and Applications Workshop (ITA)

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Abstract-Quasi-cyclic codes are the most promising class of structured LDPC codes due to their ease of implementation and excellent performance over noisy channels when decoded with message-passing algorithms as extensive simulation studies have shown. An approach for constructing quasi-cyclic LDPC codes based on Latin squares over finite fields is presented. By analyzing the parity-check matrices of these codes, expressions for their ranks are derived. Experimental results show that, with iterative decoding algorithms, the constructed codes perform very well over the AWGN and the binary erasure channels.

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Section: Introductionmentioning

confidence: 94%

Quasi-cyclic LDPC codes on Latin squares and the ranks of their parity-check matrices

Zhang

Huang

Lin

et al. 2010

2010 Information Theory and Applications Workshop (ITA)

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“…In this section, inspired by the rank analyses of some specific classes of QC-CPM-LDPC codes [7,16,17], we presented general analysis on the ranks of the parity-check matrix of a QC-LDPC code in the transform domain.…”

Section: Rank Analysis For Qc-ldpc Codesmentioning

confidence: 99%

“…Compared with their random-like counterparts, these codes have advantages in encoder and decoder implementations [2][3][4][5] in simple regular wiring and modular structure. Moreover, QC-LDPC codes can be simply encoded with linear complexity [6,7], instead of the quadratic complexity involved in computer-generated random-like LDPC codes [8]. Therefore advanced wireless communication systems [9], power-line communication systems [10] and storage systems [11] have adopted QC-LDPC codes in their error-control schemes.…”

Section: Introductionmentioning

confidence: 99%

“…It was first discussed by Diao et al [17], in 2012, but 'not involved in the SC form'. Following the diagonal structure of the transformed generator matrices, we explained the structure of the submatrices of the generator matrices of QC-LDPC codes, including the generator matrices of the subclass [7,17] of which the parity-check matrices are rank-deficient. In light of the structure of the matrices of the rank-deficient subclass, we proposed to construct SC generator matrices [6] of the QC-LDPC codes consisting of three submatrices, I, P and Q.…”

Section: Introductionmentioning

confidence: 99%

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Density optimisation of generator matrices of quasi‐cyclic low‐density parity‐check codes and their rank analysis

et al. 2014

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The efficient encoding of quasi-cyclic (QC) low-density parity-check (LDPC) codes is based on generator matrices in systematic-circulant (SC) form. The cost of the encoders of QC-LDPC codes mainly depends on the number of non-zero entries in the SC generator matrices. This study introduces a novel construction of SC generator matrices based on matrix transformations via Galois Fourier transform. By revealing the structure of SC generator matrices in the transform domain, an algorithm is proposed to reduce the density of the generator matrices of QC-LDPC codes. Furthermore, a tight upper bound on ranks of QC matrices is derived. Based on the bound, rank distributions of parity-check matrices and generator matrices in the transform domain illustrate the efficiency of the proposed algorithm. Simulation results show that the density of their SC generator matrices can be significantly decreased with moderate computational complexity.

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“…A number of QC-LDPC codes have been constructed and shown good error performance. Based on their QC structure, the computational complexity and memory cost of LDPC encoders can be efficiently reduced [10], [11]. RS-based LDPC codes are a sub-class of QC-LDPC codes [12].…”

Section: Introductionmentioning

confidence: 99%

Low complexity encoding algorithm of RS-based QC-LDPC codes

Zhang

Tang

Huang

et al. 2014

2014 Information Theory and Applications Workshop (ITA)

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Abstract-This paper presents a novel encoding algorithm for QC-LDPC codes constructed from Reed-Solomon codes. The encoding is performed in the transform domain via Galois Fourier transformation. Message bits are encoded in sections corresponding to sub-matrices of the parity-check matrix in the transform domain. Because of the structure of the paritycheck matrices of these LDPC codes, the encoding can be easily implemented with some linear-feedback shift registers, thus efficiently reduces the hardware cost.

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Efficient encoding of QC-LDPC codes related to cyclic MDS codes

Cited by 18 publications

References 18 publications

Quasi-cyclic LDPC codes on Latin squares and the ranks of their parity-check matrices

Quasi-cyclic LDPC codes on Latin squares and the ranks of their parity-check matrices

Density optimisation of generator matrices of quasi‐cyclic low‐density parity‐check codes and their rank analysis

Low complexity encoding algorithm of RS-based QC-LDPC codes

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