Construction of Regular and Irregular LDPC Codes: Geometry Decomposition and Masking

Xu, Jun; Chen, Lei; Djurdjevic, I.; Lin, Shu; Abdel-Ghaffar, Khaled

doi:10.1109/tit.2006.887082

Cited by 131 publications

(89 citation statements)

References 47 publications

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“…If the girth of the associated Tanner graph of the masking matrix Z(γ, ρ) has a girth σ > 6, the girth of the associated Tanner graph of the masked array M(γ, ρ) is at least σ. The concept of masking was recently introduced in [14], [18] for constructing binary LDPC codes.…”

Section: Array Maskingmentioning

confidence: 99%

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Non-binary LDPC codes vs. Reed-Solomon codes

Zhou

Zhang

Kang

et al. 2008

2008 Information Theory and Applications Workshop

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Abstract-This paper investigates the potential of non-binary LDPC codes to replace widely used Reed-Solomon (RS) codes for applications in communication and storage systems for combating mixed types of noise and interferences. The investigation begins with presentation of four algebraic constructions of RS-based non-binary quasi-cyclic (QC)-LDPC codes. Then, the performances of some codes constructed based on the proposed methods with iterative decoding are compared with those of RS codes of the same lengths and rates decoded with the harddecision Berlekamp-Massey (BM)-algorithm and the algebraic soft-decision Kötter-Vardy (KV)-algorithm over both the AWGN and a Rayleigh fading channels. Comparison shows that the constructed non-binary QC-LDPC codes significantly outperform their corresponding RS codes decoded with either the BMalgorithm or the KV-algorithm. Most impressively, the orders of decoding computational complexity of the constructed nonbinary QC-LDPC codes decoded with 5 and 50 iterations of a Fast Fourier Transform based sum-product algorithm are much smaller than those of their corresponding RS codes decoded with the KV-algorithm, while achieve 1.5 to 3 dB coding gains. The comparison shows that well designed non-binary LDPC codes have a great potential to replace RS codes for some applications in communication or storage systems, at least before a very efficient algorithm for decoding RS codes is devised.

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Section: Array Maskingmentioning

confidence: 99%

“…How to design masking matrices that result in good QC-LDPC codes is an interesting and challenging problem. Masking matrices can be constructed by computer search or algebraically [14], [18]. A special type of masking matrices is the circular type.…”

Section: Array Maskingmentioning

confidence: 99%

Non-binary LDPC codes vs. Reed-Solomon codes

Zhou

Zhang

Kang

et al. 2008

2008 Information Theory and Applications Workshop

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show abstract

“…Hence the Tanner graph of M(γ, ρ) has a girth of at least 6. If the girth of the associated Tanner graph of the masking matrix Z(γ, ρ) has a girth g > 6, the girth of the associated Tanner graph of the masked array M(γ, ρ) is at least g. The concept of masking was recently intorduced in [9], [10].…”

Section: A Array Maskingmentioning

confidence: 99%

“…If Z(γ, ρ) is regular, then the null space of M(γ, ρ) gives a regular code, otherwise it gives an irregular code. Regular masking matrices can be constructed algebraically [10]. (8,16) which is a 1016 × 2032 matrix over GF( 2 7 ) with column and row weights 3 and 6, respectively.…”

Section: A Array Maskingmentioning

confidence: 99%

Algebraic Constructions of Nonbinary Quasi-Cyclic LDPC Codes

Lin

Song

Tai

et al. 2006

2006 International Conference on Communications, Circuits and Systems

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Abstract-This paper is concerned with algebraic constructions of nonbinary quasi-cyclic (QC) LDPC codes based on arrays of circulant permutation matrices constructed from finite fields. Two methods, array masking and dispersion, are presented for constructing nonbinary QC-LDPC codes. Simulation results show that codes constructed by these methods perform very well with iterative decoding based on belief propagation. They achieve significant coding gains over Reed-Solomon codes of the same lengths and rates decoded with either algebraic hard-decision decoding or algebraic soft-decision decoding at the expense of larger decoding complexity.

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“…LDPC codes constructed based on finite geometries, such as Euclidean and projective geometries, are known to have large minimum distances [4]- [7]. These codes are commonly referred to as finite geometry (FG) LDPC codes.…”

Section: Introductionmentioning

confidence: 99%

Trapping set structure of LDPC codes on finite geometries

Diao¹,

Tai²,

Lin³

et al. 2013

2013 Information Theory and Applications Workshop (ITA)

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Abstract-The trapping set structure of LDPC codes constructed based on finite geometries, called finite geometry (FG) LDPC codes, is analyzed using a geometric approach. In this approach, trapping sets in the Tanner graph of an FG-LDPC code are represented by subgeometries of the geometry based on which the code is constructed. Using this geometrical representation, bounds and configurations of trapping sets of an FG-LDPC code can be derived and analyzed.

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Construction of Regular and Irregular LDPC Codes: Geometry Decomposition and Masking

Cited by 131 publications

References 47 publications

Non-binary LDPC codes vs. Reed-Solomon codes

Non-binary LDPC codes vs. Reed-Solomon codes

Algebraic Constructions of Nonbinary Quasi-Cyclic LDPC Codes

Trapping set structure of LDPC codes on finite geometries

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