High-Rate Quasi-Cyclic Low-Density Parity-Check Codes Derived From Finite Affine Planes

Kamiya, Norifumi

doi:10.1109/tit.2007.892770

Cited by 58 publications

(32 citation statements)

References 27 publications

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“…(2,17). We have |G| = 2448 and G = ka, bl, where a = (2, 3, 17, 4, 15, 8, 18, 14, 13, 5, 6, 10, 16, 7, 12, 9, 11, ) Also b ¼ a 1 a 2 where a 1 = (1, 2, 3, 10, 9, 17, 16, 7) a 2 = (5, 11, 14,8,13,18,12,15) The orders of a and b are 17 and 8, respectively. The (3, 17)-regular GP-LDPC code corresponding to the parity-check matrix H(a, b) has girth 8.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…In this direction, several algebraic constructions for LDPC codes can be found in the literature. From among these constructions we refer to those given in [3][4][5][6][7][8][9][10][13][14][15][16][17][18][19][20][21][22][23][24]. These constructions can be divided into two types.…”

Section: Introductionmentioning

confidence: 99%

“…These constructions can be divided into two types. One type is based on finite geometries ( [3,5,[13][14][15][16][17][18][19]) and another type, which initially proposed by Gallager [6], is based on circulant matrices [4,[6][7][8][9][10][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

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Approach to the construction of regular low-density parity-check codes from group permutation matrices

Sobhani¹

2012

IET Commun.

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In this study, a new method for constructing low-density parity-check (LDPC) codes is presented. This construction is based on permutation matrices which come from a finite abstract group and hence the codes constructed in this manner are called group permutation low-density parity-check (GP-LDPC) codes. A necessary and sufficient condition under which a GP-LDPC code has a cycle is given and some properties of these codes are investigated. A class of flexible-rate GP-LDPC codes without cycles of length four is also introduced. Simulation results show that GP-LDPC codes perform very well with the iterative decoding and can outperform their random-like counterparts.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Approach to the construction of regular low-density parity-check codes from group permutation matrices

Sobhani¹

2012

IET Commun.

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“…Note that c i,j in (13) is generally unequal to c i,j in (12). Next, we apply the above manip- (13).…”

Section: Buchberger's Algorithm For Gqc Codesmentioning

confidence: 99%

“…Classical cyclic codes including ubiquitous Reed-Solomon codes correspond to a special case of QC codes. Some class of low-density parity-check (LDPC) codes is investigated as QC codes [7,8,11,12,15].…”

Section: Introductionmentioning

confidence: 99%

On generator and parity-check polynomial matrices of generalized quasi-cyclic codes

Matsui

2015

Finite Fields and Their Applications

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Available online xxxx Communicated by Xiang-dong Hou MSC: 94B05 11T71 05E20Generalized quasi-cyclic (GQC) codes have been investigated as well as quasi-cyclic (QC) codes, e.g., on the construction of efficient low-density parity-check codes. While QC codes have the same length of cyclic intervals, GQC codes have different lengths of cyclic intervals. Similarly to QC codes, each GQC code can be described by an upper triangular generator polynomial matrix, from which the systematic encoder is constructed. In this paper, a complete theory of generator polynomial matrices of GQC codes, including a relation formula between generator polynomial matrices and parity-check polynomial matrices through their equations, is provided. This relation generalizes those of cyclic codes and QC codes. While the previous researches on GQC codes are mainly concerned with 1-generator case or linear algebraic approach, our argument covers the general case and shows the complete analogy of QC case. We do not use Gröbner basis theory explicitly in order that all arguments of this paper are self-contained. Numerical examples are attached to the dual procedure that extracts one from each other. Finally, we provide an efficient algorithm which calculates all generator polynomial matrices with given cyclic intervals.

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Symmetric-Key Corruption Detection: When XOR-MACs Meet Combinatorial Group Testing

Minematsu

Kamiya

2019

Lecture Notes in Computer Science

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High-Rate Quasi-Cyclic Low-Density Parity-Check Codes Derived From Finite Affine Planes

Cited by 58 publications

References 27 publications

Approach to the construction of regular low-density parity-check codes from group permutation matrices

Approach to the construction of regular low-density parity-check codes from group permutation matrices

On generator and parity-check polynomial matrices of generalized quasi-cyclic codes

Symmetric-Key Corruption Detection: When XOR-MACs Meet Combinatorial Group Testing

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