Structural Analysis of Array-Based Non-Binary LDPC Codes

Zhao, Shancheng; Huang, Xiujie; Ma, Xiao

doi:10.1109/tcomm.2016.2609906

Cited by 9 publications

(9 citation statements)

References 46 publications

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“…It should be noticed that avoiding chords is not the only way to improve d min . In fact, the graphical results in [9] showed that array-based codes with γ = 3 contain 8-cycles-wc and indicated that it is possible for LDPC codes with γ = 3 and 8-cycles-wc to have d min = 6. Proof : The smallest sizes of an (a, b) ETS with b < a in an LDPC code with g = 8, γ = 3 for b = 0, 1, 2, 3 are a = 6, 5, 4, 3; see [8].…”

Section: Chordless Short Cyclesmentioning

confidence: 99%

Construction of protograph-based LDPC codes with chordless short cycles

Amirzade¹,

Mohammad-Reza~Sadeghi²,

Panario³

2020

Preprint

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Controlling small size trapping sets and short cycles can result in LDPC codes with large minimum distance d min . We prove that short cycles with a chord are the root of several trapping sets and eliminating these cycles increases d min . We show that the lower bounds on d min of an LDPC code with chordless short cycles, girths 6 (and 8), and column weights γ (and 3), respectively, are 2γ (and 10), which is a significant improvement compared to the existing bounds γ + 1 (and 6). Necessary and sufficient conditions for exponent matrices of protograph-based LDPC codes with chordless short cycles are proposed for any type of protographs, single-edge and multiple-edge, regular and irregular.The application of our method to girth-6 QC-LDPC codes shows that the removal of those cycles improves previous results in the literature.

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Section: Chordless Short Cyclesmentioning

confidence: 99%

Construction of protograph-based LDPC codes with chordless short cycles

Amirzade¹,

Mohammad-Reza~Sadeghi²,

Panario³

2020

Preprint

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show abstract

“…Case 3: k 2 = k 3 and k 1 = k 4 . Let p k1 = a, p k2 = b, p k3 = c, and p k4 = d. Based on (3) and (4), we can see that there exist 8-cycles of type (p k1 , p k2 , p k3 , p k4 ) in the Tanner graph of C, clearly a contradiction.…”

mentioning

confidence: 96%

“…Dear editor, Many research results show that, for equivalent bit length, short nonbinary LDPC codes outperform binary LDPC codes by about 1 dB [1][2][3]. Moreover, nonbinary LDPC codes have lower errorfloor, fast iterative decoding convergence, and strong ability of correcting burst errors.…”

mentioning

confidence: 99%

Two classes of QC-LDPC cycle codes approaching Gallager lower bound

et al. 2019

Sci. China Inf. Sci.

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“…From the implementation point of view, array-based NB LDPC codes are very attractive. High-performance NB LDPC codes based on arrays were constructed in [14] for prime numbers. In this Letter, we extend the array-based construction to composite numbers to construct a large class of structured NB LDPC codes.…”

mentioning

confidence: 99%

Extended construction of array‐based non‐binary LDPC codes

Zhao

2019

Electron. lett.

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Array-based non-binary (NB) low-density parity-check (LDPC) codes are attractive in practice for their advantages in implementation and performance. However, existing construction of array-based NB LDPC codes is only with the prime number cases. In this Letter, the authors extend the array-based construction to composite numbers to give an explicit construction of structured array-based NB LDPC codes with column weights three, four, and five. The resulting codes have girth at least six. The simulation results show that the proposed structured codes perform as well as the random codes constructed by progressive edge-growth algorithm, when decoded with the Q-ary sum product algorithm and the low-complexity weighted bit-reliability-based decoding algorithm.

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Structural Analysis of Array-Based Non-Binary LDPC Codes

Cited by 9 publications

References 46 publications

Construction of protograph-based LDPC codes with chordless short cycles

Construction of protograph-based LDPC codes with chordless short cycles

Two classes of QC-LDPC cycle codes approaching Gallager lower bound

Extended construction of array‐based non‐binary LDPC codes

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