Large-Girth Nonbinary QC-LDPC Codes of Various Lengths

Huang, Jie; Liu, Lei; Zhou, Wuyang; Zhou, Shengli

doi:10.1109/tcomm.2010.101210.090757

Cited by 35 publications

(47 citation statements)

References 32 publications

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“…These weight-vector enumerators are readily evaluated using (23). The growth rate r (t) (α, β) can now be computed in a similar way as (31).…”

Section: ) Trapping Set Enumerators For a C-nbpb Ensemblementioning

confidence: 99%

“…However, a considerable amount of subsequent research effort was devoted to studying binary LPDC codes and their decoders. As pointed out in [23], non-binary LDPC codes can outperform binary LDPC codes on binary channels and can be seamlessly merged with high-order modulation techniques for multiple input, multiple output channels. With these early promising results and the emergence of a range of applications that use non-binary coding schemes, such as optical communication channels [17] and dense data storage [20], the interest in non-binary LDPC codes is being actively renewed.…”

Section: Introductionmentioning

confidence: 99%

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Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Dolecek

Divsalar

Sun

et al. 2014

IEEE Trans. Inform. Theory

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Abstract-This paper provides a comprehensive analysis of non-binary low-density parity check (LDPC) codes built out of protographs. We consider both random and constrained edgeweight labeling, and refer to the former as the unconstrained non-binary protograph-based LDPC codes (U-NBPB codes) and the latter as the constrained non-binary protograph-based LDPC codes (C-NBPB codes). Equipped with combinatorial definitions extended to the non-binary domain, ensemble enumerators of codewords, trapping sets, stopping sets, and pseudocodewords are calculated. The exact enumerators are presented in the finite-length regime, and the corresponding growth rates are calculated in the asymptotic regime. We then present an EXIT chat tool for computing the iterative decoding thresholds of protograph-based LDPC codes followed by several examples of finite-length U-NBPB and C-NBPB codes with high performance. Throughout the paper, we provide accompanying examples which demonstrate the advantage of non-binary protograph-based LDPC codes over their binary counterparts and over random constructions. The results presented in this paper advance the analytical toolbox of non-binary graph-based codes.

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“…These weight-vector enumerators are readily evaluated using (23). The growth rate r (t) (α, β) can now be computed in a similar way as (31).…”

Section: ) Trapping Set Enumerators For a C-nbpb Ensemblementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Dolecek

Divsalar

Sun

et al. 2014

IEEE Trans. Inform. Theory

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“…More generally, here following [29] we select λ once L is given. Specifically, we choose the smallest λ for any given L such that λL = γ(q − 1) where γ is an integer.…”

Section: Estimated Upper Bound Of Minimum Distance For Nonbinarymentioning

confidence: 99%

“…(11)] is 24. Second, let us consider the 'Design 4' codes listed in Table I of [29] with symbol length of 228, 492, 756, 1596 and 2496 over GF (8). Table III shows the estimated minimum weights of the 'Design 4' codes listed in Table I of [29], of all codes the mean column weight is 2.5 and the code rate is 0.5.…”

Section: B Numerical Examplementioning

confidence: 99%

“…Second, let us consider the 'Design 4' codes listed in Table I of [29] with symbol length of 228, 492, 756, 1596 and 2496 over GF (8). Table III shows the estimated minimum weights of the 'Design 4' codes listed in Table I of [29], of all codes the mean column weight is 2.5 and the code rate is 0.5. Although the estimated upper bound of the minimum distance is larger than the result obtained by the improved NNCS method, it could be meaningful to guide the design of nonbinary QC-LDPC codes achieving large minimum distance, because compared to the NNCS method, we only need the parity check matrix instead of running the decoding process to estimate the minimum distance.…”

Section: B Numerical Examplementioning

confidence: 99%

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Computing the Minimum Distance of Nonbinary LDPC Codes

Liu

Huang

Zhou

et al. 2012

IEEE Trans. Commun.

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Abstract-Finding the minimum distance of low-densityparity-check (LDPC) codes is an NP-hard problem. Different from all existing works that focus on binary LDPC codes, we in this paper aim to compute the minimum distance of nonbinary LDPC codes, motivated by the fact that operating in a large Galois field provides one important degree of freedom to achieve both good waterfall and error-floor performance. Our method is based on the existing nearest nonzero codeword search (NNCS) method, but several modifications are incorporated for nonbinary LDPC codes, including the modified error impulse pattern, the dithering method, and the nonbinary decoder. Numerical results on the estimated minimum distances show that a code's minimum distance can be increased by careful selection of nonzero elements of the parity check matrix, or by increasing the mean column weight, or by increasing the size of the Galois field. These results support observations that have been made based on simulated performance in the literature. Finally, we provide an upper bound on the minimum distance for nonbinary quasi-cyclic LDPC codes.

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2014

OFDM for Underwater Acoustic Communications

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Large-Girth Nonbinary QC-LDPC Codes of Various Lengths

Cited by 35 publications

References 32 publications

Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Non-Binary Protograph-Based LDPC Codes: Enumerators, Analysis, and Designs

Computing the Minimum Distance of Nonbinary LDPC Codes

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