Analysis and Design of Moderate Length Regular LDPC Codes with Low Error Floors

Cole, Chad A.; Wilson, Stephen G.; Hall, E.K.; Giallorenzi, T.R.

doi:10.1109/ciss.2006.286581

Cited by 22 publications

(19 citation statements)

References 9 publications

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“…This brute-force approach may lead to very high complexity to find lowweight codewords. In [17], Cole et al proposed a method to determine the candidate set of EI bits by utilizing the fact that the parity check matrix of an LDPC code is sparse, and the error impulses are applied on multiple bits which form a smallest yet dominant trapping set or codeword. We extend the approach of [17] as the error impulse pattern for finding the minimum distance of nonbinary LDPC codes.…”

Section: The Improved Nncs Methods For Nonbinary Ldpc Codesmentioning

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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Section: The Improved Nncs Methods For Nonbinary Ldpc Codesmentioning

confidence: 99%

“…Denote the error impulse pattern as a vector e = [e 1 , e 2 , · · · , e n ]. Extending the approach [17], nonzero elements in e shall be located on position i and some of the locations in i 1 , · · · , i P , so that all d i check equations that involve V i are satisfied.…”

Section: A Modified Error Impulse Patternsmentioning

confidence: 99%

Computing the Minimum Distance of Nonbinary LDPC Codes

Liu

Huang

Zhou

et al. 2012

IEEE Trans. Commun.

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“…However, when it comes to shorter codes, the weaknesses due to certain sub-graph structures such as cycles and trapping sets are made apparent, and negatively affect the performance of the decoding algorithm [5], [6], [7]. Much effort is therefore devoted to mitigate their effects.…”

Section: Introductionmentioning

confidence: 99%

Erasing Bit Nodes on the Bipartite Graph for Enhanced Performance of LDPC Codes

Catherine

Soyjaudah

2011

2011 Fourth International Conference on Emerging Trends in Engineering &Amp; Technology

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The proposed work is based on the fact that the complete set of bit nodes for an LDPC code may not always be required at the receiving side for successful decoding. A corresponding strategy is therefore built up. In contrast to common practice, the total number of iterations available is shared among different sets. The first set runs the decoding algorithm with all its bit nodes. Successive sets (in case of decoding failure) runs each with a different selection of "erased" bit nodes, leading to an overall non-monotonic behavior. The end result is a system capable of effectively dealing with the problem of cycles and trapping sets without even being aware of their existence. Reported results show an important coding gain over conventional systems.

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“…In the applications where exchanging of the short messages is solicited frequently, to avoid the unnecessary overhead or decoding delay, sometimes the LDPC code of short or medium length is the best choice [16][17][18][19] . For a class of LDPC codes with low row weight in their parity check matrix, the BF variants, while effective for FG-LDPC codes, perform far behind the BP with a gap more than 1dB commonly.…”

Section: Introductionmentioning

confidence: 99%

Application of Beam Search for the decoding of one class of LDPC codes

Feng

2008

J. Electron.(China)

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For one class of Low-Density Parity-Check (LDPC) codes with low row weight in their parity check matrix, a new Syndrome Decoding (SD) based on the heuristic Beam Search (BS), labeled as SD-BS, is put forward to improve the error performance. First, two observations are made and verified by simulation results. One is that in the SNR region of interest, the hard-decision on the corrupted sequence yields only a handful of erroneous bits. The other is that the true error pattern for the nonzero syndrome has a high probability to survive the competition in the BS, provided sufficient beam width. Bearing these two points in mind, the decoding of LDPC codes is transformed into seeking an error pattern with the known decoding syndrome. Secondly, the effectiveness of SD-BS depends closely on how to evaluate the bit reliability. Enlightened by a bit-flipping definition in the existing literature, a new metric is employed in the proposed SD-BS. The strength of SD-BS is demonstrated via applying it on the corrupted sequences directly and the decoding failures of the Belief Propagation (BP), respectively.

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Analysis and Design of Moderate Length Regular LDPC Codes with Low Error Floors

Abstract: The

Cited by 22 publications

References 9 publications

Computing the Minimum Distance of Nonbinary LDPC Codes

Computing the Minimum Distance of Nonbinary LDPC Codes

Erasing Bit Nodes on the Bipartite Graph for Enhanced Performance of LDPC Codes

Application of Beam Search for the decoding of one class of LDPC codes

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