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Amirzade Farzane, Sadeghi Mohammad-Reza, Panario Daniel. QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field[J]. Rhhz Test. doi: 10.3934/amc.2020062
Citation: Amirzade Farzane, Sadeghi Mohammad-Reza, Panario Daniel. QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field[J]. Rhhz Test. doi: 10.3934/amc.2020062
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QC-LDPC construction free of small size elementary trapping sets based on multiplicative subgroups of a finite field

doi: 10.3934/amc.2020062
  • 1.

    Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, 1591634312, Iran

  • 2.

    School of Mathematics and Statistics, Carleton University, Ottawa, K1S 5B6, Canada

Funds:  The authors were partially funded by the Natural Sciences and Engineering Research Council (NSERC) of Canada
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  • Corresponding author: * Corresponding author: Mohammad-Reza Sadeghi
  • Received Date: 2018-12-01
  • Rev Recd Date: 2019-08-01
    • Available Online: 2022-04-08
    Abstract
  • Trapping sets significantly influence the performance of low-density parity-check codes. An $ (a, b) $ elementary trapping set (ETS) causes high decoding failure rate and exert a strong influence on the error floor of the code, where $ a $ and $ b $ denote the size and the number of unsatisfied check-nodes in the ETS, respectively. The smallest size of an ETS in $ (3, n) $-regular LDPC codes with girth 6 is 4. In this paper, we provide sufficient conditions to construct fully connected $ (3, n) $-regular algebraic-based QC-LDPC codes with girth 6 whose Tanner graphs are free of $ (a, b) $ ETSs with $ a\leq5 $ and $ b\leq2 $. We apply these sufficient conditions to the exponent matrix of a new algebraic-based QC-LDPC code with girth at least 6. As a result, we obtain the maximum size of a submatrix of the exponent matrix which satisfies the sufficient conditions and yields a Tanner graph free of those ETSs with small size. Some algebraic-based QC-LDPC code constructions with girth 6 in the literature are special cases of our construction. Our experimental results show that removing ETSs with small size contribute to have better performance curves in the error floor region.

     

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