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    On Trapping Sets and Guaranteed Error Correction Capability of LDPC Codes and GLDPC Codes

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    Name:
    On_Trapping_Sets_and_Guarantee ...
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    Description:
    Final Accepted Manuscript
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    Author
    Chilappagari, Shashi Kiran
    Nguyen, Dung Viet
    Vasic, Bane
    Marcellin, Michael W.
    Affiliation
    Department of Electrical and Computer Engineering, The University of Arizona
    Issue Date
    2010-04
    Keywords
    Bit flipping algorithms
    error correction capability
    fixed sets
    generalized low-density parity-check (LDPC) codes
    low-density parity-check (LDPC) codes
    trapping sets
    
    Metadata
    Show full item record
    Publisher
    Institute of Electrical and Electronics Engineers (IEEE)
    Citation
    S. K. Chilappagari, D. V. Nguyen, B. Vasic and M. W. Marcellin, "On Trapping Sets and Guaranteed Error Correction Capability of LDPC Codes and GLDPC Codes," in IEEE Transactions on Information Theory, vol. 56, no. 4, pp. 1600-1611, April 2010, doi: 10.1109/TIT.2010.2040962.
    Journal
    IEEE Transactions on Information Theory
    Rights
    © 2010 IEEE
    Collection Information
    This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.
    Abstract
    The relation between the girth and the guaranteed error correction capability of ¿ -left-regular low-density parity-check (LDPC) codes when decoded using the bit flipping (serial and parallel) algorithms is investigated. A lower bound on the size of variable node sets which expand by a factor of at least 3 ¿/4 is found based on the Moore bound. This bound, combined with the well known expander based arguments, leads to a lower bound on the guaranteed error correction capability. The decoding failures of the bit flipping algorithms are characterized using the notions of trapping sets and fixed sets. The relation between fixed sets and a class of graphs known as cage graphs is studied. Upper bounds on the guaranteed error correction capability are then established based on the order of cage graphs. The results are extended to left-regular and right-uniform generalized LDPC codes. It is shown that this class of generalized LDPC codes can correct a linear number of worst case errors (in the code length) under the parallel bit flipping algorithm when the underlying Tanner graph is a good expander. A lower bound on the size of variable node sets which have the required expansion is established.
    ISSN
    0018-9448
    EISSN
    1557-9654
    DOI
    10.1109/tit.2010.2040962
    Version
    Final accepted manuscript
    ae974a485f413a2113503eed53cd6c53
    10.1109/tit.2010.2040962
    Scopus Count
    Collections
    UA Faculty Publications

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