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On the search of smallest QC-LDPC code with girth six and eight

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Abstract

In this paper, a new and simple method for the construction of Girth-6 (J,L) Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes is proposed. The method is further extended to the search of Girth-8 QC-LDPC codes with base matrices of order 3 × L and 4 × L. The construction is based on three different forms of exponent matrices and the parameters α, p, and q which satisfy the necessary algebraic conditions for a QC-LDPC code having girth 6 and 8. The proposed (J,L) QC-LDPC codes with girth at least six have optimal circulant permutation matrix (CPM) size for the cases where q = α + 1. Moreover, most of the girth-8 QC-LDPC codes searched by the proposed method have smaller CPM size than the existing codes of the same girth. In several cases, the method gives more than one exponent matrices for a code, as most of the existing methods cannot do so. Besides this, the proposed method not only search the QC-LDPC codes with smaller CPM size but also takes much less time than the existing search based methods to search code.

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Authors and Affiliations

  1. I.K.G. Punjab Technical University, Jalandhar, Punjab, India

    Jasvinder Singh

  2. Department of Applied Sciences, Baba Farid College of Engineering and Technology, Bathinda, Punjab, India

    Jasvinder Singh & Manish Gupta

  3. Department of Applied Sciences, Malout Institute of Management and Information Technology, Malout, Punjab, India

    Jaskarn Singh Bhullar

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  1. Jasvinder Singh
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  2. Manish Gupta
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  3. Jaskarn Singh Bhullar
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Correspondence to Manish Gupta.

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Singh, J., Gupta, M. & Bhullar, J.S. On the search of smallest QC-LDPC code with girth six and eight. Cryptogr. Commun. 12, 711–723 (2020). https://doi.org/10.1007/s12095-019-00405-2

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  • DOI: https://doi.org/10.1007/s12095-019-00405-2

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