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

  • Jasvinder Singh
  • Manish GuptaEmail author
  • Jaskarn Singh Bhullar


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.


Quasi-Cyclic Low-Density Parity-Check codes; Girth Circulant Permutation Matrix Exponent matrix 





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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Jasvinder Singh
    • 1
    • 2
  • Manish Gupta
    • 2
    Email author
  • Jaskarn Singh Bhullar
    • 3
  1. 1.I.K.G. Punjab Technical UniversityJalandharIndia
  2. 2.Department of Applied SciencesBaba Farid College of Engineering and TechnologyBathindaIndia
  3. 3.Department of Applied SciencesMalout Institute of Management and Information TechnologyMaloutIndia

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