Problems of Information Transmission

, Volume 53, Issue 3, pp 229–241 | Cite as

A special class of quasi-cyclic low-density parity-check codes based on repetition codes and permutation matrices

Coding Theory
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Abstract

We propose a new ensemble of binary low-density parity-check codes with paritycheck matrices based on repetition codes and permutation matrices. The proposed class of codes is a subensemble of quasi-cyclic codes. For the constructed ensemble, we obtain minimum distance estimates. We present simulation results for the proposed code constructions under the (Sum-Product) iterative decoding algorithm for transmission over an additive white Gaussian noise channel using binary phase-shift keying.

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References

  1. 1.
    Gallager, R.G., Low-Density Parity-Check Codes, Cambridge: MIT Press, 1963. Translated under the title Kody’s maloi plotnost’yu proverok na chetnost’, Moscow: Mir, 1966.MATHGoogle Scholar
  2. 2.
    Gabidulin, E., Moinian, A., and Honary, B., Generalized Construction of Quasi-cyclic Regular LDPC Codes Based on Permutation Matrices, in Proc. 200. IEEE Int. Sympos. on Information Theory (ISIT’2006), Seattle, WA, USA, July 9–14, 2006, pp. 679–683.Google Scholar
  3. 3.
    Hagiwara, M., Nuida, K., and Kitagawa, T., On the Minimal Length of Quasi-cyclic LDPC Codes with Girth ≥ 6, in Proc. 200. Int. Sympos. on Information Theory and Its Applications (ISITA’2006), Seoul, Korea, Oct. 29–Nov. 1, 2006.Google Scholar
  4. 4.
    Wang, Y., Yedidia, J.S., and Draper, S.C., Construction of High-Girth QC-LDPC Codes, in Proc. 5th Int. Sympos. on Turbo Codes and Related Topics, Lausanne, Switzerland, Sept. 1–5, 2008, pp. 180–185.Google Scholar
  5. 5.
    Kim S. No J.-S. Chung H. Shin D.-J. Quasi-cyclic Low-Density Parity-Check Codes with Girth Larger than 12. IEEE Trans. Inform. Theory, 2007, vol. 53, no. 8, pp. 2885–2891.CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Ivanov, F.I., Zyablov, V.V., and Potapov, V.G., Low-Density Parity-Check Codes Based on Galois Fields, Information Processes, 2012, vol. 12, no. 1, pp. 68–83. Avaiable at http://www.jip.ru/2012/68-83-2012.pdf.Google Scholar
  7. 7.
    Ivanov, F.I., Zyablov, V.V., and Potapov, V.G., Estimation ofMinimum Length of Cycles in Quasi-Cyclic Regular LDPC Codes Based on the Permutation Matrices, Informatsionno-Upravlyayushchie Sistemy, 2012, no. 3 (58), pp. 42–45.Google Scholar
  8. 8.
    Zyablov, V.V., Ivanov, F.I., and Potapov, V.G., Comparison of Various Constructions of Binary LDPC Codes Based on Permutation Matrices, Information Processes, 2012, vol. 12, no. 1, pp. 31–52. Avaiable at http://www.jip.ru/2012/31-52-2012.pdf.Google Scholar
  9. 9.
    Ivanov F.I. Zyablov V.V. Potapov V.G. Low-Density Parity-Check Codes Based on the Independent Subgroups // Proc. XIII Int. Sympos. on Problems of Redundancy in Information and Control Systems (RED’2012). St. Petersburg, Russia. September 5–10, 2012, pp. 31–34.CrossRefGoogle Scholar
  10. 10.
    Ivanov, F.I., Zyablov, V.V., and Potapov, V.G., The Score of the Minimum Length of Cycles in Generalized Quasi-cyclic Regular LDPC Codes, in Proc. 13th Int. Workshop on Algebraic and Combinatorial Coding Theory (ACCT-13), Pomorie, Bulgaria, June 15–21, 2012, pp. 162–167.Google Scholar
  11. 11.
    Esmaeili, M. and Gholami, M., Structured Quasi-cyclic LDPC Codes with Girth 18 and Column-Weight J ≥ 3. Int. J. Electron. Commun. (AEÜ), 2010, vol. 64, no. 3, pp. 202–217.CrossRefGoogle Scholar
  12. 12.
    Kou, Y., Lin, S., and Fossorier, M., Low-Density Parity Check Codes Based on Finite Geometries: A Rediscovery and New Results, IEEE Trans. Inform. Theory, 2001, vol. 47, no. 7, pp. 2711–2736.CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Vasic, B., Pedagani, K., and Ivkovic, M., High-Rate Girth-Eight Low-Density Parity-Check Codes on Rectangular Integer Lattices, IEEE Trans. Commun., 2004, vol. 52, no. 8, pp. 1248–1252.CrossRefGoogle Scholar
  14. 14.
    Johnson, S., Low-Density Parity-Check Codes from Combinatorial Designs, PhD Thesis, School of Electrical Engineering and Computer Science, Univ. of Newcastle, Australia, 2004.Google Scholar
  15. 15.
    Xiao, H. and Banihashemi, A.H., Improved Progressive-Edge-Growth (PEG) Construction of Irregular LDPC Codes, IEEE Commun. Lett., 2004, vol. 8, no. 12, pp. 715–717.CrossRefGoogle Scholar
  16. 16.
    Hu, X.-Y., Eleftheriou, E., and Arnold, D.M., Regular and Irregular Progressive Edge-Growth Tanner Graphs, IEEE Trans. Inform. Theory, 2003, vol. 51, no. 1, pp. 386–398.CrossRefMATHMathSciNetGoogle Scholar
  17. 17.
    Tian, T., Jones, C., Villasenor, J.D., and Wesel, R.D., Construction of Irregular LDPC Codes with Low Error Floors, in Proc. 200. IEEE Int. Conf. on Communications (ICC’2003), Anchorage, AK, USA, May 11–15, 2003, vol. 5, pp. 3125–3129.Google Scholar
  18. 18.
    Vukobratovic, D., Djurendic, A., and Senk, V., ACE Spectrum of LDPC Codes and Generalized ACE Design, in Proc. 200. IEEE Int. Conf. on Communications (ICC’2007), Glasgow, Scotland, June 24–28, 2007, pp. 665–670.CrossRefGoogle Scholar

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© Pleiades Publishing, Inc. 2017

Authors and Affiliations

  1. 1.Kharkevich Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia

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