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Comparison of various constructions of binary LDPC codes based on permutation matrices

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Abstract

Ensembles of low-density parity check codes based on permutation matrices are considered. Algorithms for generation of check matrices of such codes are proposed. The results of simulation of the obtained code constructions for an iterative belief propagation (sum-product) decoding algorithm applied in the case of transmission of a code word via a binary channel with an additive Gaussian white noise are presented.

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References

  1. R. G. Gallager, Low-Density Parity-Check Codes (MIT Press, Massachusetts, 1963).

    Google Scholar 

  2. T. J. Richardson, M. A. Shokrollahi, and R. L. Urbanke, “Design of Capacity-Approaching Irregular Low-Density Parity Check Codes,” IEEE Trans. on Inform. Theory 47, 619–637 (2001).

    Article  MathSciNet  MATH  Google Scholar 

  3. E. Gabidulin, A. Moinian, and B. Honary, “Generalized Construction of Quasi-Cyclic Regular LDPC Codes Based on Permutation Matrices,” in Proc. IEEE Int. Symp. Inf. Theory, Seattle, WA, 2006 (IEEE, New York, 2006), pp. 679–683.

    Chapter  Google Scholar 

  4. I. Djurdjevic, J. Xu, K. Abdel-Ghaffar, and S. Lin, “A Class of Low-Density Parity-Check Codes Constructed Based on Reed-Solomon Codes with two Information Symbols,” IEEE Commun. Lett. 7, 317–319 (2003).

    Article  Google Scholar 

  5. T. Okamura, “Designing LDPC Codes Using Cyclic Shifts,” in Proc. IEEE Int. Symp. Inf. Theory, Yokohama, 2003 (IEEE, New York, 2003), p. 151.

    Chapter  Google Scholar 

  6. P. C. Fossorier, “Quasi-Cyclic Low-Density Parity-Check Codes from Circulant Permutation Matrices,” IEEE Trans. Inform. Theory 50, 1788–1793 (2004).

    Article  MathSciNet  Google Scholar 

  7. A. A. Davydov, M. Giulietti, S. Marcugini, and F. Pambianco, “On the Spectrum of Possible Parameters of Symmetric Configurations,” in Proc. 12th Int. Symp. on Problems of Redundancy in Information and Control Systems, St. Petersburg, Russia, May, 2009, (St. Petersburg. Gos. Univ. Aerospace Instrumentation (SUAI), St. Petersburg, 2009), pp. 69–54.

    Google Scholar 

  8. A. C. H. Ling, “Difference Triangle Sets From Affine Planes,” IEEE Trans. Inform. Theory 48, 2399–2401 (2002).

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Tanner, “A Recursive Approach to Low Complexity Codes,” IEEE Trans. Inform. Theory 27, 533–547 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  10. I. V. Zhilin, P. S. Rybin, and V. V. Zyablov, “Comparison of Decoding Algorithms for Binary LDPC Codes with a Rigid Input,” in Proc. 34th Int. Conf. Young Researchers and Specialists IPPI RAN “Informational Technologies and Systems”, Gelendzhik, 2011 (IPPI RAN, Moscow, 2011), pp. 221–227.

    Google Scholar 

  11. F. R. Kschischang, B. J. Frey, and H. A. Loeliger, “Factor Graphs and the Sum-Product Algorithm,” IEEE Trans. Inform. Theory 47, 498–519 (2001).

    Article  MathSciNet  MATH  Google Scholar 

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Original Russian Text © V.V. Zyablov, F.I. Ivanov, V.G. Potapov, 2012, published in Informatsionnye Protsessy, 2012, Vol. 12, No. 1, pp. 31–52.

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Zyablov, V.V., Ivanov, F.I. & Potapov, V.G. Comparison of various constructions of binary LDPC codes based on permutation matrices. J. Commun. Technol. Electron. 57, 932–945 (2012). https://doi.org/10.1134/S1064226912080086

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  • DOI: https://doi.org/10.1134/S1064226912080086

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