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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Johnson, S., Low-Density Parity-Check Codes from Combinatorial Designs, PhD Thesis, School of Electrical Engineering and Computer Science, Univ. of Newcastle, Australia, 2004.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
The research was carried out at the Institute for Information Transmission Problems of the Russian Academy of Sciences at the expense of the Russian Science Foundation, project no. 14-50-00150.
Original Russian Text © F.I. Ivanov, 2017, published in Problemy Peredachi Informatsii, 2017, Vol. 53, No. 3, pp. 30–43.
Rights and permissions
About this article
Cite this article
Ivanov, F.I. A special class of quasi-cyclic low-density parity-check codes based on repetition codes and permutation matrices. Probl Inf Transm 53, 229–241 (2017). https://doi.org/10.1134/S0032946017030048
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0032946017030048