Wireless Personal Communications

, Volume 86, Issue 3, pp 1169–1181 | Cite as

Performance Evaluation of Non-redundant Error Correcting Scheme Using Logistic Chaotic Map

  • Hikmat N. AbdullahEmail author
  • Sarab K. Mahmood


In this paper an efficient error-correcting scheme based on logistic chaotic map for non-coherent chaos communication system without redundancy is presented and its performance is evaluated. The scheme uses one chaotic generator to generate two sequences one for each data bit value in a way that the end of the current chaotic sequence sets the initial value of the next sequence of the same symbol. With this arrangement, successive chaotic sequences having the same chaotic dynamics are created for the purpose of error correction. A suboptimal detection algorithm based on shortest distance calculation between the received sequence and the chaotic trajectories over nth-dimension is used for detecting the transmitted symbol and performing the errors-correction. The simulation results show that the scheme offers improvement in Eb/N0 over the method before the error-correcting scheme and this improvement is increased as the trajectory dimension is increased. At bit-error probability of 10−3, a gain of 0.5 dB is obtained in Eb/No over the method before the error-correcting scheme when the dimension is 4. The power point in the scheme is that error correction is based on chaotic dynamics and no redundant bits are needed. This would make the scheme a good candidate for applications that require high data transmission rates.


Channel coding Analogue coding Chaotic communication Suboptimal detection 



The authors would like to thank Prof. Dr. Alejandro Valenzuela from Bonn-Rhein-Sieg University of applied sciences in Germany for his scientific support and International Institute of Education IEE in USA for financing support of this research work.


  1. 1.
    Kolumbán, G., Vizvári, B., Schwarz, W., & Abel, A. (1996). Differential chaos shift keying: A robust coding for chaos communication. In Proceedings of NDES’96 international conference (pp. 87–92). January 1996.Google Scholar
  2. 2.
    Kennedy, M. P., & Kolumban, G. (2000). Digital communications using chaos. Journal of Signal Processing, 80(7), 1307–1320.CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Hasler, M., & Schimming, T. (2000). Chaos communication over noisy channels. International Journal on Bifurcation and Chaos, 10(4), 719–736.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Lau, F., & Tse, C. (2003). Chaos-based digital communication systems (1st ed.). Berlin: Springer publishing house.CrossRefzbMATHGoogle Scholar
  5. 5.
    Long, M. (2012). Bit error rate improvement for chaos shift keying chaotic communication systems. IET Communications, 6(16), 2639–2644.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Zaher, A. (2013). Digital communication using a novel combination of chaotic shift keying and doffing oscillators. International Journal of Innovative Computing, Information and Control, 9(5), 1865–1879.Google Scholar
  7. 7.
    Hasler, M., & Schimming, T. (2002). Optimal and suboptimal chaos receivers. Proceedings of the IEEE, 90(5), 733–746.CrossRefGoogle Scholar
  8. 8.
    Arai, S., & Nishio, Y. (2009). Suboptimal receiver using shortest distance approximation method for chaos shift keying. Journal of Signal Processing, 13(2), 161–169.Google Scholar
  9. 9.
    Arai, S., Nishio, Y., & Yamazato, T. (2008). Error-correcting method based on chaotic dynamics for non-coherent chaos communications. In Proceedings of NOLTA’08 international conference (pp. 652–655). September 2008.Google Scholar
  10. 10.
    Aria, S., Nishio, Y., Yamazato, T., & Ozawa, S. (2009). Error-correcting scheme without redundancy code using chaotic dynamics for non-coherent chaos communications. In Nonlinear Circuit Networks. Tokushima, December 2009.Google Scholar
  11. 11.
    Arai, S., Nishio, Y., & Yamazato, T. (2010). Error-correcting scheme based on chaotic dynamics and its performance for non-coherent chaos communications. Journal of Non-linear Theory and its Applications, IEICE, 1(1), 196–206.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of Al-NahrainBaghdadIraq
  2. 2.University of Al-MustansiryahBaghdadIraq

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