Class of minimax error-corecting codes based on perfect binary arrays

Authors

  • Michael I. Mazurkov Odessa National Polytechnic University, Ukraine

DOI:

https://doi.org/10.3103/S0735272711090032

Keywords:

perfect binary array, synthesis method, complementary matrix, error-correcting code, coding algorithm, decoding algorithm, maximum likelihood

Abstract

Developed the regular synthesis method of infinite family of minimax M(N)-classes of perfect binary arrays of order N = 2k, where k — arbitrary integer. On this basis, a new class of four-parameter minimax correcting  M(n)-codes of length n = N2, which have many practically attractive properties, were constructed. The task of decoding is reduced to an effective procedure of majority estimation of parameters of received code words.

References

  1. M. I. Mazurkov and V. Ya. Chechelnytskyi, “The Classes of Equivalent and Generative Perfect Binary Arrays for CDMA-Technologies,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 46(5), 54 (2003); Radioelectron. Commun. Syst. 46(5), 50 (2003).
  2. M. I. Mazurkov, V. Ya. Chechelnytskyi, and M. Yu. Gerasimenko, “Classes of Minimax Bi-Phase Signals Based on Perfect Binary Arrays,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 49(10), 25 (2006); Radioelectron. Commun. Syst. 49(10), 16 (2006).
  3. J. Jedwab and C. Mitchell, “Constructing new perfect binary arrays,” Electron. Lett. 24, 650 (1988).
  4. P. Wild, “Infinite Families of Perfect Binary Arrays,” Electron. Lett. 24, No. 14, 845 (1988).
  5. L. E. Kopilovich, “On Perfect Binary Arrays,” Electron. Lett. 24, No. 8, 566 (1988).
  6. I. A. Gepko, “Synthesis of Perfect Binary Arrays,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 41(6), 13 (1998); Radioelectron. Commun. Syst. 41(6), 10 (1998).
  7. I. A. Gepko, “Perfect Time-Frequency Codes for Multifrequency CDMA Technologies,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 43(2), 66 (2000); Radioelectron. Commun. Syst. 43(2), 53 (2000).
  8. M. I. Mazurkov and M. Yu. Gerasimenko, “Fast Orthogonal Transforms Based on Perfect Binary Arrays,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 49(9), 54 (2006); Radioelectron. Commun. Syst. 49(9), 36 (2006).
  9. P. E. Baranov, M. I. Mazurkov, V. Ya. Chechelnytskyi, and A. A. Yakovenko, “Family of Two-Dimensional Correcting Codes on a Basis of Perfect Binary Array,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 52(9), 65 (2009) [Radioelectron. Commun. Syst. 52(9), 501 (2009)].
  10. M. I. Mazurkov, V. Ya. Chechel’nitskii and P. Murr, “Information security method based on perfect binary arrays,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 51(11), 53 (2008) [Radioelectron. Commun. Syst. 51(11), 612 (2008)].
  11. M. I. Mazurkov, V. Ya. Chechelnytskyi, and K. K. Nekrasov, “Three-Level Cryptographic System for Block Data Encryption,” Izv. Vyssh. Uchebn. Zaved., Radioelektron. 53(7), 43 (2010) [Radioelectron. Commun. Syst. 53(7), 376 (2010)].
  12. L. E. Varakin, Communications Systems with Noise-Like Signals (Radio i Svyaz’, Moscow, 1985) [in Russian].
  13. A. M. Trakhtman and V. A. Trakhtman, Rudiments of the Theory of Discrete Signals on Finite Intervals (Sov. Radio, Moscow, 1975) [in Russian].
  14. G. C. Clark, Jr. and J. B. Cain, Error Correction Coding for Digital Communications (Plenum Press, New York, 1981; Radio i Svyaz’, Moscow, 1987).
  15. I. M. Vinogradov, Rudiments of the Theory of Numbers (Nauka; GRFML, Moscow, 1981) [in Russian].
  16. R. E. Blahut, Theory and Practice of Error Control Codes (Addison-Wesley Publishing Company Inc., Massachusetts, 1983; Mir, Moscow, 1986).

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Published

2011-09-01

Issue

Vol. 54 No. 9 (2011)

Section

Research Articles