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vol 67 / February, 2024
Article

DOI 10.17586/0021-3454-2019-62-7-621-631

UDC 004.052.32+681.518.5

SOME FEATURES OF ERROR DETECTION BY UNIFORM INDIVISIBLE CODES

D. V. Ephanov
PSTU; Department of Automation and Telemechanics on the Railways


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Abstract. Properties of indivisible uniform codes belonging to the class of equilibrium and the class of Hadamard codes are analyzed. The codes under consideration are widely used in data transmission and in organization of controllable discrete systems. The key characteristics of both classes of indivisible codes to be accounted for when building controllable devices and automation systems, are established. Formulas for calculating the number of errors not detected by the considered codes are presented. Characteristic tables for equilibrium codes and Hadamard codes are given. A noted feature of equilibrium codes “1 out of m” which is not characteristic of other equilibrium codes, is the ability to detect any distortions in code words except for double symmetrical errors. It is proposed to apply the Hadamard codes when organizing self-verifying embedded control schemes based on the logical addition method.
Keywords: equilibrium codes, error detection by equilibrium codes, undetectable error, code features, technical diagnostics of discrete systems

References:
  1. Freiman C.V. Information and Control, 1962, no. 1(5), pp. 64–71. DOI: 10.1016/S0019-9958(62)90223-1.
  2. Sapozhnikov V.V., Sapozhnikov Vl.V. Samoproveryaemye diskretnyye ustroystva (Self-Checked Dis-crete Devices), St. Petersburg, 1992, 224 р. (in Russ.)
  3. Sogomonyan E.S., Slabakov E.V. Samoproveryaemye ustroystva i otkazoustoychivye sistemy (The Self-Checked Devices and Failure-Safe Systems), Moscow, 1989, 208 р. (in Russ.)
  4. Piestrak S.J. Design of Self-Testing Checkers for Unidirectional Error Detecting Codes, Wrocław, Ofi-cyna Wydawnicza Politechniki Wrocłavskiej, 1995, 111 p.
  5. MacWilliams F.J., Sloane N.J.A. The Theory of Error-Correcting Codes, Amsterdam, North-Holland, 1977, 785 p.
  6. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Journal of Instrument Engineering, 2015, no. 5(58), pp. 333–343. DOI: 10.17586/0021-3454-2015-58-5-333-343.
  7. Dundua A.A., Sapozhnikov V.V., Sapozhnikov V.V., Trokhov V.G. Automation and Remote Control, 1980, no. 7, pp. 150–160. (in Russ.)
  8. Ostanin S. Proceedings of 15th IEEE East-West Design & Test Symposium (EWDTS`2017), Novi Sad, Serbia, September 29–October 2, 2017, pp. 696–699. DOI: 10.1109/EWDTS.2017.8110129.
  9. Slabakov E.V., Sogomonyan E.S. Automation and Remote Control, 1980, no. 9, pp. 173–181. (in Russ.)
  10. Slabakov E.V., Sogomonyan E.S. Automation and Remote Control, 1981, no. 11, pp. 147–167. (in Russ.)
  11. Samofalov K.G., Romankevich A.M., Valuyskiy V.N., Kanevskiy Yu.S., Pinevich M.M. Prikladnaya teoriya tsifrovykh avtomatov (Applied Theory of Digital Machines), Kyiv, 1987, 375 р. (in Russ.)
  12. Göessel M., Morosov A.V, Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2005, no. 8, pp. 161–172. (in Russ.)
  13. Göessel M., Ocheretny V., Sogomonyan E., Marienfeld D. New Methods of Concurrent Checking: Edition 1, Dordrecht, Springer Science+Business Media B.V., 2008, 184 p.
  14. Das D.K., Roy S.S., Dmitiriev A., Morozov A., Gössel M. Proceedings of the 10th International Work-shops on Boolean Problems, Freiberg, Germany, September, 2012, pp. 33–40.
  15. Anderson D.A., Metze G. IEEE Transaction on Computers, 1973, no. 3(С-33), pp. 263–269.
  16. Maznev V.I. Automation and Remote Control, 1978, no. 9, pp. 142–145. (in Russ.)
  17. Sapozhnikov V.V., Rabara V. Problems of Information Transmission, 1982, no. 3(18), pp. 62–73. (in Russ.)
  18. Sapozhnikov V.V., Sapozhnikov Vl.V. Problems of Information Transmission, 1984, no. 2(20), pp. 65–76. (in Russ.)
  19. Sapozhnikov V.V., Sapozhnikov Vl.V. Problems of Information Transmission, 1988, no. 4(24), pp. 84–92.
  20. Sapozhnikov V.V., Sapozhnikov Vl.V., Tseglovski L. Automation and Remote Control, 1988, no. 10, pp. 139–154. (in Russ.)
  21. Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 1992, no. 3, pp. 3–35. (in Russ.)
  22. Matrosova A., Ostrovsky V., Levin I., Nikitin K. Proceedings of the 9th IEEE International On-Line Testing Symposium (IOLTS’03), Kos Island, Greece, 7–9 July 2003, pp. 49–53.
  23. Matrosova A.Yu., Butorina N.B., Yakmova N.O. Russian Physics Journal, 2013, no. 9-2(56), pp. 171–173. (in Russ.)
  24. Efanov D.V., Sapozhnikov V.V. Automation and Remote Control, 2018, no. 9(79), pp. 1609–1620.
  25. Romashchenko A.E., Rumyantsev A.Yu., Shen' A. Zametki po teorii kodirovaniya (Notes on Coding Theory), Moscow, 2011, 80 р. (in Russ.)
  26. Nikolos D. Journal of Electronic Testing: Theory and Applications, 1998, no. 1-2(12), pp. 69–79. DOI: 10.1023/A:1008281822966.