Abstract. Hamming code properties are analyzed for the case of error occurrence in data bits only; it is actual for the solutions of error detecting systems synthesis. Features of detection of different type (monotonous, symmetric, asymmetric) errors in Hamming code data bits are described. It is shown that ratio of different type of undetectable errors of given multiplicity to the total number of undetectable errors of given multiplicity does not depend on data vector length and is a constant. Results of benchmark experiments demonstrate that application of Hamming code for the organization of self-checking test circuits may be more effective than the use of standard duplication circuit both for technical implementation complexity and for detection of single faults of circuit’s inner structure. 

Keywords: technical diagnostic, concurrent error detection circuits, error detection, data vector, error, Hamming code, combination test circuit, structural redundancy

References:

1. Hamming R.W. Bell System Technical Journal, 1950, no. 29(2), pp. 147–160.
2. MacWilliams F.J., Sloane N.J.A. The Theory of Error-Correcting Codes, Amsterdam, North-Holland, 1977, 785 p.
3. Hamming R.W. Coding and Information Theory, NY, Prentice-Hall, 1986, 272 p.
4. Sagalovich Yu.L. Problems of Information Transmission, 1988, no. 1(24), pp. 79–81. (in Russ.)
5. McCluskey E.J. Logic Design Principles: With Emphasis on Testable Semicustom Circuits, New Jersey, Prentice Hall PTR, 1986, 549 p.
6. Fujiwara E. Code Design for Dependable Systems: Theory and Practical Applications, New Jersey, John Wiley & Sons, 2006, 720 p.
7. Sagalovich Yu.L. Vvedenie v algebraicheskie kody (Introduction to Algebraic Codes), Moscow, 2010, 302 p. (in Russ.)
8. Lisenkov V.M., Bestem'yanov P.F., Leushin V.B., Lisenkov A.V., Van'shin A.E. Sistemy upravleniya dvizheniem poezdov na peregonakh (Control Systems of Train Service on Stages), Moscow, 2009, 324 р. (in Russ.)
9. Efanov D.V., Blyudov A.A. Proceedings of Petersburg Transport University, 2014, no. 3, pp. 69–77. (in Russ.)
10. 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.)
11. Sapozhnikov V.V., Sapozhnikov Vl.V. Samoproveryaemye diskretnye ustroystva (The Self-Checked Discrete Devices), St. Petersburg, 1992, 224 p. (in Russ.)
12. Matrosova A., Ostanin S., Kirienko I., Nikolaeva E. Proc. of 13th IEEE East-West Design & Test Symposium (EWDTS`2015), Batumi, Georgia, 26–29 Sept., 2015. P. 286–289. DOI: 10.1109/EWDTS.2015.7493129.
13. Aksenova G.P. Automation and Remote Control, 2013, no. 2, pp. 124–138. (in Russ.)
14. Drozd A.V., Kharchenko V.S., Antoshchuk S.G., Drozd Yu.V., Drozd M.A., Sulima Yu.Yu. Rabochee diagnostirovanie bezopasnykh informatsionno-upravlyayushchikh sistem (Working Diagnosing of Safe Management Information Systems), Khar'kov, 2012, 614 p. (in Russ.)
15. Kharchenko V., Kondratenko Yu., Kacprzyk J. Springer Book ser. "Studies in Systems, Decision and Control", 2017, vol. 74, 305 p. DOI: 10.1007/978-3-319-44162-7.
16. Nicolaidis M., Zorian Y. J. of Electronic Testing: Theory and Application, 1998, no. 1–2(12), pp. 7–20. DOI: 10.1023/A:1008244815697.
17. Berger J.M. Information and Control, 1961, no. 1(4), pp. 68–73
18. Busaba F.Y., Lala P.K. J. of Electronic Testing: Theory and Applications, 1994, no. 1(5), pp. 19–28. DOI: 10.1007/BF00971960.
19. Morosow A., Sapozhnikov V.V., Sapozhnikov Vl.V., Goessel M. VLSI Design, 1998, no. 4(5), pp. 333–345. DOI: 10.1155/1998/20389.
20. Matrosova A.Yu., Levin I., Ostanin S.A. VLSI Design, 2000, no. 1(11), pp. 47–58. DOI:10.1155/2000/46578.
21. Efanov D.V., Sapozhnikov V.V., Sapozhnikov Vl.V. Automation and Remote Control, 2017, no. 5, pp. 152–165. (in Russ.)
22. 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.
23. Efanov D.V. Information Science and Control Systems, 2011, no. 3, pp. 70–79. (in Russ.)
24. Efanov D.V., Blyudov A.A. Information Science and Control Systems, 2012, no. 2, pp. 100–111. (in Russ.)
25. Sapozhnikov V., Sapozhnikov Vl., Efanov D., Blyudov A. Proc. of 11th IEEE East-West Design & Test Symposium (EWDTS`2013), Rostov-on-Don, Russia, 27–30 September, 2013. P. 200–207. DOI: 10.1109/EWDTS.2013.6673097.
26. Sapozhnikov V.V., Sapozhnikov Vl.V., Efanov D.V. Automation on transport, 2015, no. 1(3), pp. 311–337. (in Russ.)
27. Huches J.L.A., McCluskey E.J., Lu D.J. IEEE Transact. on Computers, 1984, no. 6(C-33), рр. 546–550.
28. Parkhomenko P.P., Sogomonyan E.S. Osnovy tekhnicheskoy diagnostiki. Optimizatsiya algoritmov diagnostirovaniya, apparaturnye sredstva (Basics of Technical Diagnostics. Optimization of Algorithms of Diagnosing, Hardware Means), Moscow, 1981, 320 р. (in Russ.)
29. Collection of Digital Design Benchmarks, http://ddd.fit.cvut.cz/prj/Benchmarks/.
30. Sentovich E.M., Singh K. J., Lavagno L., Moon C., Murgai R., Saldanha A., Savoj H., Stephan P.R., Brayton R.K., Sangiovanni-Vincentelli A. SIS: A System for Sequential Circuit Synthesis, Rep., 4 May, 1992, Univ. of California, Berkeley, 45 p.