Skip to main content
SpringerLink
Log in

Algorithm for Constructing Modular Projections for Correcting Multiple Errors Based on a Redundant Residue Number System Using Maximum Likelihood Decoding

  • Published:
Programming and Computer Software Aims and scope Submit manuscript

Abstract

One of the most important applications of the Redundant Residual Numbers System (RRNS) is to improve the fault tolerance of the data storage, processing, and transmission. Correcting multiple errors is a challenging computational task. This complexity is mainly due to the numerous combinations of erroneous residuals at the error localization stage. In this paper, we propose an approach for constructing modular projections to correct any number of errors. The algorithm uses the Maximum Likelihood Decoding (MLD) and the Approximate Rank (AR) to reduce the number of projections and processing time. AR-RRNS with MLD algorithm can provide the number of modular projections close to the theoretical lower bound of the most efficient state-of-the-art algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.

Similar content being viewed by others

REFERENCES

  1. Nazarov, A., Babenko, M., and Golimblevskaia, E., Hardware implementation of the reverse conversion RNS-WNS on FPGA, Proc. IEEE Int. Conf. on Engineering and Telecommunication (En&T), 2020, pp. 1–5. https://doi.org/10.1109/EnT50437.2020.9431249

  2. Ding, C., Pei, D., and Salomaa, A., Chinese Remainder Theorem: Applications in Computing, Coding, Cryptography, Singapore: World Sci. Publ. Co. Ltd., 1996. https://doi.org/10.1142/3254

    Book  MATH  Google Scholar 

  3. Mandelbaum, D., On a class of arithmetic codes and a decoding algorithm (Corresp.), IEEE Trans. Inf. Theory, 1976, vol. 22, no. 1, pp. 85–88. https://doi.org/10.1109/TIT.1976.1055504

    Article  Google Scholar 

  4. Barsi, F. and Maestrini, P., Error correcting properties of redundant residue number systems, IEEE Trans. Comput., 1973, vol. C-22, no. 3, pp. 307–315. https://doi.org/10.1109/T-C.1973.223711

    Article  MathSciNet  Google Scholar 

  5. Sun, J. and Krishna, H., A coding theory approach to error control in redundant residue number systems. II. Multiple error detection and correction, IEEE Trans. Circuits Syst. II: Analog Digital Signal Process., 1992, vol. 39, no. 1, pp. 18–34. https://doi.org/10.1109/82.204107

    Article  Google Scholar 

  6. Krishna, H., Lin, K.Y., and Sun, J.D., A coding theory approach to error control in redundant residue number systems. Part I: theory and single error correction, IEEE Trans. Circuits Syst., 1992, vol. 39, pp. 8–17. https://doi.org/10.1109/82.204106

    Article  Google Scholar 

  7. Chervyakov, N.I., Lyakhov, P.A., Babenko, M.G., Lavrinenko, I.N., Lavrinenko, A.V., and Nazarov, A.S., The architecture of a fault-tolerant modular neurocomputer based on modular number projections, Neurocomputing, 2018, vol. 272, pp. 96–107. https://doi.org/10.1016/j.neucom.2017.06.063

    Article  Google Scholar 

  8. Goldreich, O., Ron, D., and Sudan, M., Chinese remaindering with errors, IEEE Trans. Inf. Theory, 2000, vol. 46, no. 4, pp. 1330–1338. https://doi.org/10.1109/18.850672

    Article  MathSciNet  Google Scholar 

  9. Ananda Mohan, P.V., Residue Number Systems: Theory and Applications, Birkhäuser: Springer Int. Publ., 2016.

  10. Yin, P. and Li, L., A new algorithm for single error correction, Proc. RRNS Int. Conf. on Communications, Circuits and Systems (ICCCAS), Chengdu, 2013, pp. 178–181. https://doi.org/10.1109/ICCCAS.2013.6765313

  11. Yau, S.S. and Yu-Cheng Liu, Error correction in redundant residue number systems, IEEE Trans. Comput., 1973, vol. C-22, no. 1, pp. 5–11. https://doi.org/10.1109/T-C.1973.223594

    Article  MathSciNet  Google Scholar 

  12. Tay, T.F. and Chang, C., A new algorithm for single residue digit error correction in redundant residue number system, Proc. IEEE Int. Symp. on Circuits and Systems (ISCAS), Melbourne, 2014, pp. 1748–1751. https://doi.org/10.1109/ISCAS.2014.6865493

  13. Tay, T.F. and Chang, C., A non-iterative multiple residue digit error detection and correction algorithm in RRNS, IEEE Trans. Comput., 2016, vol. 65, no. 2, pp. 396–408. https://doi.org/10.1109/TC.2015.2435773

    Article  MathSciNet  Google Scholar 

  14. Goh, V.T., Tinauli, M., and Siddiqi, M.U., A novel error correction scheme based on the Chinese remainder theorem, Proc. 9th Int. Conf. on Communications Systems, ICCS 2004, Singapore, 2004, pp. 461–465. https://doi.org/10.1109/ICCS.2004.1359419

  15. Goh, V.T. and Siddiqi, M.U., Multiple error detection and correction based on redundant residue number systems, IEEE Trans. Commun., 2008, vol. 56, no. 3, pp. 325–330. https://doi.org/10.1109/TCOMM.2008.050401

    Article  Google Scholar 

  16. Jenkins, W.K. and Altman, E.J., Self-checking properties of residue number error checkers based on mixed radix conversion, IEEE Trans. Circuits Syst., 1988, vol. 35, no. 2, pp. 159–167. https://doi.org/10.1109/31.1717

    Article  Google Scholar 

  17. Tang, Y., Boutillon, E., Jégo, C., and Jézéquel, M., A new single-error correction scheme based on self-diagnosis residue number arithmetic, Proc. Conf. on Design and Architectures for Signal and Image Processing (DASIP), Edinburgh, 2010, pp. 27–33. https://doi.org/10.1109/DASIP.2010.5706242

  18. Chervyakov, N.I., Lyakhov, P.A., Babenko, M.G., Garyanina, A.I., Lavrinenko, I.N., Lavrinenko, A.V., and Deryabin, M.A., An efficient method of error correction in fault-tolerant modular neurocomputers, Neurocomputing, 2016, vol. 205, pp. 32–44. https://doi.org/10.1016/j.neucom.2016.03.041

    Article  Google Scholar 

  19. Babenko, M., Kucherov, N., Tchernykh, A., Chervyakov, N., Nepretimova, E., and Vashchenko, I., Development of a control system for computations in BOINC with homomorphic encryption in residue number system, Proc. 3rd Int. Conf. BOINC-based High Performance Computing: Fundamental Research and Development. BOINC:FAST 2017, Petrozavodsk, 2017, pp. 78–84.

  20. Su, C.C. and Lo, H.Y., An algorithm for scaling and single residue error correction in residue number systems, IEEE Trans. Comput., 1990, vol. 39, no. 8, pp. 1053–1064. https://doi.org/10.1109/12.57044

    Article  Google Scholar 

  21. Dimauro, G., Impedovo, S., and Pirlo, G., A new technique for fast number comparison in the residue number system, IEEE Trans. Comput., 1993, vol. 42, no. 5, pp. 608–612. https://doi.org/10.1109/12.223680

    Article  MathSciNet  Google Scholar 

  22. Chervyakov, N., Babenko, M., Tchernykh, A., Kucherov, N., Miranda-Lopez, V., and Cortes-Mendoza, J.M., AR-RRNS: configurable, scalable and reliable systems for internet of things to ensure security, Future Gener. Comput. Syst., 2017, vol. 92, no. 5. https://doi.org/10.1016/j.future.2017.09.061

  23. Haron, N.Z. and Hamdioui, S., Redundant residue number system code for fault-tolerant hybrid memories, ACM J. Emergy Technol. Comput. Syst., 2011, vol. 7, no. 1, p. 4. https://doi.org/10.1145/1899390.1899394

    Google Scholar 

  24. Szabo, N.S. and Tanaka, R.I., Residue Arithmetic and Its Applications to Computer Technology, New York: McGraw-Hill, 1967.

    MATH  Google Scholar 

  25. Babenko, M., Tchernykh, A., Pulido-Gaytan, B., Cortés-Mendoza, J.M., Shiryaev, E., Golimblevskaia, E., Avetisyan, A., and Nesmachnow, S., RRNS base extension error-correcting code for performance optimization of scalable reliable distributed cloud data storage, Proc. IEEE Int. Parallel and Distributed Processing Symp. Workshops (IPDPSW), Portland, 2021, pp. 548–553. https://doi.org/10.1109/IPDPSW52791.2021.00087

Download references

ACKNOWLEDGMENTS

This work was supported in part by RFBR, Sirius University of Science and Technology, JSC Russian Railways and Educational Fund “Talent and success,” project no. 20-37-51004, scholarship of the President of the Russian Federation SP-1685.2019.5, SP-3149.2019.5, and RFBR and Chelyabinsk Region, project no. 20-47-740005.

Author information

Authors and Affiliations

  1. North-Caucasus Center for Mathematical Research, North-Caucasus Federal University, 355029, Stavropol, Russia

    M. Babenko, A. Nazarov & I. Vashchenko

  2. Institute for System Programming of the Russian Academy of Sciences, 109004, Moscow, Russia

    M. Babenko & A. Tchernykh

  3. Sirius University of Science and Technology, 354340, Sochi, Russia

    M. Babenko & A. Nazarov

  4. CICESE Research Center, 22860, Ensenada, B.C., Mexico

    A. Tchernykh, B. Pulido-Gaytan & J. M. Cortés-Mendoza

  5. South Ural State University, Chelyabinsk, Russia

    A. Tchernykh

Authors
  1. M. Babenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Nazarov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Tchernykh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Pulido-Gaytan
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. J. M. Cortés-Mendoza
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. I. Vashchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. Babenko, A. Nazarov, A. Tchernykh, B. Pulido-Gaytan, J. M. Cortés-Mendoza or I. Vashchenko.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Babenko, M., Nazarov, A., Tchernykh, A. et al. Algorithm for Constructing Modular Projections for Correcting Multiple Errors Based on a Redundant Residue Number System Using Maximum Likelihood Decoding. Program Comput Soft 47, 839–848 (2021). https://doi.org/10.1134/S0361768821080089

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0361768821080089

Search

Navigation