Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT)

Idris Abiodun Aremu; Kazeem Alagbe Gbolagade

doi:doi:10.11648/j.se.20170505.12

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Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT)

Idris Abiodun Aremu, Kazeem Alagbe Gbolagade

Published in Software Engineering (Volume 5, Issue 5)

Received: 16 November 2017 Accepted: 30 November 2017 Published: 10 January 2018

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Abstract

During the last decade information security and reliable communication is unavoidable in information processing. Residue Number Systems (RNS) are still attracting considerable attention from the research community in digital signal processing. In this paper a new low cost method for multiple error detection and correction based on the Redundant Residue Number System (RRNS) was exhibited. RRNS is obtained by adding some redundant residues which brings in error detection and error correction competence. The proposed multiple error correction scheme exploit the Chinese Remainder Theorem (CRT) together with a novel algorithm that significantly simplifies the error correcting process for integers. The result is slightly different from the current state of the art whereby the error value is estimated using optimization algorithm such as integer programming and the proposed multiple error correction schemes does not require complex iterations in order to correct the errors.

Published in	Software Engineering (Volume 5, Issue 5)
DOI	10.11648/j.se.20170505.12
Page(s)	72-80
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Chinese Remainder Theorem (CRT), Digital Signal Processing, Residue Number System (RNS), Redundant Residue Number System (RRNS)

References

[1]	Aremu I. A. and Gbolagade K. A “Information encoding and decoding using Residue Number System for {2²ⁿ-1, 2²ⁿ, 2²ⁿ+1} moduli sets” International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 6, Issue 8, August 2017, ISSN: 2278-1323.
[2]	S.-S. Yau, Y.-c. Liu, Error correction in redundant residue number systems, IEEE Trans. Computer. C-22 (I) (1973) 511. http://dx.doi.orgllO.1109/T-C.1973.223594.
[3]	R. W. Watson and C. W. Hastings, “Self-Checked Com-putation Using Residue Arithmetic,” Proceedings of the IEEE, Vol. 54, No. 12, 1966, pp. 1920-1931.
[4]	S. S. S. Yau and Y. C. Liu, “Error Correction in Redundant Residue Number Systems,” IEEE Transactions on Computers, Vol. C-22, No. 1, 1973, pp. 5-11.
[5]	D. Mandelbaum, “Error Correction in Residue Arithmetic-tic,” IEEE Transactions on Computers, Vol. C-21, No. 6, 1972, pp. 538-545.
[6]	M. H. Etzel and W. K. Jenkins, “Redundant Residue Number Systems for Error Detection and Correction in Digital Filters,” IEEE Transactions on Acoustics Speech and Signal Processing, Vol. 28, No. 10, 1980, pp. 588-544.
[7]	R. W. Watson, “Error Detection and Correction and Other Residue-Interacting Operations in a Redundant Residue Number System,” University of California, Berkeley.
[8]	V. Ramachandran, “Single Residue Error Correction in Residue Number Systems,” IEEE Transactions on Computers, Vol. C-32, No. 5, 1983, pp. 504-507.
[9]	Beckmann, P. E., & Musicus, B. R. (1993). Fast fault-tolerant digital convolution using a polynomial residue number system. IEEE transactions on Signal Processing, 41 (7), 2300-2313.
[10]	Katti, R. S. (1996). A new residue arithmetic error correction scheme. IEEE transactions on computers, 45 (1), 13-19.
[11]	Goh, V. T., & Siddiqi, M. U. (2008). Multiple error detection and correction based on redundant residue number systems. IEEE Transactions on Communications, 56 (3).
[12]	Pham, D. M., Premkumar, A. B., & Madhukumar, A. S. (2011). Error detection and correction in communication channels using inverse gray RSNS codes. IEEE Transactions on communications, 59 (4), 975-986.
[13]	Bankas, E. K., Gbolagade, K. A., & Cotofana, S. D. (2013, June). An effective New CRT based reverse converter for a novel moduli set {2 2n+1− 1, 2 2n+1, 2 2n−1}. In 2013 IEEE 24th International Conference on Application-Specific Systems, Architectures and Processors (pp. 142-146). IEEE.
[14]	Gbolagade, K. A. (2010). Effective reverse conversion in residue number system processors. Doctoral dissertation, TU Delft, Delft University of Technology, Netherland.
[15]	Aremu I. A. and Gbolagade K. A “Information encoding and decoding using Residue Number System for {2²ⁿ-1, 2²ⁿ, 2²ⁿ+1} moduli sets” International Journal of Advanced Research in Computer Engineering & Technology (IJARCET) Volume 6, Issue 8, August 2017, ISSN: 2278-1323.
[16]	Aremu I. A. and Gbolagade K. A ‘Generalized Information Security and Fault Tolerant Based On Redundant Residue Number System’ International Journal of Computer Applications (0975 – 8887) Volume 167-No .13, June 2017.
[17]	Younes, D., & Steffan, P. (2012). A comparative study on different moduli sets in residue number system. In Computer Systems and Industrial Informatics (ICCSII), 2012 International Conference on (pp. 1-6). IEEE.
[18]	Tay, T. F., & Chang, C. H. (2014, June). A new algorithm for single residue digit error correction in Redundant Residue Number System. In Circuits and Systems (ISCAS), 2014 IEEE International Symposium on (pp. 1748-1751). IEEE.
[19]	Hadjicostis, C. N. (2003). Non concurrent error detection and correction in fault-tolerant discrete-time LTI dynamic systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 50 (1), 45-55.
[20]	Beckmann, P. E., & Musicus, B. R. (1993). Fast fault-tolerant digital convolution using a polynomial residue number system. IEEE transactions on Signal Processing, 41 (7), 2300-2313.
[21]	T. F. Tay, C.H. Chang, A non-iterative multiple residue digit error detection and correction algorithm in RRNS. IEEE Trans. Comput. 65 (2), 396-408 (2016).

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APA Style

Idris Abiodun Aremu, Kazeem Alagbe Gbolagade. (2018). Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT). Software Engineering, 5(5), 72-80. https://doi.org/10.11648/j.se.20170505.12

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ACS Style

Idris Abiodun Aremu; Kazeem Alagbe Gbolagade. Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT). Softw. Eng. 2018, 5(5), 72-80. doi: 10.11648/j.se.20170505.12

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AMA Style

Idris Abiodun Aremu, Kazeem Alagbe Gbolagade. Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT). Softw Eng. 2018;5(5):72-80. doi: 10.11648/j.se.20170505.12

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@article{10.11648/j.se.20170505.12,
  author = {Idris Abiodun Aremu and Kazeem Alagbe Gbolagade},
  title = {Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT)},
  journal = {Software Engineering},
  volume = {5},
  number = {5},
  pages = {72-80},
  doi = {10.11648/j.se.20170505.12},
  url = {https://doi.org/10.11648/j.se.20170505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.se.20170505.12},
  abstract = {During the last decade information security and reliable communication is unavoidable in information processing. Residue Number Systems (RNS) are still attracting considerable attention from the research community in digital signal processing. In this paper a new low cost method for multiple error detection and correction based on the Redundant Residue Number System (RRNS) was exhibited. RRNS is obtained by adding some redundant residues which brings in error detection and error correction competence. The proposed multiple error correction scheme exploit the Chinese Remainder Theorem (CRT) together with a novel algorithm that significantly simplifies the error correcting process for integers. The result is slightly different from the current state of the art whereby the error value is estimated using optimization algorithm such as integer programming and the proposed multiple error correction schemes does not require complex iterations in order to correct the errors.},
 year = {2018}
}

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TY  - JOUR
T1  - Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT)
AU  - Idris Abiodun Aremu
AU  - Kazeem Alagbe Gbolagade
Y1  - 2018/01/10
PY  - 2018
N1  - https://doi.org/10.11648/j.se.20170505.12
DO  - 10.11648/j.se.20170505.12
T2  - Software Engineering
JF  - Software Engineering
JO  - Software Engineering
SP  - 72
EP  - 80
PB  - Science Publishing Group
SN  - 2376-8037
UR  - https://doi.org/10.11648/j.se.20170505.12
AB  - During the last decade information security and reliable communication is unavoidable in information processing. Residue Number Systems (RNS) are still attracting considerable attention from the research community in digital signal processing. In this paper a new low cost method for multiple error detection and correction based on the Redundant Residue Number System (RRNS) was exhibited. RRNS is obtained by adding some redundant residues which brings in error detection and error correction competence. The proposed multiple error correction scheme exploit the Chinese Remainder Theorem (CRT) together with a novel algorithm that significantly simplifies the error correcting process for integers. The result is slightly different from the current state of the art whereby the error value is estimated using optimization algorithm such as integer programming and the proposed multiple error correction schemes does not require complex iterations in order to correct the errors.
VL  - 5
IS  - 5
ER  -

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Author Information

Idris Abiodun Aremu

Computer Science Department, School of Technology, Lagos State Polytechnics, Ikorodu, Lagos
Kazeem Alagbe Gbolagade

Department of Computer Science, College of Information Communication Technology, Kwara State University, Ilorin,Kwara

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Plain Text BibTeX RIS

APA Style

Idris Abiodun Aremu, Kazeem Alagbe Gbolagade. (2018). Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT). Software Engineering, 5(5), 72-80. https://doi.org/10.11648/j.se.20170505.12

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ACS Style

Idris Abiodun Aremu; Kazeem Alagbe Gbolagade. Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT). Softw. Eng. 2018, 5(5), 72-80. doi: 10.11648/j.se.20170505.12

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AMA Style

Idris Abiodun Aremu, Kazeem Alagbe Gbolagade. Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT). Softw Eng. 2018;5(5):72-80. doi: 10.11648/j.se.20170505.12

Copy | Download

@article{10.11648/j.se.20170505.12,
  author = {Idris Abiodun Aremu and Kazeem Alagbe Gbolagade},
  title = {Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT)},
  journal = {Software Engineering},
  volume = {5},
  number = {5},
  pages = {72-80},
  doi = {10.11648/j.se.20170505.12},
  url = {https://doi.org/10.11648/j.se.20170505.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.se.20170505.12},
  abstract = {During the last decade information security and reliable communication is unavoidable in information processing. Residue Number Systems (RNS) are still attracting considerable attention from the research community in digital signal processing. In this paper a new low cost method for multiple error detection and correction based on the Redundant Residue Number System (RRNS) was exhibited. RRNS is obtained by adding some redundant residues which brings in error detection and error correction competence. The proposed multiple error correction scheme exploit the Chinese Remainder Theorem (CRT) together with a novel algorithm that significantly simplifies the error correcting process for integers. The result is slightly different from the current state of the art whereby the error value is estimated using optimization algorithm such as integer programming and the proposed multiple error correction schemes does not require complex iterations in order to correct the errors.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Redundant Residue Number System Based Multiple Error Detection and Correction Using Chinese Remainder Theorem (CRT)
AU  - Idris Abiodun Aremu
AU  - Kazeem Alagbe Gbolagade
Y1  - 2018/01/10
PY  - 2018
N1  - https://doi.org/10.11648/j.se.20170505.12
DO  - 10.11648/j.se.20170505.12
T2  - Software Engineering
JF  - Software Engineering
JO  - Software Engineering
SP  - 72
EP  - 80
PB  - Science Publishing Group
SN  - 2376-8037
UR  - https://doi.org/10.11648/j.se.20170505.12
AB  - During the last decade information security and reliable communication is unavoidable in information processing. Residue Number Systems (RNS) are still attracting considerable attention from the research community in digital signal processing. In this paper a new low cost method for multiple error detection and correction based on the Redundant Residue Number System (RRNS) was exhibited. RRNS is obtained by adding some redundant residues which brings in error detection and error correction competence. The proposed multiple error correction scheme exploit the Chinese Remainder Theorem (CRT) together with a novel algorithm that significantly simplifies the error correcting process for integers. The result is slightly different from the current state of the art whereby the error value is estimated using optimization algorithm such as integer programming and the proposed multiple error correction schemes does not require complex iterations in order to correct the errors.
VL  - 5
IS  - 5
ER  -

Copy | Download