iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.1007/s12095-023-00687-7
Integer codes correcting burst errors within one byte and single errors within two bytes | Cryptography and Communications Skip to main content
Springer Nature Link
Log in

Integer codes correcting burst errors within one byte and single errors within two bytes

  • Research
  • Published:
Cryptography and Communications Aims and scope Submit manuscript

Abstract

This paper presents a class of integer codes that are suitable for use in various optical networks. The presented codes are generated with the help of a computer and have the ability to correct l-bit burst errors corrupting one b-bit byte (1 ≤ l < b) and single errors corrupting two b-bit bytes. To evaluate the performance of the presented codes, we analyze their probabilities of incorrect decoding for two types of channels. In addition, the paper shows that the proposed codes can be interleaved without using an interleaver, which allows the decoder to correct all l-bit burst errors as well as many random errors.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data availability

Data sharing is not applicable to this article as no datasets were generated or analysed during the current study.

References

  1. Ono, T, et al.: Bit error statistical analysis of optical transmission systems.In: Faulkner, D.W., Harmer, A.L. (eds.) pp. 43–49. IOS Press (2000)

  2. James, L.: Error behaviour in optical networks. Ph.D. dissertation,Dept. Eng., Univ. Cambridge, U.K. (2005)

  3. Anslow, P., Ishida, O.: Error distribution in optical links. IEEE 802.3 HSSG Interim Meeting, Nov. (2007)

  4. Das, A., Touba, N.: A new class of single burst error correcting codes with parallel decoding. IEEE Trans. Comput. 69(2), 253–259 (2020)

    Article  MathSciNet  Google Scholar 

  5. Wicker, S., Bhargava, V.: Reed-solomon codes and their applications. Wiley, Hoboken, NJ, USA (1999)

  6. Overveld, W.: Multiple-burst error-correcting cyclic product codes. IEEE Trans. Inf. Theory 33(6), 919–923 (1987)

    Article  MathSciNet  Google Scholar 

  7. Song, L., Huang, Q., Wang, Z.: Construction of multiple-burst-correction codes in transform domain and its relation to LDPC codes. IEEE Trans. Commun. 68(1), 40–54 (2020)

    Article  Google Scholar 

  8. Hashim, A.: Linear block codes for nonindependent errors. Electron. Lett. 12(11), 276–277 (1976)

    Article  Google Scholar 

  9. Villalba, L., et al.: Efficient shortened cyclic codes correcting either random errors or bursts. IEEE Commun. Lett. 15(7), 749–751 (2011)

    Article  Google Scholar 

  10. Giladi, R.: Network processors: Architecture, programming, and implementation. Elsevier, Inc. (2008)

  11. Sahu, P.: Optical networks and components: Fundamentals and advances. CRC Press (2020)

  12. Radonjic, A., Vujicic, V.: Integer codes correcting burst errors within a byte. IEEE Trans. Comput. 62(2), 411–415 (2013)

    Article  MathSciNet  Google Scholar 

  13. Radonjic, A., Vujicic, V.: Integer codes correcting high-density byte asymmetric errors. IEEE Commun. Lett. 21(4), 694–697 (2017)

    Article  Google Scholar 

  14. Radonjic, A., Vujicic, V.: Integer codes correcting single errors and burst asymmetric errors within a byte. Inform. Process. Lett. 121, 45–50 (2017)

    Article  MathSciNet  Google Scholar 

  15. Radonjic, A.: Integer codes correcting double errors and triple-adjacent errors within a byte. IEEE Trans. VLSI Syst. 28(8), 1901–1908 (2020)

    Article  Google Scholar 

  16. Pokhrel, N.K., Das, P.K., Radonjic, A.: Integer codes capable of correcting burst asymmetric errors. J. Appl. Math. Comput. 69(1), 711–784 (2023)

    Article  MathSciNet  Google Scholar 

  17. Vinck, A.J.H., Morita, H.: Codes over the ring of integer modulo m. IEICE Trans. Fundam. E81-A(10), 2013–2018 (1998)

  18. Fossorier, M.: Universal burst error correction. Proc. IEEE Int'l Symp. Inform. Theory (ISIT '06), pp. 1969–1973 (2006)

  19. Tinnirello, C.: Cyclic codes: Low-weight codewords and locators. Ph.D. dissertation, Dept. Math., Univ. Trento, Italy (2016)

  20. Radonjic, A., Vujicic, V.: Logarithmic time encoding and decoding of integer error control codes. Eng. Rep. 5(11), e12675 (2023)

  21. Wu, Z., Gong, C., Liu, D.: Computational complexity analysis of FEC decoding on SDR platforms. J. Signal Process. Syst. 89(2), 209–224 (2017)

    Article  Google Scholar 

  22. Fog, A.: The microarchitecture of Intel, AMD and via CPUs: An optimization guide for assembly programmers and compiler makers,” Technical University of Denmark, May 26, 2023. https://www.agner.org/optimize/microarchitecture.pdf

Download references

Funding

This paper is supported by the Ministry of Science, Technological Development and Innovation of the Republic of Serbia (Grant No. 451–03-47/2023–01/200175).

Author information

Authors and Affiliations

  1. Institute of Technical Sciences of the Serbian Academy of Sciences and Arts, Belgrade, Serbia

    Aleksandar Radonjic & Vladimir Vujicic

  2. Department of Mathematical Sciences, Tezpur University, Napaam, Sonitpur, India

    Pankaj Kumar Das

Authors
  1. Aleksandar Radonjic
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Pankaj Kumar Das
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Vladimir Vujicic
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.R., P.K.D and V.V. wrote the main manuscript text and A.R. prepared figures 1 and 2. All authors reviewed the manuscript.

Corresponding author

Correspondence to Vladimir Vujicic.

Ethics declarations

Ethics approval and consent to participate

Not applicable.

Consent for publication

Not applicable.

Competing interests

The authors declare no competing interests.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix MATLAB Code for finding the Coefficients C i

Appendix MATLAB Code for finding the Coefficients C i

figure a

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Radonjic, A., Das, P.K. & Vujicic, V. Integer codes correcting burst errors within one byte and single errors within two bytes. Cryptogr. Commun. 16, 961–974 (2024). https://doi.org/10.1007/s12095-023-00687-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12095-023-00687-7

Keywords

MSC (2010)

Search

Navigation