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Integer Codes Correcting Single Errors within Two Bytes

    https://doi.org/10.1142/S0218126621502601Cited by:2 (Source: Crossref)

    This paper presents a class of integer codes suitable for use in optical networks with low error rates. The presented codes are constructed with the help of a computer and have two important features: first, they can correct single errors affecting one or two b-bit bytes, and second, they use processor-friendly operations to encode/decode data bits. The effectiveness of the presented codes is demonstrated on theoretical models of four-core and six-core processors. The obtained results show that the decoder throughput reaches 14.70Gbps, which is above the operating speed of 10G networks. Finally, the paper compares the proposed codes with BCH codes of similar properties. The comparison is made in terms of redundancy and the number of decoding operations.

    This paper was recommended by Regional Editor Tongquan Wei.

    References

    • 1. A. Willig et al., Measurements of a wireless link in an industrial environment using an IEEE 802.11-compliant physical layer, IEEE Trans. Ind. Electron. 49 (2002) 1265–1282. Crossref, Web of ScienceGoogle Scholar
    • 2. S. A. Khayam et al., Performance analysis and modeling of errors and losses over 802.11b LANs for high-bit-rate real-time multimedia, Signal Process., Image Commun. 18 (2003) 575–595. Crossref, Web of ScienceGoogle Scholar
    • 3. T. Ono et al., Bit error statistical analysis of optical transmission systems, WDM and Photonic Networks, eds. D. W. Faulkner and A. L. Harmer (IOS Press, 2000), pp. 43–49. Google Scholar
    • 4. L. James, Error behaviour in optical networks, Ph.D. thesis, Department of Engineering, University of Cambridge (2005). Google Scholar
    • 5. P. Anslow and O. Ishida , Error distribution in optical links, Proc. IEEE 802.3 HSSG Interim Meeting (2007). Google Scholar
    • 6. L. H. Zetterberg , Cyclic codes from irreducible polynomials for correction of multiple errors, IEEE Trans. Inf. Theory 8 (1962) 13–20. Crossref, Web of ScienceGoogle Scholar
    • 7. R. C. Bose and D. K. Ray-Chaudhuri , On a class of error correcting binary group codes, Inf. Control 3 (1960) 68–79. CrossrefGoogle Scholar
    • 8. M. Y. Hsiao, D. C. Bossen and R. T. Chien , Orthogonal Latin square codes, IBM J. Res. Dev. 14 (1970) 390–394. Crossref, Web of ScienceGoogle Scholar
    • 9. F. Boinck and H. Van Tilborg , Constructions and bounds for systematic t-EC/AUED codes, IEEE Trans. Inf. Theory 36 (1990) 1381–1390. Crossref, Web of ScienceGoogle Scholar
    • 10. J. Bruck and M. Blaum , New techniques for constructing t-EC/AUED codes, IEEE Trans. Comput. 41 (1992) 1318–1324. Crossref, Web of ScienceGoogle Scholar
    • 11. R. Katti and M. Blaum , An improvement on constructions of t-EC/AUED codes, IEEE Trans. Comput. 45 (1996) 607–608. Crossref, Web of ScienceGoogle Scholar
    • 12. S. Al-Bassam , Another method for constructing t-EC/AUED codes, IEEE Trans. Comput. 49 (2000) 964–966. Crossref, Web of ScienceGoogle Scholar
    • 13. I. Naydenova and T. Klove , Some optimal binary and ternary t-EC-AUED codes, IEEE Trans. Inf. Theory 55 (2009) 4898–4904. Crossref, Web of ScienceGoogle Scholar
    • 14. G. Feng, X. Wu and T. R. N. Rao , New double-byte error-correcting codes for memory systems, IEEE Trans. Inf. Theory 44 (1998) 1152–1163. Crossref, Web of ScienceGoogle Scholar
    • 15. K. Suzuki, T. Kashiyama and E. Fujiwara , A general class of M-spotty byte error control codes, IEICE Trans. Fundam. Electron. Commun. Comput. Sci. 90-A (2007) 1418–1427. Crossref, Web of ScienceGoogle Scholar
    • 16. J. Bhaumik and D. Roy Chowdhury , New architectural design of CA-based codec, IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 18 (2010) 1139–1144. Crossref, Web of ScienceGoogle Scholar
    • 17. J. Cho and W. Sung , Efficient software-based encoding and decoding of BCH codes, IEEE Trans. Comput. 58 (2009) 878–889. Crossref, Web of ScienceGoogle Scholar
    • 18. A. Subbiah and T. Ogunfunmi , A flexible hybrid BCH decoder for modern NAND flash memories using GPGPUs, Micromachines 10 (2019) 365. Crossref, Web of ScienceGoogle Scholar
    • 19. A. Radonjic, K. Bala and V. Vujicic , Integer codes correcting double asymmetric errors, IET Commun. 10 (2016) 1691–1696. Crossref, Web of ScienceGoogle Scholar
    • 20. A. Radonjic and V. Vujicic , Integer codes correcting high-density byte asymmetric errors, IEEE Commun. Lett. 21 (2017) 694–697. Crossref, Web of ScienceGoogle Scholar
    • 21. A. Radonjic and V. Vujicic , Integer codes correcting burst and random asymmetric errors within a byte, J. Franklin Inst. 355 (2018) 981–996. Crossref, Web of ScienceGoogle Scholar
    • 22. A. Radonjic , (Perfect) integer codes correcting single errors, IEEE Commun. Lett. 22 (2018) 17–20. Crossref, Web of ScienceGoogle Scholar
    • 23. A. Radonjic and V. Vujicic , Integer codes correcting sparse byte errors, Cryptogr. Commun. 11 (2019) 1069–1077. CrossrefGoogle Scholar
    • 24. A. Radonjic and V. Vujicic , Integer codes correcting burst asymmetric errors within a byte and double asymmetric errors, Cryptogr. Commun. 12 (2020) 221–230. CrossrefGoogle Scholar
    • 25. C. Hartmann , A note on the decoding of double-error-correcting binary BCH codes of primitive length (Corresp.), IEEE Trans. Inf. Theory 17 (1971) 765–766. Crossref, Web of ScienceGoogle Scholar
    • 26. T. P. Berger , The automorphism group of double-error-correcting BCH codes, IEEE Trans. Inf. Theory 40 (1994) 538–542. Crossref, Web of ScienceGoogle Scholar
    • 27. P. Charpin , Weight distributions of cosets of two-error-correcting binary BCH codes, extended or not, IEEE Trans. Inf. Theory 40 (1994) 1425–1442. Crossref, Web of ScienceGoogle Scholar
    • 28. E.-H. Lu and T. Chang , New decoder for double-error-correcting binary BCH codes, IEE Proc., Commun. 143 (1996) 129–132. CrossrefGoogle Scholar
    • 29. P. Crepeau , Classification of error locator polynomials for double error correcting BCH codes, IEEE Trans. Commun. 46 (1998) 977–980. Crossref, Web of ScienceGoogle Scholar
    • 30. T. A. Gulliver, W. Lin and F. Dehne , Fast parallel decoding of double error correcting binary BCH codes, Appl. Math. Lett. 11 (1998) 11–14. Crossref, Web of ScienceGoogle Scholar
    • 31. R. Blahut , Algebraic Codes for Data Transmission (Cambridge University Press, 2003). CrossrefGoogle Scholar
    • 32. D. Schipani, M. Elia and J. Rosenthal , On the decoding complexity of cyclic codes up to the BCH bound, Proc. 2011 IEEE Int. Symp. Information Theory (2011), pp. 835–839. CrossrefGoogle Scholar
    • 33. A. Fog, The microarchitecture of Intel, AMD and via CPUs: An optimization guide for assembly programmers and compiler makers, Manual, Techical University of Denmark (2020). Google Scholar