Advertisement

Two-Erasure Codes from 3-Plexes

  • Liping YiEmail author
  • Rebecca J. StonesEmail author
  • Gang WangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11783)

Abstract

We present a family of parity array codes called 3-PLEX for tolerating two disk failures in storage systems. It only uses exclusive-or operations to compute parity symbols. We give two data/parity layouts for 3-PLEX: (a) When the number of disks in array is at most 6, we use a horizontal layout which is similar to EVENODD codes, (b) otherwise we choose hybrid layout like HoVer codes. The major advantage of 3-PLEX is that it has optimal encoding/decoding/updating complexity in theory and the number of disks in a 3-PLEX disk array is less constrained than other array codes, which enables greater parameter flexibility for trade-offs in storage efficiency and performances.

Keywords

Latin squares Array codes Storage efficiency Computational complexity Data/parity layout 

References

  1. 1.
    Blaum, M., Brady, J., Bruck, J., Menon, J.: EVENODD: an efficient scheme for tolerating double disk failures in RAID architectures. IEEE Trans. Comput. 44(2), 192–202 (1995)CrossRefGoogle Scholar
  2. 2.
    Blaum, M., Roth, R.M.: On lowest density MDS codes. Trans. Inform. Theory 45(1), 46–59 (1999)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Corbett, P., et al.: Row-diagonal parity for double disk failure correction. In: Proceedings of the FAST, pp. 1–14 (2004)Google Scholar
  4. 4.
    Gang, W., Sheng, L., Xiaoguang, L., Jing, L.: Representing X-Code using latin squares. In: Proceedings of the PRDC, pp. 177–182 (2009)Google Scholar
  5. 5.
    Gang, W., Xiaoguang, L., Sheng, L., Guangjun, X., Jing, L.: Constructing double-erasure HoVer codes using Latin squares. In: Proceedings of the ICPADS, pp. 533–540 (2008)Google Scholar
  6. 6.
    Gang, W., Xiaoguang, L., Sheng, L., Guangjun, X., Jing, L.: Constructing liberation codes using Latin squares. In: Proceedings of the PRDC, pp. 73–80 (2008)Google Scholar
  7. 7.
    Gang, W., Xiaoguang, L., Sheng, L., Guangjun, X., Jing, L.: Generalizing RDP codes using the combinatorial method. In: Proceedings of the NCA, pp. 93–100 (2008)Google Scholar
  8. 8.
    Hafner, J.L.: WEAVER codes: Highly fault tolerant erasure codes for storage systems. In: Proceedings of the FAST, vol. 5 (2005)Google Scholar
  9. 9.
    Hafner, J.L.: HoVer erasure codes for disk arrays. In: Proceedings of the DSN, pp. 217–226 (2006)Google Scholar
  10. 10.
    Hu, Y., Yu, C.M., Li, Y.K., Lee, P.P., Lui, J.C.: NCFS: on the practicality and extensibility of a network-coding-based distributed file system. In: Proceedings of the NetCod, pp. 1–6. IEEE (2011)Google Scholar
  11. 11.
    Huang, C., Xu, L.: Star: an efficient coding scheme for correcting triple storage node failures. Trans. Comput. 57(7), 889–901 (2008)MathSciNetCrossRefGoogle Scholar
  12. 12.
    MacWilliams, F.J., Sloane, N.J.A.: The theory of error-correcting codes, vol. 16. North Holland (1977)Google Scholar
  13. 13.
    Plank, J.S.: Optimizing Cauchy Reed-Solomon codes for fault-tolerant storage applications. University of Tennessee, Technical Report CS-05-569 (2005)Google Scholar
  14. 14.
    Wanless, I.M.: A generalisation of transversals for Latin squares. Electron. J. Combin. 9(1), r12 (2002)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Wanless, I.M.: Diagonally cyclic Latin squares. Euro. J. Combin. 25, 393–413 (2004)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Xu, L., Bruck, J.: X-Code: MDS array codes with optimal encoding. IEEE Trans. Inform. Theory 45, 272–276 (1999)MathSciNetCrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2019

Authors and Affiliations

  1. 1.College of Computer ScienceNankai UniversityTianjinChina

Personalised recommendations