Advertisement

Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

A class of binary MDS array codes with asymptotically weak-optimal repair

Abstract

Binary maximum distance separable (MDS) array codes contain k information columns and r parity columns in which each entry is a bit that can tolerate r arbitrary erasures. When a column in an MDS code fails, it has been proven that we must download at least half of the content from each helper column if k+1 columns are selected as the helper columns. If the lower bound is achieved such that the k+1 helper columns can be selected from any k + r − 1 surviving columns, then the repair is an optimal repair. Otherwise, if the lower bound is achieved with k + 1 specific helper columns, the repair is a weak-optimal repair. This paper proposes a class of binary MDS array codes with k ⩾ 3 and r ⩾ 2 that asymptotically achieve weak-optimal repair of an information column with k + 1 helper columns. We show that there exist many encoding matrices such that the corresponding binary MDS array codes can asymptotically achieve weak-optimal repair for repairing any information column.

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

References

  1. 1

    Blaum M, Brady J, Bruck J, et al. EVENODD: an efficient scheme for tolerating double disk failures in RAID architectures. IEEE Trans Comput, 1995, 44: 192–202

  2. 2

    Corbett P, English B, Goel A, et al. Row-diagonal parity for double disk failure correction. In: Proceedings of the 3rd USENIX Conference on File and Storage Technologies, San Jose, 2004. 1–14

  3. 3

    Huang C, Xu L. STAR: an efficient coding scheme for correcting triple storage node failures. IEEE Trans Comput, 2008, 57: 889–901

  4. 4

    Blaum M. A family of MDS array codes with minimal number of encoding operations. In: Proceedings of IEEE International Symposium on Information Theory, Seattle, 2006. 2784–2788

  5. 5

    Blaum M, Brady J, Bruck J, et al. The EVENODD code and its generalization. In: Proceedings of High Performance Mass Storage and Parallel I/O. Hoboken: John Wiley & Sons, Inc., 2001. 187–208

  6. 6

    Blaum M, Bruck J, Vardy A. MDS array codes with independent parity symbols. IEEE Trans Inform Theor, 1996, 42: 529–542

  7. 7

    Feng G-L, Deng R-H, Bao F, et al. New efficient MDS array codes for RAID. Part II. Rabin-like codes for tolerating multiple (= 4) disk failures. IEEE Trans Comput, 2005, 54: 1473–1483

  8. 8

    Hou H, Han Y S. A new construction and an efficient decoding method for rabin-like codes. IEEE Trans Commun, 2018, 66: 521–533

  9. 9

    Dimakis A, Godfrey P, Wu Y, et al. Network coding for distributed storage systems. IEEE Trans Inf Theory, 2010, 56: 4539–4551

  10. 10

    Hou H X, Han Y-S, Lee P-P-C, et al. A new design of binary MDS array codes with asymptotically weak-optimal repair. 2018. ArXiv:1802.07891

  11. 11

    Hou H X, Shum K W, Chen M, et al. BASIC codes: low-complexity regenerating codes for distributed storage systems. IEEE Trans Inform Theor, 2016, 62: 3053–3069

  12. 12

    Li J, Tang X H, Tian C. A generic transformation for optimal repair bandwidth and rebuilding access in MDS codes. In: Proceedings of IEEE International Symposium on Information Theory (ISIT), Aachen, 2017. 1623–1627

  13. 13

    Rashmi K V, Shah N B, Kumar P V. Optimal exact-regenerating codes for distributed storage at the MSR and MBR points via a product-matrix construction. IEEE Trans Inform Theor, 2011, 57: 5227–5239

  14. 14

    Tamo I, Wang Z, Bruck J. Zigzag codes: MDS array codes with optimal rebuilding. IEEE Trans Inform Theor, 2013, 59: 1597–1616

  15. 15

    Ye M, Barg A. Explicit constructions of high-rate MDS array codes with optimal repair bandwidth. IEEE Trans Inform Theor, 2017, 63: 2001–2014

  16. 16

    Gad E-E, Mateescu R, Blagojevic F, et al. Repair-optimal MDS array codes over GF(2). In: Proceedings of IEEE International Symposium Information Theory, Istanbul, 2013. 887–891

  17. 17

    Pamies J-L, Blagojevic F, Mateescu R, et al. Opening the chrysalis: on the real repair performance of MSR codes. In: Proceedings of 14th USENIX Conference on File and Storage Technologies, Santa Clara, 2016. 81–94

  18. 18

    Hou H, Lee P-P-C, Han Y-S, et al. Triple-fault-tolerant binary MDS array codes with asymptotically optimal repair. In: Proceedings of IEEE International Symposium Information Theory, Aachen, 2017. 839–843

  19. 19

    Wang Y, Yin X, Wang X. MDR codes: a new class of RAID-6 codes with optimal rebuilding and encoding. IEEE J Sele Areas Commun, 2014, 32: 1008–1018

  20. 20

    Wang Y, Yin X, Wang X. Two new classes of two-parity MDS array codes with optimal repair. IEEE Commun Lett, 2016, 20: 1293–1296

  21. 21

    Xiang L, Xu Y, Lui J, et al. Optimal recovery of single disk failure in RDP code storage systems. In: Proceedings of ACM SIGMETRICS Performance Evaluation Rev, New York, 2010. 119–130

  22. 22

    Xu S, Li R, Lee P P C, et al. Single disk failure recovery for X-code-based parallel storage systems. IEEE Trans Comput, 2014, 63: 995–1007

  23. 23

    Wang Z Y, Dimakis A-G, Bruck J. Rebuilding for array codes in distributed storage systems. In: Proceedings of GLOBECOM Workshops, Miami, 2010. 1905–1909

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61701115, 61671007).

Author information

Correspondence to Hanxu Hou.

Additional information

Invited paper

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hou, H., Han, Y.S. A class of binary MDS array codes with asymptotically weak-optimal repair. Sci. China Inf. Sci. 61, 100302 (2018). https://doi.org/10.1007/s11432-018-9485-7

Download citation

Keywords

  • MDS codes
  • binary MDS array codes
  • optimal repair
  • encoding matrix
  • asymptotically weakoptimal repair