Partial-MDS codes and their application to RAID type of architectures

IEEE Transactions on Information Theory

Volumn 59, Issue 7, 2013, Pages 4510-4519

  Blaum, Mario ^a   Hafner, James Lee ^a   Hetzler, Steven ^a  

^a IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

Array codes; Error correcting codes (ECCs); Flash storage devices; Hard errors; Maximum distance separable (MDS) codes; RAID architectures; Reed Solomon codes; Solid state drives (SSDs)

Indexed keywords

ARCHITECTURE; ERRORS; VIRTUAL STORAGE;

ARRAY CODES; ERROR CORRECTING CODE; HARD ERRORS; MAXIMUM DISTANCE SEPARABLE CODE; SOLID-STATE DRIVES;

REED-SOLOMON CODES;

EID: 84897696633     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIT.2013.2252395     Document Type: Article

References (34)

1. M. Balakrishnan, A. Kadav, V. Prabhakaran, and D. Malkhi, "Differential RAID: Rethinking RAID for SSD reliability," ACMTrans. Storage, vol. 6, no. 2, Jul. 2010.
2. M. Blaum, J. Brady, J. Bruck, and J. Menon, "EVENODD: An efficient scheme for tolerating double disk failures in RAID architectures," IEEE Trans. Comput., vol. C-44, no. 2, pp. 192-202, Feb. 1995.
3. M. Blaum, P. G. Farrell, and H. C. A. van Tilborg, "Array codes," in Handbook of Coding Theory, V. S. Pless and W. C. Huffman, Eds. New York, NY, USA: Elsevier, 1998, ch. 22.
4. M. Blaum, J. L. Hafner, and S. Hetzler, "Partial-MDS codes and their application to RAID type of architectures," IBM, New York, NY, USA, 2012, Res. Rep. RJ10498.
5. M. Blaum and R. J. McEliece, "Coding protection for magnetic tapes: Ageneralization of the Patel-Hong code," IEEE Trans. Inf. Theory, vol. IT-31, no. 5, pp. 690-693, Sep. 1985. (Pubitemid 16508896)
6. M. Blaum and R.M. Roth, "New array codes for multiple phased burst correction," IEEE Trans. Inf. Theory, vol. IT-39, no. 1, pp. 66-77, Jan. 1993. (Pubitemid 23643526)
7. E. L. Blokh and V. V. Zyablov, "Coding of generalized concatenated codes," Problemy Peredachii Inf., vol. 10, no. 3, pp. 218-222, 1974.
8. P. Corbett, B. English, A. Goel, T. Grcanac, S. Kleiman, J. Leong, and S. Sankar, "Row-diagonal parity for double disk failure correction," in Proc. 3rd Conf. File Storage Technol., San Francisco, CA, USA, Mar.-Apr. 2004.
9. P. Delsarte, "Bilinear forms over a finite field, with applications to coding theory," J. Combin. Theory Ser. A, vol. 25, pp. 226-241, 1978.
10. E. M. Gabidulin, "Theory of codes with maximum rank distance," Prob. Inf. Transmiss., vol. 21, no. 1, pp. 3-16, 1985.
11. G. A. Gibson, Redundant Disk Arrays. NewYork, NY, USA:MIT Press, 1992.
12. P. Gopalan, C. Huang, H. Simitci, and S. Yekhanin, "On the locality of codeword symbols," IEEE Trans. Inf. Theory, vol. IT-58, no. 11, pp. 6925-6934, Nov. 2012.
13. K. M. Greenan, D. D. Long, E. L. Miller, T. J. E. Schwarz, and A. Wildani, "Building flexible, fault-tolerant flash-based storage systems," presented at the 5th Workshop Hot Topics Dependability, Lisbon, Portugal, Jun. 2009.
14. J. Han and L. A. Lastras-Montaño, "Reliable memories with subline accesses," in Proc. IEEE Int. Symp. Inf. Theory, Jun. 2007, pp. 2531-2535.
15. M. Hassner, K. Abdel-Ghaffar, A. Patel, R. Koetter, and B. Trager, "Integrated interleaving-Anovel ECC architecture," IEEE Trans. Magn., vol. 37, no. 2, pp. 773-775, Mar. 2001.
16. C. Huang, M. Chen, and J. Li, "Pyramid codes: flexible schemes to trade space for access efficiency in reliable data storage systems," in Proc. IEEE Netw. Comput. Appl., Cambridge, MA, USA, Jul. 2007, pp. 79-86.
17. C. Huang, H. Simitci, Y. Xu, A. Ogus, B. Calder, P. Gopalan, J. Li, and S. Yekhanin, "Erasure coding inWindows Azure storage," presented at the USENIX Annu. Tech. Conf., Boston, MA, USA, Jun. 2012.
18. W. Hutsell, An in-depth look at the RamSan-500 cached flash solid state disk [Online]. Available: http://www.texmemsys.com/files/ f000233.pdf
19. S. Im and D. Shin, "Flash-aware RAID techniques for dependable and high-performance flash memory SSD," IEEE Trans. Comput., vol. C-60, no. 1, pp. 80-92, Jan. 2011.
20. L. A. Lastras-Montaño, P. J. Meaney, E. Stephens, B. M. Trager, J. O'Connor, and L. C. Alves, "A new class of array codes for memory storage," presented at the Inf. Theory Appl. Workshop, La Jolla, CA, USA, Feb. 2011.
21. M. Li and J. Shu, "C-Codes: Cyclic lowest-density MDS array codes constructed using starters for RAID 6," IBM, New York, NY, USA, 2011, Res. Rep. RC25218.
22. S. Lin and D. J. Costello, Error Control Coding, 2nd ed. Englewood Cliffs, NJ, USA: Prentice-Hall, 2004.
23. F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes. Amsterdam, The Netherlands: North Holland, 1977.
24. N-29-17: NAND flash design and use considerations introduction Micron [Online]. Available: http://download.micron.com/pdf/technotes/ nand/tn2917.pdf
25. A. Park, D. Lee, Y. Woo, G. Lee, J. Lee, and D. Kim, "Reliability and performance enhancement technique for SSD array storage system using RAID mechanism," in Proc. 9th Int. Conf. Commun. Inf. Technol., 2009, pp. 140-145.
26. J. S. Plank, "A tutorial on Reed-Solomon coding for fault-tolerance in RAID-like systems," Softw.-Practice Exp., vol. 27, no. 9, pp. 995-1012, Sep. 1997. (Pubitemid 127582114)
27. J. S. Plank, "The RAID-6 liberation codes," in Proc. 6th USENIX Conf. File Storage Technol., San Francisco, CA, USA, 2008, pp. 97-110.
28. J. S. Plank, M. Blaum, and J. L. Hafner, "SD codes: Erasure codes designed for how storage systems really fail," presented at the 13th Conf. File Storage Technol., San Jose, CA, USA, Feb. 2013.
29. R. M. Roth, "Maximum rank array codes and their application to crisscross error correction," IEEE Trans. Inf. Theory, vol. IT-37, no. 2, pp. 328-336, Mar. 1991.
30. X. Tang and R. Koetter, "A novel method for combining algebraic decoding and iterative processing," in Proc. IEEE Int. Symp. Inf. Theory, Jul. 2006, pp. 474-478. (Pubitemid 351244137)
31. A. Thomasian and M. Blaum, "Higher reliability redundant disk arrays: Organization, operation, and coding," ACM Trans. Storage, vol. 5, no. 3, Nov. 2009.
32. W. Wesley Peterson and E. J. Weldon Jr., Error-Correcting Codes, 2nd ed. New York, NY, USA: MIT Press, 1984.
33. L. Xu, V. Bohossian, J. Bruck, and D. G. Wagner, "Low-density MDS codes and factors of complete graphs," IEEE Trans. Inf. Theory, vol. IT-45, no. 6, pp. 1817-1826, Sep. 1999. (Pubitemid 32077611)
34. L. Xu and J. Bruck, "X-code: MDS array codes with optimal encoding," IEEE Trans. Inf. Theory, vol. IT-45, no. 1, pp. 272-276, Jan. 1999.