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An erasure-resilient encoding system for flexible reading and writing in storage networks

Published:30 July 2012Publication History
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Abstract

We introduce the Read-Write-Coding-System (RWC), a very flexible class of linear block codes that generate efficient and flexible erasure codes for storage networks. In particular, given a message x of k symbols and a codeword y of n symbols, an RW code defines additional parameters k≤ r,w≤ n that offer enhanced possibilities to adjust the fault-tolerance capability of the code. More precisely, an RWC provides linear (n,r,d)-codes that have: (a) minimum (Hamming) distance d = n-r+1 for any two codewords, and (b) for any codeword y1 there exists a codeword y2 with distance of at most w. Furthermore, depending on the values r,w and the code alphabet, different block codes such as parity codes (e.g., RAID 4/5) or Reed-Solomon (RS) codes (if r = k and thus, w = n) can be generated. In storage networks in which I/O accesses are very costly and redundancy is crucial, this flexibility has considerable advantages as r and w can optimally be adapted to read or write intensive applications; only w symbols must be updated if the message x changes completely, which is different from other codes that always need to rewrite y completely as x changes. In this article, we first state a tight lower bound and basic conditions for all RW codes. Furthermore, we introduce special RW codes in which all mentioned parameters are adjustable even online, that is, RW codes which are adaptive to changing demands. At last, we investigate the question for which choices of (k,r,w,n) a coding system exists over the binary alphabet F2 = {0,1} and discuss how RW codes can be combined.

References

  1. Adler, M., Bartal, Y., Byers, J. W., Luby, M., and Raz, D. 1997. A modular analysis of network transmission protocols. In Proceedings of the Israel Symposium on Theory of Computing Systems. 54--62. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. Aguilera, M. K., Janakiraman, R., and Xu, L. 2012. Reliable and secure distributed storage using erasure codes. citeseerx.ist.psu.edu/viewdoc/download?doi = 10-2.1.1.11.2434.pdfGoogle ScholarGoogle Scholar
  3. Blaum, M., Brady, J., Bruck, F., and van Tilborg, H. 1999. Array codes. In Handbook of Coding Theory, vol. 2. V. S. Pless and W. C. Huffman, Chapter 22.Google ScholarGoogle Scholar
  4. Blaum, M., Brady, J., Bruck, J., and Menon, J. 1994. Evenodd: An optimal scheme for tolerating double disk failures in raid architectures. In Proceedings of the 21st Annual International Symposium on Computer Architecture. IEEE Computer Society Press, 245--254. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Burkhard, W. A. and Menon, J. 1993. Disk array storage system reliability. In Proceedings of the Symposium on Fault-Tolerant Computing. 432--441.Google ScholarGoogle Scholar
  6. Byers, J., Luby, M., and Mitzenmacher, M. 2002. A digital fountain approach to asynchronous reliable multicast. IEEE J. Select. Areas Comm. 20, 8. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Cassuto, Y. and Bruck, J. 2009. Cyclic lowest density mds array codes. IEEE Trans. Inf. Theory 55, 1721--1729. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Huffman, C. and Pless, V. 2003. Fundamentals of Error-Correcting Codes. Cambridge University Press, Cambridge, UK.Google ScholarGoogle Scholar
  9. Mac Williams, F. J. 1977. The Theory of Error Correcting Codes. North-Holland Mathematical Library.Google ScholarGoogle Scholar
  10. Mense, M. 2009. On fault-tolerant data placement in storage networks. Ph.D. thesis, University of Paderborn.Google ScholarGoogle Scholar
  11. Patterson, D. A., Gibson, G., and Katz, R. H. 1988. A case for redundant arrays of inexpensive disks (RAID). In Proceedings of the ACM Conference on Management of Data (SIGMOD). 109--116. Google ScholarGoogle ScholarDigital LibraryDigital Library
  12. Plank, J. S. 1997. A tutorial on Reed-Solomon coding for fault-tolerance in RAID-like systems. Softw. Pract. Exper. 27, 9, 995--1012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Plank, J. S., Luo, J., Schuman, C. D., Xu, L., and Wilcox-O'Hearn, Z. 2009. A performance evaluation and examination of open-source erasure coding libraries for storage. In Proceedings of the 7th Conference on File and Storage Technologies. USENIX Association, 253--265. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Rhea, S., Wells, C., Eaton, P., Geels, D., Zhao, B., Weatherspoon, H., and Kubiatowicz, J. 2001. Maintenance-Free global data storage. IEEE Internet Comput. 5. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Rizzo, L. 1997. Effective erasure codes for reliable computer communication protocols. ACM Comput. Comm. Rev. 27, 2, 24--36. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Tate, J. and Kanth, R. 2005. Introduction to storage area networks. Tech. rep., IBM. May.Google ScholarGoogle Scholar

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    • Published in

      cover image ACM Transactions on Autonomous and Adaptive Systems
      ACM Transactions on Autonomous and Adaptive Systems  Volume 7, Issue 2
      July 2012
      275 pages
      ISSN:1556-4665
      EISSN:1556-4703
      DOI:10.1145/2240166
      Issue’s Table of Contents

      Copyright © 2012 ACM

      Publisher

      Association for Computing Machinery

      New York, NY, United States

      Publication History

      • Published: 30 July 2012
      • Accepted: 1 March 2012
      • Revised: 1 February 2011
      • Received: 1 February 2010
      Published in taas Volume 7, Issue 2

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