Abstract
Storage systems and coding theory are two very different but highly interdependent engineering disciplines. The development of storage systems has impacted research in coding theory, and coding-theoretic contributions changed the way storage systems work. The presentation aims to give a short summary of the different problems solved by coding theory at the service of storage systems.
- M. Blaum, J. Brady, J. Bruck, and J. Menon, "EVENODD: an efficient scheme for tolerating double disk failures in RAID architectures," IEEE Transactions on Computers, vol. 44, no. 2, pp. 192--202, 1995. Google ScholarDigital Library
- M. Blaum, J. Bruck, and A. Vardy, "MDS array codes with independent parity symbols," IEEE Transactions on Information Theory, vol. 42, no. 2, pp. 529--542, 1996. Google ScholarDigital Library
- M. Blaum, P. Farrell, and H. van Tilborg, "Array codes," Handbook of Coding Theory, V.S. Pless and W.C. Huffman, pp. 1855--1909, 1998.Google Scholar
- M. Blaum and R. Roth, "New array codes for multiple phased burst correction," IEEE Transactions on Information Theory, vol. 39, no. 1, pp. 66--77, 1993. Google ScholarDigital Library
- ______, "On lowest density MDS codes," IEEE Transactions on Information Theory, vol. 45, no. 1, pp. 46--59, 1999. Google ScholarDigital Library
- J. Blomer, M. Kalfane, M. Karpinski, R. Karp, M. Luby, and D. Zuckerman, "An XOR-based erasure-resilient coding scheme," TR-95-048, International Computer Science Institute, Tech. Rep., August 1995.Google Scholar
- J. W. Byers, M. Luby, M. Mitzenmacher, and A. Rege, "A digital fountain approach to reliable distribution of bulk data," in Proc. ACM SIGCOMM'98, Vancouver BC,Canada, 1998, pp. 56--67. Google ScholarDigital Library
- Y. Cassuto and J. Bruck, "Cyclic lowest-density MDS array codes," IEEE Transactions on Information Theory, vol. 55, no. 4, pp. 1721--1729, 2009. Google ScholarDigital Library
- ______, "Low-complexity array codes for random and clustered 4-erasures," IEEE Transactions on Information Theory, vol. 58, no. 1, pp. 146--158, 2012. Google ScholarDigital Library
- Y. Cassuto and M. A. Shokrollahi, "Array-code ensembles -or- two-dimensional LDPC codes," in Proc. of the IEEE International Symposium on Info. Theory, St. Petersburg Russia, 2011.Google Scholar
- ______, "On-line fountain codes for semi-random loss channels," in Proc. IEEE Information Theory Workshop, Paraty, Brazil, 2011.Google Scholar
- P. Corbett, B. English, A. Goel, T. Grcanac, S. Kleiman, J. Leong, and S. Sankar, "Rowdiagonal parity for double disk failure correction," in In Proceedings of the 3rd USENIX Conference on File and Storage Technologies, San-Francisco CA, 2004. Google ScholarDigital Library
- A. Dimakis, P. Godfrey, Y. Wu, M. Wainwright, and K. Ramchandran, "Network coding for distributed storage systems," IEEE Transactions on Information Theory, vol. 56, no. 9, pp. 4539--4551, 2010. Google ScholarDigital Library
- P. Elias, "The binary erasure channel," MIT Information Theory Lectures, 1954.Google Scholar
- J. L. Fan, "Array codes as low-density parity check codes," in Proc. of the Intl. Symp. on Turbo Codes, 2000, pp. 543--546.Google Scholar
- P. Gopalan, C. Huang, H. Simitci, and S. Yekhanin, "On the locality of codeword symbols," ECCC: TR11-100, 2011, to appear in IEEE Trans. Info. Theory.Google Scholar
- C. Huang, M. Chen, and J. Li, "Pyramid codes: flexible schemes to trade space for access efficiency in reliable data storage systems," in In Proceedings of the Sixth IEEE International Symposium on Network Computing and Applications, Cambridge, MA USA, 2007.Google Scholar
- C. Huang and L. Xu, "Star: An efficient coding scheme for correcting triple storage node failures," in In Proceedings of the 4th USENIX Conference on File and Storage Technologies, San-Francisco CA, 2005. Google ScholarDigital Library
- E. Louidor and R. Roth, "Lowest-density MDS codes over extension alphabets," IEEE Transactions on Information Theory, vol. 52, no. 7, pp. 3186--3197, 2006. Google ScholarDigital Library
- M. Luby, "LT codes," in Proc. of the Annual IEEE Symposium on Foundations of Computer Science FOCS, Vancouver BC, Canada, 2002, pp. 271--280. Google ScholarDigital Library
- I. S. Reed and G. Solomon, "Polynomial codes over certain finite fields," SIAM J. Appl. Math., vol. 8, pp. 300--304, 1960.Google ScholarCross Ref
- T. Richardson and R. Urbanke, Modern coding theory. New York USA: Cambridge University Press, 2008. Google ScholarDigital Library
- C. Shannon, "A mathematical theory of communication," Bell System Technical Journal, vol. 27, no. 9, pp. 379--423, Oct. 1948.Google ScholarCross Ref
- M. A. Shokrollahi, "Raptor codes," IEEE Transactions on Information Theory, vol. 52, no. 6, pp. 2551--2567, 2006.Google ScholarDigital Library
- I. Tamo, Z. Wang, and J. Bruck, "Zigzag codes: MDS array codes with optimal rebuilding," arXiv:1112.0371 {cs.IT}, 2011, submitted to IEEE Trans. Info. Theory, 10/2011.Google Scholar
- L. Xu, V. Bohossian, J. Bruck, and D. Wagner, "Low-density MDS codes and factors of complete graphs," IEEE Transactions on Information Theory, vol. 45, no. 6, pp. 1817--1826, 1999. Google ScholarDigital Library
- G. Zaitsev, V. Zinovév, and N. Semakov, "Minimum-check-density codes for correcting bytes of errors, erasures, or defects," Problems Inform. Transm., vol. 19, pp. 197--204, 1981.Google Scholar
Index Terms
- What can coding theory do for storage systems?
Recommendations
Erasure coding in windows azure storage
USENIX ATC'12: Proceedings of the 2012 USENIX conference on Annual Technical ConferenceWindows Azure Storage (WAS) is a cloud storage system that provides customers the ability to store seemingly limitless amounts of data for any duration of time. WAS customers have access to their data from anywhere, at any time, and only pay for what ...
Network coding for distributed storage systems
Distributed storage systems provide reliable access to data through redundancy spread over individually unreliable nodes. Application scenarios include data centers, peer-to-peer storage systems, and storage in wireless networks. Storing data using an ...
Comments