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Efficient erasure correcting codes
Open accessAbstract
We introduce a simple erasure recovery algorithm for codes derived from cascades of sparse bipartite graphs and analyze the algorithm by analyzing a corresponding discrete-time random process. As a result, we obtain a simple criterion involving the fractions of nodes of different degrees on both sides of the graph which is necessary and sufficient for the decoding process to finish successfully with high probability. By carefully designing these graphs we can construct for any given rate R and any given real number /spl epsiv/ a family of linear codes of rate R which can be encoded in time proportional to ln(1//spl epsiv/) times their block length n. Furthermore, a codeword can be recovered with high probability from a portion of its entries of length (1+/spl epsiv/)Rn or more. The recovery algorithm also runs in time proportional to n ln(1//spl epsiv/). Our algorithms have been implemented and work well in practice; various implementation issues are discussed.
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Cited by
Luby, M. (2003) · The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings. · doi:10.1109/sfcs.2002.1181950 · Cited by 2,757
Self-citationA digital fountain approach to asynchronous reliable multicast
Byers, J. W., Luby, M., & Mitzenmacher, M. (2002) · IEEE Journal on Selected Areas in Communications · doi:10.1109/jsac.2002.803996 · Cited by 580
Self-citationFault-Tolerant Encryption for Space Applications
Banu, R., & Vladimirova, T. (2009) · IEEE Transactions on Aerospace and Electronic Systems · doi:10.1109/taes.2009.4805278 · Cited by 46
Metadata
- Authors
- Luby, M. G., Mitzenmacher, M., Shokrollahi, M. A., & Spielman, D. A.
- Venue
- IEEE Transactions on Information Theory
- Published
- 2001
- Volume
- 47
- Issue
- 2
- Pages
- 569-584
- ISSN
- 0018-9448 (ISSN-L)
- OpenAlex
- W2115104320
- Cited by
- 1,180
- References
- 0
- FWCI
- 53.61
- Type
- journal article
- Language
- en
- Open access
- green
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- Luby, M. G., Mitzenmacher, M., Shokrollahi, M. A., & Spielman, D. A. (2001). Efficient erasure correcting codes. IEEE Transactions on Information Theory. https://doi.org/10.1109/18.910575
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