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Optimal linear codes with a local-error-correction property
Open accessAbstract
Motivated by applications to distributed storage, Gopalan et al recently introduced the interesting notion of information-symbol locality in a linear code. By this it is meant that each message symbol appears in a parity-check equation associated with small Hamming weight, thereby enabling recovery of the message symbol by examining a small number of other code symbols. This notion is expanded to the case when all code symbols, not just the message symbols, are covered by such “local” parity. In this paper, we extend the results of Gopalan et. al. so as to permit recovery of an erased code symbol even in the presence of errors in local parity symbols. We present tight bounds on the minimum distance of such codes and exhibit codes that are optimal with respect to the local error-correction property. As a corollary, we obtain an upper bound on the minimum distance of a concatenated code.
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Cites
Fundamentals of Error-Correcting Codes
Huffman, W. C., & Pless, V. (2003) · Cambridge University Press eBooks · doi:10.1017/cbo9780511807077 · Cited by 2,460
Serial concatenation of interleaved codes: performance analysis, design, and iterative decoding
Benedetto, S., Divsalar, D., Montorsi, G., & Pollara, F. (1998) · IEEE Transactions on Information Theory · doi:10.1109/18.669119 · Cited by 1,261
On the Locality of Codeword Symbols
Gopalan, P., Huang, C., Simitci, H., & Yekhanin, S. (2012) · IEEE Transactions on Information Theory · doi:10.1109/tit.2012.2208937 · Cited by 831
EVENODD: an efficient scheme for tolerating double disk failures in RAID architectures
Blaum, M., Brady, J., Bruck, J., & Menon, J. (1995) · IEEE Transactions on Computers · doi:10.1109/12.364531 · Cited by 689
Row-diagonal parity for double disk failure correction
Corbett, P. F., English, B., Goel, A., et al. (2004) · Cited by 490
Huang, C., Chen, M., & Li, J. (2007) · Sixth IEEE International Symposium on Network Computing and Applications (NCA 2007) · doi:10.1109/nca.2007.37 · Cited by 298
Cited by
Speeding Up Distributed Machine Learning Using Codes
Lee, K., Lam, M., Pedarsani, R., Papailiopoulos, D., & Ramchandran, K. (2018) · IEEE Transactions on Information Theory · doi:10.1109/tit.2017.2736066 · Cited by 829
Metadata
- Authors
- Prakash, N., Kamath, G. M., Lalitha, V., & Kumar, P. V.
- Venue
- 2012 IEEE International Symposium on Information Theory Proceedings
- Publisher
- IEEE
- Published
- 2012-07
- Pages
- 2776-2780
- OpenAlex
- W2050500290
- Cited by
- 295
- References
- 6
- FWCI
- 15.26
- Type
- conference paper
- Language
- en
- Open access
- green
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- Prakash, N., Kamath, G. M., Lalitha, V., & Kumar, P. V. (2012). Optimal linear codes with a local-error-correction property. 2012 IEEE International Symposium on Information Theory Proceedings. https://doi.org/10.1109/isit.2012.6284028
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