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Balanced and sparse Tamo-Barg codes

Halbawi, Wael and Duursma, Iwan and Dau, Hoang and Hassibi, Babak (2017) Balanced and sparse Tamo-Barg codes. In: 2017 IEEE International Symposium on Information Theory (ISIT). IEEE , Piscataway, NJ, pp. 1018-1022. ISBN 978-1-5090-4096-4. http://resolver.caltech.edu/CaltechAUTHORS:20170816-172424731

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Abstract

We construct balanced and sparse generator matrices for Tamo and Barg's Locally Recoverable Codes (LRCs). More specifically, for a cyclic Tamo-Barg code of length n, dimension k and locality r, we show how to deterministically construct a generator matrix where the number of nonzeros in any two columns differs by at most one, and where the weight of every row is d + r − 1, where d is the minimum distance of the code. Since LRCs are designed mainly for distributed storage systems, the results presented in this work provide a computationally balanced and efficient encoding scheme for these codes. The balanced property ensures that the computational effort exerted by any storage node is essentially the same, whilst the sparse property ensures that this effort is minimal. The work presented in this paper extends a similar result previously established for Reed-Solomon (RS) codes, where it is now known that any cyclic RS code possesses a generator matrix that is balanced as described, but is sparsest, meaning that each row has d nonzeros.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISIT.2017.8006682DOIArticle
http://ieeexplore.ieee.org/document/8006682/PublisherArticle
Additional Information:© 2017 IEEE. The work of Wael Halbawi was supported by the Qatar Foundation-Research Division. The work of Iwan Duursma was supported in part by the NSF grant CCF 1619189. The work of Hoang Dau has been supported in part by the NSF grant CCF 1526875 and the Center for Science of Information under the grant NSF 093937. The work of Babak Hassibi was supported in part by the National Science Foundation under grants CNS-0932428, CCF-1018927, CCF-1423663 and CCF-1409204, by a grant from Qualcomm Inc., by NASAs Jet Propulsion Laboratory through the President and Directors Fund, by King Abdulaziz University, and by King Abdullah University of Science and Technology.
Funders:
Funding AgencyGrant Number
Qatar FoundationUNSPECIFIED
NSFCCF-1619189
NSFCCF-1526875
Center for Science of Information (CSoI)UNSPECIFIED
NSFCNS- 0932428
NSFCCF-1018927
NSFCCF-1423663
NSFCCF-1409204
Qualcomm Inc.UNSPECIFIED
JPL President and Director's FundUNSPECIFIED
King Abdulaziz UniversityUNSPECIFIED
King Abdullah University of Science and Technology (KAUST)UNSPECIFIED
NSFCCF-0939370
Record Number:CaltechAUTHORS:20170816-172424731
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170816-172424731
Official Citation:W. Halbawi, I. Duursma, H. Dau and B. Hassibi, "Balanced and sparse Tamo-Barg codes," 2017 IEEE International Symposium on Information Theory (ISIT), Aachen, Germany, 2017, pp. 1018-1022. doi: 10.1109/ISIT.2017.8006682
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80539
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:17 Aug 2017 15:55
Last Modified:17 Aug 2017 15:55

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