TY - GEN
T1 - Balanced and sparse Tamo-Barg codes
AU - Halbawi, Wael
AU - Duursma, Iwan
AU - Dau, Hoang
AU - Hassibi, Babak
N1 - 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.
PY - 2017/8/9
Y1 - 2017/8/9
N2 - 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.
AB - 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.
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U2 - 10.1109/ISIT.2017.8006682
DO - 10.1109/ISIT.2017.8006682
M3 - Conference contribution
AN - SCOPUS:85034115147
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1018
EP - 1022
BT - 2017 IEEE International Symposium on Information Theory, ISIT 2017
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2017 IEEE International Symposium on Information Theory, ISIT 2017
Y2 - 25 June 2017 through 30 June 2017
ER -