TY - GEN
T1 - Optimal repair schemes for some families of full-length reed-solomon codes
AU - Dau, Hoang
AU - Milenkovic, Olgica
N1 - Proof. The first statement follows from Lemma 7 and Lemma 8. The second statement holds due to Corollary 1. \u25A0 ACKNOWLEDGMENT This work has been supported in part by the NSF grant CCF 1526875 and the Center for Science of Information under the grant NSF 0939370. The authors thank Iwan Duursma for helpful discussions.
PY - 2017/8/9
Y1 - 2017/8/9
N2 - Reed-Solomon codes have found many applications in practical storage systems, but were until recently considered unsuitable for distributed storage applications due to the widely-held belief that they have poor repair bandwidth. The work of Guruswami and Wootters (STOC'16) has shown that one can actually perform bandwidth-efficient linear repair with Reed-Solomon codes: When the codes are over the field Fqt and the number of parities r ≥ qs, where (t - s) divides t, there exists a linear scheme that achieves a repair bandwidth of (n - 1)(t - s) logg q bits. We extend this result by showing the existence of such a linear repair scheme for every 1 ≤ s < t. Moreover, our new schemes are optimal among all linear repair schemes for Reed-Solomon codes when n = qt and r = qs. Additionally, we improve the lower bound on the repair bandwidth for Reed-Solomon codes, also established in the work of Guruswami and Wootters.
AB - Reed-Solomon codes have found many applications in practical storage systems, but were until recently considered unsuitable for distributed storage applications due to the widely-held belief that they have poor repair bandwidth. The work of Guruswami and Wootters (STOC'16) has shown that one can actually perform bandwidth-efficient linear repair with Reed-Solomon codes: When the codes are over the field Fqt and the number of parities r ≥ qs, where (t - s) divides t, there exists a linear scheme that achieves a repair bandwidth of (n - 1)(t - s) logg q bits. We extend this result by showing the existence of such a linear repair scheme for every 1 ≤ s < t. Moreover, our new schemes are optimal among all linear repair schemes for Reed-Solomon codes when n = qt and r = qs. Additionally, we improve the lower bound on the repair bandwidth for Reed-Solomon codes, also established in the work of Guruswami and Wootters.
UR - https://www.scopus.com/pages/publications/85034092857
UR - https://www.scopus.com/pages/publications/85034092857#tab=citedBy
U2 - 10.1109/ISIT.2017.8006547
DO - 10.1109/ISIT.2017.8006547
M3 - Conference contribution
AN - SCOPUS:85034092857
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 346
EP - 350
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 -