TY - GEN
T1 - On Optimal Locally Repairable Codes and Generalized Sector-Disk Codes
AU - Cai, Han
AU - Schwartz, Moshe
N1 - Funding Information:
This work was supported in part by a German Israeli Project Cooperation (DIP) grant under grant no. PE2398/1-1.
Publisher Copyright:
© 2020 IEEE.
PY - 2020/6/1
Y1 - 2020/6/1
N2 - Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper. The length of the constructed codes is super-linear in the alphabet size, which improves upon the well known pyramid codes, whose length is only linear in the alphabet size. The recoverable erasure patterns are also analyzed for the new codes. Based on the recoverable erasure patterns, we construct generalized sector-disk (GSD) codes, which can recover from disk erasures mixed with sector erasures in a more general setting than known sector-disk (SD) codes. Additionally, the number of sectors in the constructed GSD codes is superlinear in the alphabet size, compared with known SD codes, whose number of sectors is only linear in the alphabet size.
AB - Optimal locally repairable codes with information locality are considered. Optimal codes are constructed, whose length is also order-optimal with respect to a new bound on the code length derived in this paper. The length of the constructed codes is super-linear in the alphabet size, which improves upon the well known pyramid codes, whose length is only linear in the alphabet size. The recoverable erasure patterns are also analyzed for the new codes. Based on the recoverable erasure patterns, we construct generalized sector-disk (GSD) codes, which can recover from disk erasures mixed with sector erasures in a more general setting than known sector-disk (SD) codes. Additionally, the number of sectors in the constructed GSD codes is superlinear in the alphabet size, compared with known SD codes, whose number of sectors is only linear in the alphabet size.
UR - http://www.scopus.com/inward/record.url?scp=85090411017&partnerID=8YFLogxK
U2 - 10.1109/ISIT44484.2020.9174051
DO - 10.1109/ISIT44484.2020.9174051
M3 - Conference contribution
AN - SCOPUS:85090411017
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 571
EP - 576
BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PB - Institute of Electrical and Electronics Engineers
T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020
Y2 - 21 July 2020 through 26 July 2020
ER -