TY - JOUR
T1 - Bounds on the Parameters of Locally Recoverable Codes
AU - Tamo, Itzhak
AU - Barg, Alexander
AU - Frolov, Alexey
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/6
Y1 - 2016/6
N2 - A locally recoverable code (LRC code) is a code over a finite alphabet, such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. In this paper, we derive new finite-length and asymptotic bounds on the parameters of LRC codes. For LRC codes with a single recovering set for every coordinate, we derive an asymptotic Gilbert-Varshamov type bound for LRC codes and find the maximum attainable relative distance of asymptotically good LRC codes. Similar results are established for LRC codes with two disjoint recovering sets for every coordinate. For the case of multiple recovering sets (the availability problem), we derive a lower bound on the parameters using expander graph arguments. Finally, we also derive finite-length upper bounds on the rate and the distance of LRC codes with multiple recovering sets.
AB - A locally recoverable code (LRC code) is a code over a finite alphabet, such that every symbol in the encoding is a function of a small number of other symbols that form a recovering set. In this paper, we derive new finite-length and asymptotic bounds on the parameters of LRC codes. For LRC codes with a single recovering set for every coordinate, we derive an asymptotic Gilbert-Varshamov type bound for LRC codes and find the maximum attainable relative distance of asymptotically good LRC codes. Similar results are established for LRC codes with two disjoint recovering sets for every coordinate. For the case of multiple recovering sets (the availability problem), we derive a lower bound on the parameters using expander graph arguments. Finally, we also derive finite-length upper bounds on the rate and the distance of LRC codes with multiple recovering sets.
KW - Availability problem
KW - Gilbert-Varshamov bound
KW - asymptotic bounds
KW - graph expansion
KW - recovery graph
UR - http://www.scopus.com/inward/record.url?scp=84976433431&partnerID=8YFLogxK
U2 - 10.1109/TIT.2016.2518663
DO - 10.1109/TIT.2016.2518663
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84976433431
SN - 0018-9448
VL - 62
SP - 3070
EP - 3083
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 6
M1 - 7384487
ER -