TY - GEN

T1 - Repairing Reed-Solomon Codes Evaluated on Subspaces

AU - Berman, Amit

AU - Buzaglo, Sarit

AU - Dor, Avner

AU - Shany, Yaron

AU - Tamo, Itzhak

N1 - Publisher Copyright:
© 2021 IEEE.

PY - 2021/7/12

Y1 - 2021/7/12

N2 - We consider the repair problem for Reed-Solomon (RS) codes, evaluated on an \mathbb{F}_{q}-linear subspace U \subseteq \mathbb{F}_{q^{m}} of dimension d, where q is a prime power, m is a positive integer, and \mathbb{F}_{q} is the Galois field of size q. For q > 2, we show the existence of a linear repair scheme for the RS code of length n=q^{d} and codimension q^{s}, s < d, evaluated on U, in which each of the n-1 surviving nodes transmits only r symbols of \mathbb{F}_{q}, provided that ms\geq d(m-r). For the case q=2, we prove a similar result, with some restrictions on the evaluation linear subspace U. Our proof is based on a probabilistic argument, however the result is not merely an existence result; the success probability is fairly large (at least 1/3) and there is a simple criterion for checking the validity of the randomly chosen linear repair scheme.

AB - We consider the repair problem for Reed-Solomon (RS) codes, evaluated on an \mathbb{F}_{q}-linear subspace U \subseteq \mathbb{F}_{q^{m}} of dimension d, where q is a prime power, m is a positive integer, and \mathbb{F}_{q} is the Galois field of size q. For q > 2, we show the existence of a linear repair scheme for the RS code of length n=q^{d} and codimension q^{s}, s < d, evaluated on U, in which each of the n-1 surviving nodes transmits only r symbols of \mathbb{F}_{q}, provided that ms\geq d(m-r). For the case q=2, we prove a similar result, with some restrictions on the evaluation linear subspace U. Our proof is based on a probabilistic argument, however the result is not merely an existence result; the success probability is fairly large (at least 1/3) and there is a simple criterion for checking the validity of the randomly chosen linear repair scheme.

UR - http://www.scopus.com/inward/record.url?scp=85115095639&partnerID=8YFLogxK

U2 - 10.1109/ISIT45174.2021.9517961

DO - 10.1109/ISIT45174.2021.9517961

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AN - SCOPUS:85115095639

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 867

EP - 871

BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021

Y2 - 12 July 2021 through 20 July 2021

ER -