Optimal repair schemes for some families of full-length reed-solomon codes

Abstract

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 F q t 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 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.