Repair Duality with Locally Repairable and Locally Regenerating Codes

摘要

We construct an explicit family of locally repairable and locallyregenerating codes whose existence was proven in a recent work by Kamath et al.about codes with local regeneration but no explicit construction was given.This explicit family of codes is based on HashTag codes. HashTag codes arerecently defined vector codes with different vector length $\alpha$ (alsocalled a sub-packetization level) that achieve the optimal repair bandwidth ofMSR codes or near-optimal repair bandwidth depending on the sub-packetizationlevel. We applied the technique of parity-splitting code construction. We showthat the lower bound on the size of the finite field for the presented explicitcode constructions can be lower than the one given in the work of Kamath et al.Finally, we discuss the importance of having two ways for node repair withlocally regenerating HashTag codes: repair only with local parity nodes orrepair with both local and global parity nodes. To the best of the authors'knowledge, this is the first work where this duality in repair process isdiscussed. We give a practical example and experimental results in Hadoop wherewe show the benefits of having this repair duality.