An erasure code with reduced average locality for distributed storage systems

Abstract

A linear block code with dimension k and length n is called a locally repairable code (LRC) with locality r if it can retrieve any coded symbol by at most r other coded symbols. LRCs have been recently proposed and used in practice in distributed storage systems such as Windows Azure Storage and Facebook HDFS-RAID. Theoretical bounds on the maximum locality of LRCs have been established, and optimal LRCs that achieve the obtained bound have been designed. Average locality of LRCs (r) is directly proportional to the costly repair bandwidth, disk I/O, and number of nodes involved in a repair process of a missing data block. There is a gap in the literature establishing the theoretical bounds on r. As an initial attempt to fill this gap, in this paper, we establish a lower bound on r for the same code parameters used by Facebook HDFS-RAID. We also present a code that achieves the obtained bound. Comparing with the LRC used in Facebook HDFS-RAID, our proposed LRC improves the average locality by 22.5% without sacrificing the rate and minimum distance of the code.