An Improved Bound and Singleton-Optimal Constructions of Fractional Repetition Codes

Abstract

Fractional repetition (FR) codes are a class of repair efficient erasure codes that can recover a failed storage node with both optimal repair bandwidth and complexity. In this paper, we study the minimum distance of FR codes, which is the smallest number of nodes whose failure leads to the unrecoverable loss of the stored file. We derive a new upper bound on the minimum distance of FR codes, which is tighter than the Singleton bound and a Singleton-like bound that takes locality into account. Based on regular graphs and combinatorial designs, several families of FR codes with optimal minimum distance are obtained.