The repair problem under connectivity constraints: Explicit MSR codes for the rack-aware model of distributed storage

Abstract

Recent papers of Min Ye and the second-named author introduced constructions of MSR codes based on parity-check equations. In this note we modify the approach of these works to construct explicit MSR codes for the rack-based model of distributed storage. The codes that we construct can recover any single failed node by downloading information from a subset of the surviving nodes relying on the rack structure of the system. The underlying finite field is of size at most $n^{2}/u$, where n is the block length of the code and u is the size of the rack.