The Repair Problem in Distributed Storage Systems

Abstract :One of the characteristics of the Information era is the enormous amounts of data being generated and stored each day. Large data centers and distributed storage systems (DSS) are becoming more widespread, and they will have an increasing role in our everyday computational tasks.Storage efficiency is of high importance in data centers, hence large scale DSS are currently transitioning to erasure codes. One of the prevalent problem that DSS are facing is the repair problem. Namely, repairing the lost data of a single failed disk. Classical codes like Reed-Solomon are suboptimal for distributed environments, since they provide poor performance during the repair process. Thus, new codes that better address this problem need to be constructed.In the first part of the talk I will introduce formally the repair problem and an optimal repair code construction. In the second part I will address the limitations of data protection in such codes. Namely, for a given amount of redundancy, what is the maximum number of disks that can be protected in an optimal repair code. I will present an upper bound for the general case, and two tight bounds in the special cases of two important families of codes.