Fractional Repetition Codes for Repair in Distributed Storage Systems

TL;DR

This paper introduces Fractional Repetition codes, a new class of exact MBR codes for distributed storage that enable low-complexity, uncoded repair and are constructed using combinatorial designs, achieving optimal storage capacity in a table-based repair model.

Contribution

The paper proposes a novel class of Fractional Repetition codes combining MDS and repetition codes, with constructions based on graphs and Steiner systems, and introduces the concept of Fractional Repetition capacity.

Findings

Codes achieve storage capacity for random access repair.

Constructed codes based on regular graphs and Steiner systems.

Upper bounds on Fractional Repetition capacity provided.

Abstract

We introduce a new class of exact Minimum-Bandwidth Regenerating (MBR) codes for distributed storage systems, characterized by a low-complexity uncoded repair process that can tolerate multiple node failures. These codes consist of the concatenation of two components: an outer MDS code followed by an inner repetition code. We refer to the inner code as a Fractional Repetition code since it consists of splitting the data of each node into several packets and storing multiple replicas of each on different nodes in the system. Our model for repair is table-based, and thus, differs from the random access model adopted in the literature. We present constructions of Fractional Repetition codes based on regular graphs and Steiner systems for a large set of system parameters. The resulting codes are guaranteed to achieve the storage capacity for random access repair. The considered model motivates a new definition of capacity for distributed storage systems, that we call Fractional Repetition capacity. We provide upper bounds on this capacity while a precise expression remains an open problem.