Scalable constructions of fractional repetition codes in distributed storage systems

Abstract

In distributed storage systems built using commodity hardware, it is necessary to have data redundancy in order to ensure system reliability. In such systems, it is also often desirable to be able to quickly repair storage nodes that fail. We consider a scheme-introduced by El Rouayheb and Ramchandran-which uses combinatorial block design in order to design storage systems that enable efficient (and exact) node repair. In this work, we investigate systems where node sizes may be much larger than replication degrees, and explicitly provide algorithms for constructing these storage designs. Our designs, which are related to projective geometries, are based on the construction of bipartite cage graphs (with girth 6) and the concept of mutually-orthogonal Latin squares. Via these constructions, we can guarantee that the resulting designs require the fewest number of storage nodes for the given parameters, and can further show that these systems can be easily expanded without need for frequent reconfiguration.

Construction of Fractional Repetition Codes with Variable Parameters for Distributed Storage Systems

“…It is known that regular FR codes are good for load balancing [15] while irregular FR codes are suitable for heterogeneous networks [21]. Though various irregular FR codes have been proposed, for example, in [17,18,20,21], we focus on introducing existing regular FR codes related to our proposed construction.…”

“…Also, we consider only the regular FR codes for 3 ≤ ρ ≤ α and β = 1. It is noted that ρ = 2 could not be enough for practical systems to have good reliability in general and ρ ≤ α is a common scenario in DSSs [15].…”

“…FR codes can be seen as a variant of exact MBR codes and they aim to minimize disk I/O as well as network bandwidth for repair. Various construction methods for FR codes are proposed using graphs, design theory, algebraic structures, and so on [14][15][16][17][18][19]. Note that the existing construction methods result in FR codes with quite restricted code parameter values, which will be discussed in Section 2.…”

Construction of New Fractional Repetition Codes from Relative Difference Sets with λ=1

“…In [16], the existence of FR codes for each parameter set is shown by algorithm-based search, and some examples for each parameter set are provided. Many kinds of FR codes have been constructed mostly based on algebraic structures, combinatorial designs and graph theory [15,[17][18][19][20][21][22]. In [15], Steiner systems are used as a class of (v, (v − 1)/(k − 1), k) FR codes with β = 1 under the existence of Steiner system S(2, k, v).…”

“…In [15], Steiner systems are used as a class of (v, (v − 1)/(k − 1), k) FR codes with β = 1 under the existence of Steiner system S(2, k, v). In [17], ((q n+2 − 1)/(q − 1), (q n+1 − 1)/(q − 1), q + 1) FR codes are constructed for a prime power q and n ≥ 1, which are based on the projective geometry and Latin squares. These FR codes are a subclass of the FR codes from Steiner systems in [15] and additionally designed to have a scalable property.…”