Repairable replication-based storage systems using resolvable designs

Abstract

Abstract-We consider the design of regenerating codes for distributed storage systems at the minimum bandwidth regeneration (MBR) point. The codes allow for a repair process that is exact and uncoded, but table-based. These codes were introduced in prior work and consist of an outer MDS code followed by an inner fractional repetition (FR) code where copies of the coded symbols are placed on the storage nodes. The main challenge in this domain is the design of the inner FR code.In our work, we consider generalizations of FR codes, by establishing their connection with a family of combinatorial structures known as resolvable designs. Our constructions based on affine geometries, Hadamard designs and mutually orthogonal Latin squares allow the design of systems where a new node can be exactly regenerated by downloading β ≥ 1 packets from a subset of the surviving nodes (prior work only considered the case of β = 1). Our techniques allow the design of systems over a large range of parameters. Specifically, the repetition degree of a symbol, which dictates the resilience of the system can be varied over a large range in a simple manner. Moreover, the actual table needed for the repair can also be implemented in a rather straightforward way. Furthermore, we answer an open question posed in prior work by demonstrating the existence of codes with parameters that are not covered by Steiner systems.

On low repair complexity storage codes via group divisible designs

“…Finite projective planes are adopted in the scalable construction of FR codes. Olmez et al proposed in [11] constructions using resolvable designs, where repetition degree can be varied over a large range in a simple manner. In [12], Anil et al considered the usage of incidence matrix, and enumerated several FR codes up to a given number of nodes.…”

“…In the work of [11], the authors show that an FR code with repetition degree ρ ≤ γ can be obtained by choosing ρ distinct parallel classes, where γ is the total number of parallel classes. Specifically, each parallel class contains one copy of all coded packets.…”

General Fractional Repetition Codes for Distributed Storage Systems

“…However, in [12], only code constructions with ρ = 2 are given. For ρ ≥ 2, several explicit constructions for the special case of FR codes are given in references [5] to [8].…”

“…Previous works [6], [7], [8] provide constructions of FR codes with identical block size. However, heterogeneous storage systems, in which the storage nodes need not to store the same amount of data, are preferred in many cases.…”

Fractional Repetition and Erasure Batch Codes

“…An FR code should satisfy the requirement that from any set of k nodes it is possible to reconstruct the stored file, that is, M = min |I|=k | ∪ i∈I N i |. Note that for FR codes it holds that α = d and β = 1, since when some node i fails, it can be repaired by using α other nodes which store common symbols with node i. Constructions of FR codes based on different types of regular graphs and combinatorial designs can be found in [6,9,11,14].…”