Repairable Replication-based Storage Systems Using Resolvable Designs

TL;DR

This paper introduces new regenerating codes for distributed storage that leverage resolvable designs, enabling flexible, exact, and uncoded repairs over a wide range of parameters, including cases beyond Steiner systems.

Contribution

It establishes a novel connection between fractional repetition codes and resolvable designs, providing new constructions using affine geometries, Hadamard designs, and Latin squares.

Findings

Codes can be designed with variable repetition degrees for enhanced resilience.

The repair table can be constructed straightforwardly for practical implementation.

Demonstrates existence of codes with parameters beyond Steiner system limitations.

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 $\beta \geq 1$ packets from a subset of the surviving nodes (prior work only considered the case of $\beta = 1$). 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.