Fractional repetition codes with flexible repair from combinatorial designs

TL;DR

This paper introduces new fractional repetition codes for distributed storage, utilizing combinatorial designs like Steiner systems and affine geometries, with flexible repair capabilities and explicit code rate calculations.

Contribution

It presents novel FR code constructions based on combinatorial designs, including a Kronecker product method, and analyzes the tradeoff between locality and resilience.

Findings

Codes with normalized repair bandwidth greater than one.

Explicit code rate calculations for most constructions.

Tradeoff between local repair and failure resilience.

Abstract

Fractional repetition (FR) codes are a class of regenerating codes for distributed storage systems with an exact (table-based) repair process that is also uncoded, i.e., upon failure, a node is regenerated by simply downloading packets from the surviving nodes. In our work, we present constructions of FR codes based on Steiner systems and resolvable combinatorial designs such as affine geometries, Hadamard designs and mutually orthogonal Latin squares. The failure resilience of our codes can be varied in a simple manner. We construct codes with normalized repair bandwidth ($\beta$) strictly larger than one; these cannot be obtained trivially from codes with $\beta = 1$. Furthermore, we present the Kronecker product technique for generating new codes from existing ones and elaborate on their properties. FR codes with locality are those where the repair degree is smaller than the number of nodes contacted for reconstructing the stored file. For these codes we establish a tradeoff between the local repair property and failure resilience and construct codes that meet this tradeoff. Much of prior work only provided lower bounds on the FR code rate. In our work, for most of our constructions we determine the code rate for certain parameter ranges.