On the Duality of Fractional Repetition Codes

TL;DR

This paper explores the duality properties of fractional repetition codes in distributed storage, establishing a dual bound on supported file size to optimize repair efficiency and bandwidth.

Contribution

It introduces a duality framework for FR codes and derives a new bound on their supported file size, advancing understanding of their repair capabilities.

Findings

Established a duality relationship between FR codes and their duals.

Derived a dual bound on the supported file size of FR codes.

Enhanced understanding of repair efficiency in distributed storage systems.

Abstract

Erasure codes have emerged as an efficient technology for providing data redundancy in distributed storage systems. However, it is a challenging task to repair the failed storage nodes in erasure-coded storage systems, which requires large quantities of network resources. In this paper, we study fractional repetition (FR) codes, which enable the minimal repair complexity and also minimum repair bandwidth during node repair. We focus on the duality of FR codes, and investigate the relationship between the supported file size of an FR code and its dual code. Furthermore, we present a dual bound on the supported file size of FR codes.