Flexible Fractional Repetition Codes for Distributed Storage Networks

TL;DR

This paper introduces flexible fractional repetition codes that extend existing FR codes to arbitrary distributed storage network parameters, enabling improved storage-bandwidth tradeoffs with practical repair properties.

Contribution

It develops a generalized FR code construction compatible with any (n,k,d), bridging the gap between theoretical analysis and practical code design.

Findings

Flexible FR codes apply to all (n,k,d) values.

They retain small repair bandwidth and exact-repair features.

The codes are nearly repairable-by-transfer.

Abstract

Consider the following fundamental question of distributed storage networks: Given any arbitrary $(n,k,d)$ values, whether there exists an intelligent helper selection scheme (assuming unlimited memory and computing power) that can strictly improve the storage-bandwidth (S-B) tradeoff. Ahmad et al. 18' answered this question by proving that for a subset of $(n,k,d)$ values, no helper selection scheme can ever improve the S-B tradeoff, and for the $(n,k,d)$ not in that subset, a new scheme called family helper selection (FHS) can strictly improve the S-B tradeoff over a blind helper selection scheme. Nonetheless, the analysis of FHS is done by a min-cut analysis with no actual code construction. This work fills this gap between pure min-cut analysis and actual code construction by pairing FHS with a new, generalized version of the existing fractional repetition (FR) codes. Specifically, existing FR codes are exact-repair codes that admit the highly-desirable repair-by-transfer property, but its unique construction limits the application to a restricted set of $(n,k,d)$ values. In contrast, our new construction, termed flexible fractional repetition codes, can be applied to arbitrary $(n,k,d)$ while retaining most of the practical benefits of FR codes, i.e., admitting small repair bandwidth, being exact-repair, and being almost repairable-by-transfer.