Searching for Minimum Storage Regenerating Codes

TL;DR

This paper conducts a systematic computer search to discover new optimal systematic minimum storage regenerating codes for distributed storage, successfully finding codes that meet the theoretical bounds for the first time.

Contribution

It introduces a novel search methodology with symmetry constraints and code representation, leading to the discovery of previously unknown optimal codes for specific parameters.

Findings

Identified new optimal codes for n=5, k=3 over various finite fields

Matched the information theoretic cut-set bound for these codes

Established the first known codes meeting the theoretical optimality criteria

Abstract

Regenerating codes allow distributed storage systems to recover from the loss of a storage node while transmitting the minimum possible amount of data across the network. We present a systematic computer search for optimal systematic regenerating codes. To search the space of potential codes, we reduce the potential search space in several ways. We impose an additional symmetry condition on codes that we consider. We specify codes in a simple alternative way, using additional recovered coefficients rather than transmission coefficients and place codes into equivalence classes to avoid redundant checking. Our main finding is a few optimal systematic minimum storage regenerating codes for $n=5$ and $k=3$, over several finite fields. No such codes were previously known and the matching of the information theoretic cut-set bound was an open problem.