Space Bounds for Reliable Storage: Fundamental Limits of Coding

TL;DR

This paper establishes fundamental space lower bounds for reliable storage in asynchronous systems with faults, and proposes a hybrid coding technique that approaches these bounds while adapting to concurrency levels.

Contribution

It proves inherent space bounds in fault-tolerant storage without bounded concurrency and introduces a hybrid coding algorithm that nearly attains these bounds.

Findings

Storage cost is at least f+1 times data size without bounded concurrency.

A hybrid erasure-code and replication scheme approaches the theoretical lower bound.

The proposed algorithm adapts to different concurrency levels efficiently.

Abstract

We study the inherent space requirements of shared storage algorithms in asynchronous fault-prone systems. Previous works use codes to achieve a better storage cost than the well-known replication approach. However, a closer look reveals that they incur extra costs somewhere else: Some use unbounded storage in communication links, while others assume bounded concurrency or synchronous periods. We prove here that this is inherent, and indeed, if there is no bound on the concurrency level, then the storage cost of any reliable storage algorithm is at least f+1 times the data size, where f is the number of tolerated failures. We further present a technique for combining erasure-codes with full replication so as to obtain the best of both. We present a storage algorithm whose storage cost is close to the lower bound in the worst case, and adapts to the concurrency level.