On the Effectiveness of Polynomial Realization of Reed-Solomon Codes for Storage Systems

TL;DR

This paper evaluates the performance of polynomial realization of Reed-Solomon codes in storage systems, comparing it with matrix-based methods, and finds polynomial methods generally less efficient despite optimizations.

Contribution

The paper provides an empirical performance comparison between polynomial and matrix realizations of RS codes, including optimized implementations, highlighting their efficiency differences.

Findings

Polynomial realization is less efficient than matrix realization in practice.

Optimizations improve polynomial implementation performance but do not surpass matrix methods.

Cauchy bit matrices outperform polynomial realization in storage system applications.

Abstract

There are different ways to realize Reed Solomon (RS) codes. While in the storage community, using the generator matrices to implement RS codes is more popular, in the coding theory community the generator polynomials are typically used to realize RS codes. Prominent exceptions include HDFS-RAID, which uses generator polynomial based erasure codes, and extends the Apache Hadoop's file system. In this paper we evaluate the performance of an implementation of polynomial realization of Reed-Solomon codes, along with our optimized version of it, against that of a widely-used library (Jerasure) that implements the main matrix realization alternatives. Our experimental study shows that despite significant performance gains yielded by our optimizations, the polynomial implementations' performance is constantly inferior to those of matrix realization alternatives in general, and that of Cauchy bit matrices in particular.