Improving the coding speed of erasure codes with polynomial ring transforms

TL;DR

This paper introduces PYRIT, a novel polynomial ring transform method that enhances erasure code encoding speed by simplifying operations within a larger ring structure, outperforming existing implementations.

Contribution

The paper presents a new polynomial ring transform technique that reduces coding complexity and improves encoding speed for erasure codes.

Findings

Coding speeds increased by 1.5 to 2 times compared to existing methods.

Simplified XOR-based implementation due to ring properties.

Effective for Maximum Distance Separable erasure codes.

Abstract

Erasure codes are widely used in today's storage systems to cope with failures. Most of them use the finite field arithmetic. In this paper, we propose an implementation and a coding speed evaluation of an original method called PYRIT (PolYnomial RIng Transform) to perform operations between elements of a finite field into a bigger ring by using fast transforms between these two structures. Working in such a ring is much easier than working in a finite field. Firstly, it reduces the coding complexity by design. Secondly, it allows simple but efficient \texttt{xor}-based implementations by unrolling the operations thanks to the properties of the ring structure. We evaluate this proposition for Maximum Distance Separable erasure codes and we show that our method has better performances than common codes. Compared to the best known implementations, the coding speeds are increased by a factor varying from $1.5$ to $2$.