Fast Encoding and Decoding of Gabidulin Codes

TL;DR

This paper introduces the fastest known encoding and decoding algorithms for Gabidulin codes, leveraging low-complexity normal bases and a transform-domain approach to enhance error control in network coding.

Contribution

It presents novel, highly efficient algorithms for Gabidulin code encoding and decoding, significantly improving computational speed over previous methods.

Findings

Encoding and decoding algorithms are faster than existing methods.

Utilizes low-complexity normal bases for efficiency.

Proposes a transform-domain decoding approach.

Abstract

Gabidulin codes are the rank-metric analogs of Reed-Solomon codes and have a major role in practical error control for network coding. This paper presents new encoding and decoding algorithms for Gabidulin codes based on low-complexity normal bases. In addition, a new decoding algorithm is proposed based on a transform-domain approach. Together, these represent the fastest known algorithms for encoding and decoding Gabidulin codes.