Modified Euclidean Algorithms for Decoding Reed-Solomon Codes
Abstract
The extended Euclidean algorithm (EEA) for polynomial greatest common divisors is commonly used in solving the key equation in the decoding of Reed-Solomon (RS) codes, and more generally in BCH decoding. For this particular application, the iterations in the EEA are stopped when the degree of the remainder polynomial falls below a threshold. While determining the degree of a polynomial is a simple task for human beings, hardware implementation of this stopping rule is more complicated. This paper describes a modified version of the EEA that is specifically adapted to the RS decoding problem. This modified algorithm requires no degree computation or comparison to a threshold, and it uses a fixed number of iterations. Another advantage of this modified version is in its application to the errors-and-erasures decoding problem for RS codes where significant hardware savings can be achieved via seamless computation.
Cite
@article{arxiv.0906.3778,
title = {Modified Euclidean Algorithms for Decoding Reed-Solomon Codes},
author = {Dilip V. Sarwate and Zhiyuan Yan},
journal= {arXiv preprint arXiv:0906.3778},
year = {2009}
}
Comments
This paper is a corrected version of a paper with the same title that will appear in the Proceedings of the 2009 IEEE International Symposium on Information Theory. The major change is in Algorithm II of Section IV