An Algebraic View to Gradient Descent Decoding
Information Theory
2010-08-27 v1 Combinatorics
math.IT
Abstract
There are two gradient descent decoding procedures for binary codes proposed independently by Liebler and by Ashikhmin and Barg. Liebler in his paper mentions that both algorithms have the same philosophy but in fact they are rather different. The purpose of this communication is to show that both algorithms can be seen as two ways of understanding the reduction process algebraic monoid structure related to the code. The main tool used for showing this is the Gr\"obner representation of the monoid associated to the linear code.
Cite
@article{arxiv.1008.4474,
title = {An Algebraic View to Gradient Descent Decoding},
author = {M. Borges Quintana and M. A. Borges Trenard and I. Marquez-Corbella and E. Martinez-Moro},
journal= {arXiv preprint arXiv:1008.4474},
year = {2010}
}