An Algebraic View to Gradient Descent Decoding

Details An Algebraic View to Gradient Descent Decoding An Algebraic View to Gradient Descent Decoding

2010-08-26

arxiv.org/abs/1008.4474v1

Information Theory Workshop, Dublin 2010

Computer Science

Information Theory

Scientific paper

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.

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