State spaces of convolutional codes, codings and encoders
Information Theory
2017-12-07 v1 math.IT
Abstract
In this paper we give a compact presentation of the theory of abstract spaces for convolutional codes and convolutional encoders, and show a connection between them that seems to be missing in the literature. We use it for a short proof of two facts: the size of a convolutional encoder of a polynomial matrix is at least its inner degree, and the minimal encoder has the size of the external degree if the matrix is reduced.
Keywords
Cite
@article{arxiv.1712.01914,
title = {State spaces of convolutional codes, codings and encoders},
author = {Štěpán Holub},
journal= {arXiv preprint arXiv:1712.01914},
year = {2017}
}
Comments
Submitted to IEEE Transactions on Information Theory