Fuchsian codes with arbitrarily high code rates

Loading...
Thumbnail Image

Access rights

openAccess
acceptedVersion

URL

Journal Title

Journal ISSN

Volume Title

A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Major/Subject

Mcode

Degree programme

Language

en

Pages

17

Series

Journal of Pure and Applied Algebra, Volume 220, issue 1, pp. 180-196

Abstract

Recently, Fuchsian codes have been proposed in Blanco-Chacon et al. (2014) [2] for communication over channels subject to additive white Gaussian noise (AWGN). The two main advantages of Fuchsian codes are their ability to compress information, i.e., high code rate, and their logarithmic decoding complexity. In this paper, we improve the first property further by constructing Fuchsian codes with arbitrarily high code rates while maintaining logarithmic decoding complexity. Namely, in the case of Fuchsian groups derived from quaternion algebras over totally real fields we obtain a code rate that is proportional to the degree of the base field. In particular, we consider arithmetic Fuchsian groups of signature (1; e) to construct explicit codes having code rate six, meaning that we can transmit six independent integers during one channel use. (C) 2015 Elsevier B.V. All rights reserved.

Description

Other note

Citation

Blanco-Chacon, I, Hollanti, C, Alsina, M & Remón, D 2016, 'Fuchsian codes with arbitrarily high code rates', Journal of Pure and Applied Algebra, vol. 220, no. 1, pp. 180-196. https://doi.org/10.1016/j.jpaa.2015.06.005