Fuchsian codes with arbitrarily high code rates

I. Blanco-Chacon*, C. Hollanti, M. Alsina, D. Remon

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
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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.

Original languageEnglish
Pages (from-to)180-196
Number of pages17
JournalJOURNAL OF PURE AND APPLIED ALGEBRA
Volume220
Issue number1
DOIs
Publication statusPublished - Jan 2016
MoE publication typeA1 Journal article-refereed

Keywords

  • TIME BLOCK-CODES
  • DOMAINS

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