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Four-Dimensional Hurwitz Signal Constellations, Set Partitioning, Detection, and Multilevel Coding

  • The Hurwitz lattice provides the densest four-dimensional packing. This fact has motivated research on four-dimensional Hurwitz signal constellations for optical and wireless communications. This work presents a new algebraic construction of finite sets of Hurwitz integers that is inherently accompanied by a respective modulo operation. These signal constellations are investigated for transmission over the additive white Gaussian noise (AWGN) channel. It is shown that these signal constellations have a better constellation figure of merit and hence a better asymptotic performance over an AWGN channel when compared with conventional signal constellations with algebraic structure, e.g., two-dimensional Gaussian-integer constellations or four-dimensional Lipschitz-integer constellations. We introduce two concepts for set partitioning of the Hurwitz integers. The first method is useful to reduce the computational complexity of the symbol detection. This suboptimum detection approach achieves near-maximum-likelihood performance. In the second case, the partitioning exploits the algebraic structure of the Hurwitz signal constellations. We partition the Hurwitz integers into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is larger than in the original set. This enables multilevel code constructions for the new signal constellations.

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Metadaten
Author:Daniel RohwederORCiD, Sebastian SternORCiD, Robert F. H. FischerORCiD, Sergo ShavgulidzeORCiD, Jürgen FreudenbergerORCiDGND
DOI:https://doi.org/10.1109/TCOMM.2021.3083323
ISSN:0090-6778
ISSN:1558-0857
Parent Title (English):IEEE Transactions on Communications
Volume:69
Publisher:IEEE
Place of publication:New York, NY
Document Type:Article
Language:English
Year of Publication:2021
Release Date:2022/01/10
Tag:Hurwitz integers; Lattices; Signal constellations; Digital modulation; Coded modulation
Issue:8
First Page:5079
Last Page:5090
Note:
Volltext im Campusnetz der Hochschule Konstanz abrufbar.
Note:
Corresponding author: Jürgen Freudenberger
Institutes:Institut für Systemdynamik - ISD
Relevance:Peer reviewed Publikation in Master Journal List
Open Access?:Nein
Licence (German):License LogoUrheberrechtlich geschützt