TY  - JOUR
U1  - Wissenschaftlicher Artikel
A1  - Rohweder, Daniel
A1  - Stern, Sebastian
A1  - Fischer, Robert F. H.
A1  - Shavgulidze, Sergo
A1  - Freudenberger, Jürgen
T1  - Four-Dimensional Hurwitz Signal Constellations, Set Partitioning, Detection, and Multilevel Coding
JF  - IEEE Transactions on Communications
N2  - 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.
KW  - Hurwitz integers
KW  - Lattices
KW  - Signal constellations
KW  - Digital modulation
KW  - Coded modulation
Y1  - 2021
SN  - 0090-6778
SS  - 0090-6778
SN  - 1558-0857
SS  - 1558-0857
U6  - https://doi.org/10.1109/TCOMM.2021.3083323
DO  - https://doi.org/10.1109/TCOMM.2021.3083323
N1  - Volltext im Campusnetz der Hochschule Konstanz abrufbar.
N1  - Corresponding author: Jürgen Freudenberger
VL  - 69
IS  - 8
SP  - 5079
EP  - 5090
PB  - IEEE
CY  - New York, NY
ER  -