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New Four-Dimensional Signal Constellations From Lipschitz Integers for Transmission Over the Gaussian Channel

  • Codes over quotient rings of Lipschitz integers have recently attracted some attention. This work investigates the performance of Lipschitz integer constellations for transmission over the AWGN channel by means of the constellation figure of merit. A construction of sets of Lipschitz integers that leads to a better constellation figure of merit compared to ordinary Lipschitz integer constellations is presented. In particular, it is demonstrated that the concept of set partitioning can be applied to quotient rings of Lipschitz integers where the number of elements is not a prime number. It is shown that it is always possible to partition such quotient rings into additive subgroups in a manner that the minimum Euclidean distance of each subgroup is strictly larger than in the original set. The resulting signal constellations have a better performance for transmission over an additive white Gaussian noise channel compared to Gaussian integer constellations and to ordinary Lipschitz integer constellations. In addition, we present multilevel code constructions for the new signal constellations.

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Metadaten
Author:Jürgen FreudenbergerORCiDGND, Sergo ShavgulidzeORCiD
DOI:https://doi.org/10.1109/TCOMM.2015.2441691
ISSN:1558-0857
Parent Title (English):IEEE Transactions on Communications
Volume:Volume 63
Document Type:Article
Language:English
Year of Publication:2015
Release Date:2017/03/29
Issue:Issue 7
First Page:2420
Last Page:2427
Open Access?:Nein
Licence (English):License LogoLizenzbedingungen IEEE