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Multilevel coding over Eisenstein integers with ternary codes

  • This work introduces new signal constellations based on Eisenstein integers, i.e., the hexagonal lattice. These sets of Eisenstein integers have a cardinality which is an integer power of three. They are proposed as signal constellations for representation in the equivalent complex baseband model, especially for applications like physical-layer network coding or MIMO transmission where the constellation is required to be a subset of a lattice. It is shown that these constellations form additive groups where the addition over the complex plane corresponds to the addition with carry over ternary Galois fields. A ternary set partitioning is derived that enables multilevel coding based on ternary error-correcting codes. In the subsets, this partitioning achieves a gain of 4.77 dB, which results from an increased minimum squared Euclidean distance of the signal points. Furthermore, the constellation-constrained capacities over the AWGN channel and the related level capacities in case of ternary multilevel coding are investigated. Simulation results for multilevel coding based on ternary LDPC codes are presented which show that a performance close to the constellation-constrained capacities can be achieved.

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Author:Sebastian SternORCiD, Daniel RohwederORCiD, Jürgen FreudenbergerORCiDGND, Robert F. H. FischerORCiD
Parent Title (English):SCC 2019; 12th International ITG Conference on Systems, Communications and Coding, February 11 - 14, 2019, Rostock, Germany
Publisher:VDE Verlag
Place of publication:Berlin ; Offenbach
Document Type:Conference Proceeding
Year of Publication:2019
Release Date:2020/01/13
First Page:23
Last Page:28
Volltextzugriff für Hochschulangehörige via Datenbank IEEE Xplore möglich
Institutes:Institut für Systemdynamik - ISD
DDC functional group:000 Allgemeines, Informatik, Informationswissenschaft
Relevance:Keine peer reviewed Publikation (Wissenschaftlicher Artikel und Aufsatz, Proceeding, Artikel in Tagungsband)
Open Access?:Nein
Licence (German):License LogoUrheberrechtlich geschützt