Lattice Construction C∗ from Self-Dual Codes

Maiara F. Bollauf; Sueli I.R. Costa; Ram Zamir

doi:10.1109/ISIT44484.2020.9174473

Lattice Construction C^∗ from Self-Dual Codes

Maiara F. Bollauf, Sueli I.R. Costa, Ram Zamir

School of Electrical Engineering

Universidade Estadual de Campinas

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Scopus citations

Abstract

Construction C^∗ was recently introduced as a generalization of the multilevel Construction C (or Forney's code-formula), such that the coded levels may be dependent. Both constructions do not produce a lattice in general, hence the central idea of this paper is to present a 3-level lattice Construction C^∗ scheme that admits an efficient nearest-neighborhood decoding. In order to achieve this objective, we choose coupled codes for levels 1 and 3, and set the second level code C 2 as an independent linear binary self-dual code, which is known to have a rich mathematical structure among families of linear codes. Our main result states a necessary and sufficient condition for this construction to generate a lattice. We then present examples of efficient lattices and also non-lattice constellations with good packing properties.

Original language	English
Title of host publication	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	537-541
Number of pages	5
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174473
State	Published - Jun 2020
Event	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: 21 Jul 2020 → 26 Jul 2020

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2020-June
ISSN (Print)	2157-8095

Conference

Conference	2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/Territory	United States
City	Los Angeles
Period	21/07/20 → 26/07/20

Funding

Funders	Funder number
Fundação de Amparo à Pesquisa do Estado de São Paulo	2013/25977-7
Conselho Nacional de Desenvolvimento Científico e Tecnológico	313326/2017-7
Israel Science Foundation	676/15

Keywords

Construction C
Construction C
Multilevel construction
self-dual codes
sphere packing

Access to Document

10.1109/ISIT44484.2020.9174473

Cite this

Bollauf, M. F., Costa, S. I. R., & Zamir, R. (2020). Lattice Construction C^∗ from Self-Dual Codes. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 537-541). Article 9174473 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT44484.2020.9174473

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Bollauf, MF, Costa, SIR & Zamir, R 2020, Lattice Construction C^∗ from Self-Dual Codes. in 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174473, IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June, Institute of Electrical and Electronics Engineers Inc., pp. 537-541, 2020 IEEE International Symposium on Information Theory, ISIT 2020, Los Angeles, United States, 21/07/20. https://doi.org/10.1109/ISIT44484.2020.9174473

Lattice Construction C^∗ from Self-Dual Codes. / Bollauf, Maiara F.; Costa, Sueli I.R.; Zamir, Ram.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2020. p. 537-541 9174473 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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