Towards a complete DMT classification of division algebra codes

Laura Luzzi; Roope Vehkalahti; Alexander Gorodnik

doi:10.1109/ISIT.2016.7541848

Towards a complete DMT classification of division algebra codes

Laura Luzzi, Roope Vehkalahti, Alexander Gorodnik

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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Abstract

This work aims at providing new lower bounds for the diversity-multiplexing gain trade-off of a general class of lattice codes based on division algebras. In the low multiplexing gain regime, some bounds were previously obtained from the high signal-to-noise ratio estimate of the union bound for the pairwise error probabilities. Here these results are extended to cover a larger range of multiplexing gains. The improvement is achieved by using ergodic theory in Lie groups to estimate the behavior of the sum arising from the union bound. In particular, the new bounds for lattice codes derived from Q-central division algebras suggest that these codes can be divided into two classes based on their Hasse invariants at the infinite places. Algebras with ramification at the infinite place seem to provide a better diversity-multiplexing gain trade-off.

Original language	English
Title of host publication	2016 IEEE International Symposium on Information Theory (ISIT 2016)
Subtitle of host publication	Proceedings of a meeting held 10-15 July 2016, Barcelona, Spain
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Pages	2993-2997
Number of pages	5
ISBN (Electronic)	9781509018062
ISBN (Print)	9781509018079
DOIs	https://doi.org/10.1109/ISIT.2016.7541848
Publication status	Published - Sept 2016
Event	2016 IEEE International Symposium on Information Theory, ISIT 2016 - Barcelona, Spain Duration: 10 Jul 2016 → 15 Jul 2016

Publication series

Name	Proceedings of the IEEE International Symposium on Information Theory (ISIT)
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
ISSN (Print)	2157-8117

Conference

Conference	2016 IEEE International Symposium on Information Theory, ISIT 2016
Country/Territory	Spain
City	Barcelona
Period	10/07/16 → 15/07/16

Keywords

cs.IT
math.IT
math.NT

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10.1109/ISIT.2016.7541848

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Luzzi, L., Vehkalahti, R., & Gorodnik, A. (2016). Towards a complete DMT classification of division algebra codes. In 2016 IEEE International Symposium on Information Theory (ISIT 2016): Proceedings of a meeting held 10-15 July 2016, Barcelona, Spain (pp. 2993-2997). Article 7541848 (Proceedings of the IEEE International Symposium on Information Theory (ISIT)). Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ISIT.2016.7541848

Luzzi, Laura ; Vehkalahti, Roope ; Gorodnik, Alexander. / Towards a complete DMT classification of division algebra codes. 2016 IEEE International Symposium on Information Theory (ISIT 2016): Proceedings of a meeting held 10-15 July 2016, Barcelona, Spain. Institute of Electrical and Electronics Engineers (IEEE), 2016. pp. 2993-2997 (Proceedings of the IEEE International Symposium on Information Theory (ISIT)).

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Luzzi, L, Vehkalahti, R & Gorodnik, A 2016, Towards a complete DMT classification of division algebra codes. in 2016 IEEE International Symposium on Information Theory (ISIT 2016): Proceedings of a meeting held 10-15 July 2016, Barcelona, Spain., 7541848, Proceedings of the IEEE International Symposium on Information Theory (ISIT), Institute of Electrical and Electronics Engineers (IEEE), pp. 2993-2997, 2016 IEEE International Symposium on Information Theory, ISIT 2016, Barcelona, Spain, 10/07/16. https://doi.org/10.1109/ISIT.2016.7541848

Towards a complete DMT classification of division algebra codes. / Luzzi, Laura; Vehkalahti, Roope; Gorodnik, Alexander.
2016 IEEE International Symposium on Information Theory (ISIT 2016): Proceedings of a meeting held 10-15 July 2016, Barcelona, Spain. Institute of Electrical and Electronics Engineers (IEEE), 2016. p. 2993-2997 7541848 (Proceedings of the IEEE International Symposium on Information Theory (ISIT)).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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Luzzi L, Vehkalahti R, Gorodnik A. Towards a complete DMT classification of division algebra codes. In 2016 IEEE International Symposium on Information Theory (ISIT 2016): Proceedings of a meeting held 10-15 July 2016, Barcelona, Spain. Institute of Electrical and Electronics Engineers (IEEE). 2016. p. 2993-2997. 7541848. (Proceedings of the IEEE International Symposium on Information Theory (ISIT)). Epub 2016 Aug 11. doi: 10.1109/ISIT.2016.7541848

Towards a complete DMT classification of division algebra codes

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