A1 Journal article (refereed)
The DMT of Real and Quaternionic Lattice Codes and DMT Classification of Division Algebra Codes (2022)

Vehkalahti, R., & Luzzi, L. (2022). The DMT of Real and Quaternionic Lattice Codes and DMT Classification of Division Algebra Codes. IEEE Transactions on Information Theory, 68(5), 2999-3013. https://doi.org/10.1109/tit.2021.3137153

JYU authors or editors

Publication details

All authors or editors: Vehkalahti, Roope; Luzzi, Laura

Journal or series: IEEE Transactions on Information Theory

ISSN: 0018-9448

eISSN: 1557-9654

Publication year: 2022

Volume: 68

Issue number: 5

Pages range: 2999-3013

Publisher: IEEE

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1109/tit.2021.3137153

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85365

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2102.09910

Abstract

In this paper we consider the diversity-multiplexing gain tradeoff (DMT) of so-called minimum delay asymmetric space-time codes for the n × m MIMO channel. Such codes correspond to lattices in Mn(C) with dimension smaller than 2n2. Currently, very little is known about their DMT, except in the case m = 1, corresponding to the multiple input single output (MISO) channel. Further, apart from the MISO case, no DMT optimal asymmetric codes are known. We first discuss previous criteria used to analyze the DMT of space-time codes and comment on why these methods fail when applied to asymmetric codes. We then consider two special classes of asymmetric codes where the code-words are restricted to either real or quaternion matrices. We prove two separate diversity-multiplexing gain trade-off (DMT) upper bounds for such codes and provide a criterion for a lattice code to achieve these upper bounds. We also show that lattice codes based on Q-central division algebras satisfy this optimality criterion. As a corollary this result provides a DMT classification for all Q-central division algebra codes that are based on standard embeddings. While the Q-central division algebra based codes achieve the largest possible DMT of a code restricted to either real or quaternion space, they still fall short of the optimal DMT apart from the MISO case.

Keywords: algebra; coding theory; data transfer; MIMO technology

Free keywords: lattices; algebra; space-time codes; encoding; MIMO communication; maximum likelihood decoding; upper bound

Contributing organizations

Ministry reporting: Yes

Reporting Year: 2022

JUFO rating: 3