Optimal matrix lattices for MIMO codes from division algebras

Camilla Hollanti; Jyrki Lahtonen; Kalle Ranto; Roope Vehkalahti

doi:10.1109/ISIT.2006.261720

Optimal matrix lattices for MIMO codes from division algebras

Camilla Hollanti^*, Jyrki Lahtonen, Kalle Ranto, Roope Vehkalahti

^*Corresponding author for this work

Not published at Aalto University

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

13 Citations (Scopus)

Abstract

We show why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed non-vanishing minimal determinant. Using results from class field theory we derive a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas). We also give examples of division algebras achieving our bound. E.g. we construct a matrix lattice with QAM coefficients that has (inside 'large' subsets of the signal space) 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant. We also give another matrix lattice with coefficients from the hexagonal lattice with an even higher density.

Original language	English
Title of host publication	IEEE International Symposium on Information Theory - Proceedings
Pages	783-787
Number of pages	5
DOIs	https://doi.org/10.1109/ISIT.2006.261720
Publication status	Published - 2006
MoE publication type	A4 Article in a conference publication
Event	IEEE International Symposium on Information Theory - Seattle, United States Duration: 9 Jul 2006 → 14 Jul 2006

Conference

Conference	IEEE International Symposium on Information Theory
Abbreviated title	ISIT
Country	United States
City	Seattle
Period	09/07/2006 → 14/07/2006

Access to Document

10.1109/ISIT.2006.261720

Link to publication in Scopus

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title = "Optimal matrix lattices for MIMO codes from division algebras",

abstract = "We show why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed non-vanishing minimal determinant. Using results from class field theory we derive a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas). We also give examples of division algebras achieving our bound. E.g. we construct a matrix lattice with QAM coefficients that has (inside 'large' subsets of the signal space) 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant. We also give another matrix lattice with coefficients from the hexagonal lattice with an even higher density.",

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AU - Hollanti, Camilla

AU - Lahtonen, Jyrki

AU - Ranto, Kalle

AU - Vehkalahti, Roope

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N2 - We show why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed non-vanishing minimal determinant. Using results from class field theory we derive a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas). We also give examples of division algebras achieving our bound. E.g. we construct a matrix lattice with QAM coefficients that has (inside 'large' subsets of the signal space) 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant. We also give another matrix lattice with coefficients from the hexagonal lattice with an even higher density.

AB - We show why the discriminant of a maximal order within a cyclic division algebra must be minimized in order to get the densest possible matrix lattices with a prescribed non-vanishing minimal determinant. Using results from class field theory we derive a lower bound to the minimum discriminant of a maximal order with a given center and index (= the number of Tx/Rx antennas). We also give examples of division algebras achieving our bound. E.g. we construct a matrix lattice with QAM coefficients that has (inside 'large' subsets of the signal space) 2.5 times as many codewords as the celebrated Golden code of the same minimum determinant. We also give another matrix lattice with coefficients from the hexagonal lattice with an even higher density.

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DO - 10.1109/ISIT.2006.261720

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BT - IEEE International Symposium on Information Theory - Proceedings

T2 - IEEE International Symposium on Information Theory

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