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Maximal Orders in the Design of Dense Space-Time Lattice Codes

Camilla Hollanti, Jyrki Lahtonen, Hsiao-feng (Francis) Lu, Maximal Orders in the Design of Dense Space-Time Lattice Codes. IEEE Transactions on Information Theory 54(10), 2008.

Abstract:

We construct explicit rate-one, full-diversity, geometrically dense
matrix lattices with large, non-vanishing determinants (NVD) for four
transmit antenna multiple-input single-output (MISO) space-time (ST)
applications. The constructions are based on the theory of rings of
algebraic integers and related subrings of the Hamiltonian quaternions
and can be extended to a larger number of Tx antennas. The usage of
ideals guarantees a non-vanishing determinant larger than one and an
easy way to present the exact proofs for the minimum determinants. The
idea of finding denser sublattices within a given division algebra
is then generalized to a multiple-input multiple-output (MIMO) case with
an arbitrary number of Tx antennas by using the theory of cyclic division
algebras (CDA) and maximal orders. It is also shown that the explicit constructions in this paper all have a simple decoding method based on sphere decoding. Related to the decoding complexity, the notion of
sensitivity is introduced, and experimental evidence indicating a
connection between sensitivity, decoding complexity and performance is
provided. Simulations in a quasi-static Rayleigh fading channel show that
our dense quaternionic constructions outperform both the earlier rectangular lattices and the rotated ABBA lattice as well as the DAST
lattice. We also show that our quaternionic lattice is better than the
DAST lattice in terms of the diversity-multiplexing gain tradeoff.

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BibTeX entry:

@ARTICLE{jHoLaLu08a,
  title = {Maximal Orders in the Design of Dense Space-Time Lattice Codes},
  author = {Hollanti, Camilla and Lahtonen, Jyrki and Lu, Hsiao-feng (Francis)},
  journal = {IEEE Transactions on Information Theory},
  volume = {54},
  number = {10},
  year = {2008},
}

Belongs to TUCS Research Unit(s): FUNDIM, Fundamentals of Computing and Discrete Mathematics

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