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

Camilla Hollanti, Jyrki Lahtonen, Maximal Orders in the Design of Dense Space-Time Lattice Codes. TUCS Technical Reports 790, Turku Centre for Computer Science, 2006.

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 defect is introduced for the first time and shown to be relevant both in theory and practice. 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.

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BibTeX entry:

@TECHREPORT{tHoLa06a,
  title = {Maximal Orders in the Design of Dense Space-Time Lattice Codes},
  author = {Hollanti, Camilla and Lahtonen, Jyrki},
  number = {790},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2006},
  keywords = {Cyclic division algebras, defect, dense lattices, maximal orders, multi{\-}ple-input multiple-output channels, multiple-input single-output channels, number fields, quaternions,  space-time block codes, sphere decoding},
  ISBN = {952-12-1789-8},
}

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

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