5 research outputs found
Division algebra codes achieve MIMO block fading channel capacity within a constant gap
This work addresses the question of achieving capacity with lattice codes in
multi-antenna block fading channels when the number of fading blocks tends to
infinity. In contrast to the standard approach in the literature which employs
random lattice ensembles, the existence results in this paper are derived from
number theory. It is shown that a multiblock construction based on division
algebras achieves rates within a constant gap from block fading capacity both
under maximum likelihood decoding and naive lattice decoding. First the gap to
capacity is shown to depend on the discriminant of the chosen division algebra;
then class field theory is applied to build families of algebras with small
discriminants. The key element in the construction is the choice of a sequence
of division algebras whose centers are number fields with small root
discriminants.Comment: Submitted to ISIT 201
Fast-Decodable Asymmetric Space-Time Codes from Division Algebras
Multiple-input double-output (MIDO) codes are important in the near-future
wireless communications, where the portable end-user device is physically small
and will typically contain at most two receive antennas. Especially tempting is
the 4 x 2 channel due to its immediate applicability in the digital video
broadcasting (DVB). Such channels optimally employ rate-two space-time (ST)
codes consisting of (4 x 4) matrices. Unfortunately, such codes are in general
very complex to decode, hence setting forth a call for constructions with
reduced complexity.
Recently, some reduced complexity constructions have been proposed, but they
have mainly been based on different ad hoc methods and have resulted in
isolated examples rather than in a more general class of codes. In this paper,
it will be shown that a family of division algebra based MIDO codes will always
result in at least 37.5% worst-case complexity reduction, while maintaining
full diversity and, for the first time, the non-vanishing determinant (NVD)
property. The reduction follows from the fact that, similarly to the Alamouti
code, the codes will be subsets of matrix rings of the Hamiltonian quaternions,
hence allowing simplified decoding. At the moment, such reductions are among
the best known for rate-two MIDO codes. Several explicit constructions are
presented and shown to have excellent performance through computer simulations.Comment: 26 pages, 1 figure, submitted to IEEE Trans. Inf. Theory, October
201