916 research outputs found
Perfect Mannheim, Lipschitz and Hurwitz weight codes
In this paper, upper bounds on codes over Gaussian integers, Lipschitz
integers and Hurwitz integers with respect to Mannheim metric, Lipschitz and
Hurwitz metric are given.Comment: 21 page
Nonuniform Fuchsian codes for noisy channels
We develop a new transmission scheme for additive white Gaussian noisy (AWGN)
channels based on Fuchsian groups from rational quaternion algebras. The
structure of the proposed Fuchsian codes is nonlinear and nonuniform, hence
conventional decoding methods based on linearity and symmetry do not apply.
Previously, only brute force decoding methods with complexity that is linear in
the code size exist for general nonuniform codes. However, the properly
discontinuous character of the action of the Fuchsian groups on the complex
upper half-plane translates into decoding complexity that is logarithmic in the
code size via a recently introduced point reduction algorithm
Representation theory for high-rate multiple-antenna code design
Multiple antennas can greatly increase the data rate and reliability of a wireless communication link in a fading environment, but the practical success of using multiple antennas depends crucially on our ability to design high-rate space-time constellations with low encoding and decoding complexity. It has been shown that full transmitter diversity, where the constellation is a set of unitary matrices whose differences have nonzero determinant, is a desirable property for good performance. We use the powerful theory of fixed-point-free groups and their representations to design high-rate constellations with full diversity. Furthermore, we thereby classify all full-diversity constellations that form a group, for all rates and numbers of transmitter antennas. The group structure makes the constellations especially suitable for differential modulation and low-complexity decoding algorithms. The classification also reveals that the number of different group structures with full diversity is very limited when the number of transmitter antennas is large and odd. We, therefore, also consider extensions of the constellation designs to nongroups. We conclude by showing that many of our designed constellations perform excellently on both simulated and real wireless channels
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