85 research outputs found
On the capacity of Lagrangians in the cotangent disc bundle of the torus
18pagesThis paper was withdrawn due to a critical error. For recent results in this direction, see Shelukhin's papers on the subject https://arxiv.org/abs/1904.06798 , https://arxiv.org/abs/1811.05552 and BIran-Cornea https://arxiv.org/abs/2008.04756--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Former abstract: We prove that a Lagrangian torus in Hamiltonianly isotopic to the zero section and contained in the unit disc bundle has bounded -capacity, where is the norm on Lagrangian submanifold. On one hand this gives new obstructions to Lagrangian embeddings of a quantitative kind. On the other hand, it gives a certain control on the topology in terms f the Hausdorff topology. Finally this result is a crucial ingredient in establishing symplectic homogenization theory
Golden Space-Time Trellis Coded Modulation
In this paper, we present a concatenated coding scheme for a high rate
multiple-input multiple-output (MIMO) system over slow fading
channels. The inner code is the Golden code \cite{Golden05} and the outer code
is a trellis code. Set partitioning of the Golden code is designed specifically
to increase the minimum determinant. The branches of the outer trellis code are
labeled with these partitions. Viterbi algorithm is applied for trellis
decoding. In order to compute the branch metrics a lattice sphere decoder is
used. The general framework for code optimization is given. The performance of
the proposed concatenated scheme is evaluated by simulation. It is shown that
the proposed scheme achieves significant performance gains over uncoded Golden
code.Comment: 33 pages, 13 figure
Cyclic division algebras: a tool for space-time coding
Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requires that the difference of any two distinct codewords has full rank.
Extensive work has been done on Space–Time coding, aiming at
finding fully diverse codes with high rate. Division algebras have been proposed as a new tool for constructing Space–Time codes, since they are non-commutative algebras that naturally yield linear fully diverse codes. Their algebraic properties can thus be further exploited to
improve the design of good codes.
The aim of this work is to provide a tutorial introduction to the algebraic tools involved in the design of codes based on cyclic division algebras. The different design criteria involved will be illustrated, including the constellation shaping, the information lossless property, the non-vanishing determinant property, and the diversity multiplexing trade-off. The final target is to give the complete mathematical background underlying the construction of the Golden code and the other Perfect Space–Time block codes
Estimates of Characteristic numbers of real algebraic varieties
International audienceWe give some explicit bounds for the number of cobordism classes of real algebraic manifolds of real degree less than , and for the size of the sum of Betti numbers for the real form of complex manifolds of complex degree less than
On the topology of fillings of contact manifolds and applications.
32 pages, one figure, one tableInternational audienceThe aim of this paper is to address the following question: given a contact manifold , what can be said about the aspherical symplectic manifolds bounded by ? We first extend a theorem of Eliashberg, Floer and McDuff to prove that under suitable assumptions the map from to induced by inclusion is surjective. We then apply this method in the case of contact manifolds having a contact embedding in or in a subcritical Stein manifold. We prove in many cases that the homology of the fillings is uniquely determined. Finally we use more recent methods of symplectic topology to prove that, if a contact hypersurface has a Stein subcritical filling, then all its weakly subcritical fillings have the same homology. A number of applications are given, from obstructions to the existence of Lagrangian or contact embeddings, to the exotic nature of some contact structures
Perfect Space–Time Block Codes
In this paper, we introduce the notion of perfect space–time block codes (STBCs). These codes have full-rate, full-diversity, nonvanishing constant minimum determinant for increasing spectral efficiency, uniform average transmitted energy per antenna and good shaping. We present algebraic constructions of perfect STBCs for 2, 3, 4, and 6 antennas
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