12,081 research outputs found
Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff
A recent result of Zheng and Tse states that over a quasi-static channel,
there exists a fundamental tradeoff, referred to as the diversity-multiplexing
gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity
gain that can be simultaneously achieved by a space-time (ST) block code. This
tradeoff is precisely known in the case of i.i.d. Rayleigh-fading, for T>=
n_t+n_r-1 where T is the number of time slots over which coding takes place and
n_t,n_r are the number of transmit and receive antennas respectively. For T <
n_t+n_r-1, only upper and lower bounds on the D-MG tradeoff are available.
In this paper, we present a complete solution to the problem of explicitly
constructing D-MG optimal ST codes, i.e., codes that achieve the D-MG tradeoff
for any number of receive antennas. We do this by showing that for the square
minimum-delay case when T=n_t=n, cyclic-division-algebra (CDA) based ST codes
having the non-vanishing determinant property are D-MG optimal. While
constructions of such codes were previously known for restricted values of n,
we provide here a construction for such codes that is valid for all n.
For the rectangular, T > n_t case, we present two general techniques for
building D-MG-optimal rectangular ST codes from their square counterparts. A
byproduct of our results establishes that the D-MG tradeoff for all T>= n_t is
the same as that previously known to hold for T >= n_t + n_r -1.Comment: Revised submission to IEEE Transactions on Information Theor
Generalized Color Codes Supporting Non-Abelian Anyons
We propose a generalization of the color codes based on finite groups .
For non-abelian groups, the resulting model supports non-abelian anyonic
quasiparticles and topological order. We examine the properties of these models
such as their relationship to Kitaev quantum double models, quasiparticle
spectrum, and boundary structure.Comment: 17 pages, 8 figures; references added, typos remove
Low ML-Decoding Complexity, Large Coding Gain, Full-Rate, Full-Diversity STBCs for 2 X 2 and 4 X 2 MIMO Systems
This paper (Part of the content of this manuscript has been accepted for
presentation in IEEE Globecom 2008, to be held in New Orleans) deals with low
maximum likelihood (ML) decoding complexity, full-rate and full-diversity
space-time block codes (STBCs), which also offer large coding gain, for the 2
transmit antenna, 2 receive antenna () and the 4 transmit antenna, 2
receive antenna () MIMO systems. Presently, the best known STBC for
the system is the Golden code and that for the system is
the DjABBA code. Following the approach by Biglieri, Hong and Viterbo, a new
STBC is presented in this paper for the system. This code matches
the Golden code in performance and ML-decoding complexity for square QAM
constellations while it has lower ML-decoding complexity with the same
performance for non-rectangular QAM constellations. This code is also shown to
be \emph{information-lossless} and \emph{diversity-multiplexing gain} (DMG)
tradeoff optimal. This design procedure is then extended to the
system and a code, which outperforms the DjABBA code for QAM constellations
with lower ML-decoding complexity, is presented. So far, the Golden code has
been reported to have an ML-decoding complexity of the order of for
square QAM of size . In this paper, a scheme that reduces its ML-decoding
complexity to is presented.Comment: 28 pages, 5 figures, 3 tables, submitted to IEEE Journal of Selected
Topics in Signal Processin
Rectangular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion
We describe a new data format for storing triangular, symmetric, and
Hermitian matrices called RFPF (Rectangular Full Packed Format). The standard
two dimensional arrays of Fortran and C (also known as full format) that are
used to represent triangular and symmetric matrices waste nearly half of the
storage space but provide high performance via the use of Level 3 BLAS.
Standard packed format arrays fully utilize storage (array space) but provide
low performance as there is no Level 3 packed BLAS. We combine the good
features of packed and full storage using RFPF to obtain high performance via
using Level 3 BLAS as RFPF is a standard full format representation. Also, RFPF
requires exactly the same minimal storage as packed format. Each LAPACK full
and/or packed triangular, symmetric, and Hermitian routine becomes a single new
RFPF routine based on eight possible data layouts of RFPF. This new RFPF
routine usually consists of two calls to the corresponding LAPACK full format
routine and two calls to Level 3 BLAS routines. This means {\it no} new
software is required. As examples, we present LAPACK routines for Cholesky
factorization, Cholesky solution and Cholesky inverse computation in RFPF to
illustrate this new work and to describe its performance on several commonly
used computer platforms. Performance of LAPACK full routines using RFPF versus
LAPACK full routines using standard format for both serial and SMP parallel
processing is about the same while using half the storage. Performance gains
are roughly one to a factor of 43 for serial and one to a factor of 97 for SMP
parallel times faster using vendor LAPACK full routines with RFPF than with
using vendor and/or reference packed routines
CD-independent subsets in meet-distributive lattices
A subset of a finite lattice is CD-independent if the meet of any two
incomparable elements of equals 0. In 2009, Cz\'edli, Hartmann and Schmidt
proved that any two maximal CD-independent subsets of a finite distributive
lattice have the same number of elements. In this paper, we prove that if
is a finite meet-distributive lattice, then the size of every CD-independent
subset of is at most the number of atoms of plus the length of . If,
in addition, there is no three-element antichain of meet-irreducible elements,
then we give a recursive description of maximal CD-independent subsets.
Finally, to give an application of CD-independent subsets, we give a new
approach to count islands on a rectangular board.Comment: 14 pages, 4 figure
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