8,544 research outputs found
Error Rates of the Maximum-Likelihood Detector for Arbitrary Constellations: Convex/Concave Behavior and Applications
Motivated by a recent surge of interest in convex optimization techniques,
convexity/concavity properties of error rates of the maximum likelihood
detector operating in the AWGN channel are studied and extended to
frequency-flat slow-fading channels. Generic conditions are identified under
which the symbol error rate (SER) is convex/concave for arbitrary
multi-dimensional constellations. In particular, the SER is convex in SNR for
any one- and two-dimensional constellation, and also in higher dimensions at
high SNR. Pairwise error probability and bit error rate are shown to be convex
at high SNR, for arbitrary constellations and bit mapping. Universal bounds for
the SER 1st and 2nd derivatives are obtained, which hold for arbitrary
constellations and are tight for some of them. Applications of the results are
discussed, which include optimum power allocation in spatial multiplexing
systems, optimum power/time sharing to decrease or increase (jamming problem)
error rate, an implication for fading channels ("fading is never good in low
dimensions") and optimization of a unitary-precoded OFDM system. For example,
the error rate bounds of a unitary-precoded OFDM system with QPSK modulation,
which reveal the best and worst precoding, are extended to arbitrary
constellations, which may also include coding. The reported results also apply
to the interference channel under Gaussian approximation, to the bit error rate
when it can be expressed or approximated as a non-negative linear combination
of individual symbol error rates, and to coded systems.Comment: accepted by IEEE IT Transaction
Symbol Error Rates of Maximum-Likelihood Detector: Convex/Concave Behavior and Applications
Convexity/concavity properties of symbol error rates (SER) of the maximum
likelihood detector operating in the AWGN channel (non-fading and fading) are
studied. Generic conditions are identified under which the SER is a
convex/concave function of the SNR. Universal bounds for the SER 1st and 2nd
derivatives are obtained, which hold for arbitrary constellations and are tight
for some of them. Applications of the results are discussed, which include
optimum power allocation in spatial multiplexing systems, optimum power/time
sharing to decrease or increase (jamming problem) error rate, and implication
for fading channels.Comment: To appear in 2007 IEEE International Symposium on Information Theory
(ISIT 2007), Nice, June 200
A Framework for Globally Optimizing Mixed-Integer Signomial Programs
Mixed-integer signomial optimization problems have broad applicability in engineering. Extending the Global Mixed-Integer Quadratic Optimizer, GloMIQO (Misener, Floudas in J. Glob. Optim., 2012. doi:10.1007/s10898-012-9874-7), this manuscript documents a computational framework for deterministically addressing mixed-integer signomial optimization problems to ε-global optimality. This framework generalizes the GloMIQO strategies of (1) reformulating user input, (2) detecting special mathematical structure, and (3) globally optimizing the mixed-integer nonconvex program. Novel contributions of this paper include: flattening an expression tree towards term-based data structures; introducing additional nonconvex terms to interlink expressions; integrating a dynamic implementation of the reformulation-linearization technique into the branch-and-cut tree; designing term-based underestimators that specialize relaxation strategies according to variable bounds in the current tree node. Computational results are presented along with comparison of the computational framework to several state-of-the-art solvers. © 2013 Springer Science+Business Media New York
Probing quantum state space: does one have to learn everything to learn something?
Determining the state of a quantum system is a consuming procedure. For this
reason, whenever one is interested only in some particular property of a state,
it would be desirable to design a measurement setup that reveals this property
with as little effort as possible. Here we investigate whether, in order to
successfully complete a given task of this kind, one needs an informationally
complete measurement, or if something less demanding would suffice. The first
alternative means that in order to complete the task, one needs a measurement
which fully determines the state. We formulate the task as a membership problem
related to a partitioning of the quantum state space and, in doing so, connect
it to the geometry of the state space. For a general membership problem we
prove various sufficient criteria that force informational completeness, and we
explicitly treat several physically relevant examples. For the specific cases
that do not require informational completeness, we also determine bounds on the
minimal number of measurement outcomes needed to ensure success in the task.Comment: 23 pages, 4 figure
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