108,817 research outputs found
Adapting the interior point method for the solution of LPs on serial, coarse grain parallel and massively parallel computers
In this paper we describe a unified scheme for implementing an interior point algorithm (IPM) over a range of computer architectures. In the inner iteration of the IPM a search direction is computed using Newton's method. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system, and the design of data structures to take advantage of serial, coarse grain parallel and massively parallel computer architectures, are considered in detail. We put forward arguments as to why integration of the system within a sparse simplex solver is important and outline how the system is designed to achieve this integration
A Belief Propagation Based Framework for Soft Multiple-Symbol Differential Detection
Soft noncoherent detection, which relies on calculating the \textit{a
posteriori} probabilities (APPs) of the bits transmitted with no channel
estimation, is imperative for achieving excellent detection performance in
high-dimensional wireless communications. In this paper, a high-performance
belief propagation (BP)-based soft multiple-symbol differential detection
(MSDD) framework, dubbed BP-MSDD, is proposed with its illustrative application
in differential space-time block-code (DSTBC)-aided ultra-wideband impulse
radio (UWB-IR) systems. Firstly, we revisit the signal sampling with the aid of
a trellis structure and decompose the trellis into multiple subtrellises.
Furthermore, we derive an APP calculation algorithm, in which the
forward-and-backward message passing mechanism of BP operates on the
subtrellises. The proposed BP-MSDD is capable of significantly outperforming
the conventional hard-decision MSDDs. However, the computational complexity of
the BP-MSDD increases exponentially with the number of MSDD trellis states. To
circumvent this excessive complexity for practical implementations, we
reformulate the BP-MSDD, and additionally propose a Viterbi algorithm
(VA)-based hard-decision MSDD (VA-HMSDD) and a VA-based soft-decision MSDD
(VA-SMSDD). Moreover, both the proposed BP-MSDD and VA-SMSDD can be exploited
in conjunction with soft channel decoding to obtain powerful iterative
detection and decoding based receivers. Simulation results demonstrate the
effectiveness of the proposed algorithms in DSTBC-aided UWB-IR systems.Comment: 14 pages, 12 figures, 3 tables, accepted to appear on IEEE
Transactions on Wireless Communications, Aug. 201
A conjugate gradient algorithm for the astrometric core solution of Gaia
The ESA space astrometry mission Gaia, planned to be launched in 2013, has
been designed to make angular measurements on a global scale with
micro-arcsecond accuracy. A key component of the data processing for Gaia is
the astrometric core solution, which must implement an efficient and accurate
numerical algorithm to solve the resulting, extremely large least-squares
problem. The Astrometric Global Iterative Solution (AGIS) is a framework that
allows to implement a range of different iterative solution schemes suitable
for a scanning astrometric satellite. In order to find a computationally
efficient and numerically accurate iteration scheme for the astrometric
solution, compatible with the AGIS framework, we study an adaptation of the
classical conjugate gradient (CG) algorithm, and compare it to the so-called
simple iteration (SI) scheme that was previously known to converge for this
problem, although very slowly. The different schemes are implemented within a
software test bed for AGIS known as AGISLab, which allows to define, simulate
and study scaled astrometric core solutions. After successful testing in
AGISLab, the CG scheme has been implemented also in AGIS. The two algorithms CG
and SI eventually converge to identical solutions, to within the numerical
noise (of the order of 0.00001 micro-arcsec). These solutions are independent
of the starting values (initial star catalogue), and we conclude that they are
equivalent to a rigorous least-squares estimation of the astrometric
parameters. The CG scheme converges up to a factor four faster than SI in the
tested cases, and in particular spatially correlated truncation errors are much
more efficiently damped out with the CG scheme.Comment: 24 pages, 16 figures. Accepted for publication in Astronomy &
Astrophysic
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