359 research outputs found
Multiple Description Quantization via Gram-Schmidt Orthogonalization
The multiple description (MD) problem has received considerable attention as
a model of information transmission over unreliable channels. A general
framework for designing efficient multiple description quantization schemes is
proposed in this paper. We provide a systematic treatment of the El Gamal-Cover
(EGC) achievable MD rate-distortion region, and show that any point in the EGC
region can be achieved via a successive quantization scheme along with
quantization splitting. For the quadratic Gaussian case, the proposed scheme
has an intrinsic connection with the Gram-Schmidt orthogonalization, which
implies that the whole Gaussian MD rate-distortion region is achievable with a
sequential dithered lattice-based quantization scheme as the dimension of the
(optimal) lattice quantizers becomes large. Moreover, this scheme is shown to
be universal for all i.i.d. smooth sources with performance no worse than that
for an i.i.d. Gaussian source with the same variance and asymptotically optimal
at high resolution. A class of low-complexity MD scalar quantizers in the
proposed general framework also is constructed and is illustrated
geometrically; the performance is analyzed in the high resolution regime, which
exhibits a noticeable improvement over the existing MD scalar quantization
schemes.Comment: 48 pages; submitted to IEEE Transactions on Information Theor
Gabor analysis over finite Abelian groups
The topic of this paper are (multi-window) Gabor frames for signals over
finite Abelian groups, generated by an arbitrary lattice within the finite
time-frequency plane. Our generic approach covers simultaneously
multi-dimensional signals as well as non-separable lattices. The main results
reduce to well-known fundamental facts about Gabor expansions of finite signals
for the case of product lattices, as they have been given by Qiu, Wexler-Raz or
Tolimieri-Orr, Bastiaans and Van-Leest, among others. In our presentation a
central role is given to spreading function of linear operators between
finite-dimensional Hilbert spaces. Another relevant tool is a symplectic
version of Poisson's summation formula over the finite time-frequency plane. It
provides the Fundamental Identity of Gabor Analysis.In addition we highlight
projective representations of the time-frequency plane and its subgroups and
explain the natural connection to twisted group algebras. In the
finite-dimensional setting these twisted group algebras are just matrix
algebras and their structure provides the algebraic framework for the study of
the deeper properties of finite-dimensional Gabor frames.Comment: Revised version: two new sections added, many typos fixe
Electronic energies from coupled fermionic "Zombie" states' imaginary time evolution
Zombie states are a recently introduced formalism to describe coupled coherent fermionic states that address the fermionic sign problem in a computationally tractable manner. Previously, it has been shown that Zombie states with fractional occupations of spin orbitals obeyed the correct fermionic creation and annihilation algebra and presented results for real-time evolution [D. V. Shalashilin, J. Chem. Phys. 148, 194109 (2018)]. In this work, we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie states and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie states, that allows much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" that removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure. The proposed algorithm of imaginary time propagation on biased random grids of Zombie states may present an alternative to the existing quantum Monte Carlo methods
Optimal Space Station solar array gimbal angle determination via radial basis function neural networks
The potential for excessive plume impingement loads on Space Station Freedom solar arrays, caused by jet firings from an approaching Space Shuttle, is addressed. An artificial neural network is designed to determine commanded solar array beta gimbal angle for minimum plume loads. The commanded angle would be determined dynamically. The network design proposed involves radial basis functions as activation functions. Design, development, and simulation of this network design are discussed
Sparse Linear Representation
This paper studies the question of how well a signal can be reprsented by a
sparse linear combination of reference signals from an overcomplete dictionary.
When the dictionary size is exponential in the dimension of signal, then the
exact characterization of the optimal distortion is given as a function of the
dictionary size exponent and the number of reference signals for the linear
representation. Roughly speaking, every signal is sparse if the dictionary size
is exponentially large, no matter how small the exponent is. Furthermore, an
iterative method similar to matching pursuit that successively finds the best
reference signal at each stage gives asymptotically optimal representations.
This method is essentially equivalent to successive refinement for multiple
descriptions and provides a simple alternative proof of the successive
refinability of white Gaussian sources.Comment: 5 pages, to appear in proc. IEEE ISIT, June 200
Multi-user linear equalizer and precoder scheme for hybrid sub-connected wideband systems
Millimeter waves and massive multiple-input multiple output (MIMO) are two promising
key technologies to achieve the high demands of data rate for the future mobile communication
generation. Due to hardware limitations, these systems employ hybrid analog–digital architectures.
Nonetheless, most of the works developed for hybrid architectures focus on narrowband channels,
and it is expected that millimeter waves be wideband. Moreover, it is more feasible to have a
sub-connected architecture than a fully connected one, due to the hardware constraints. Therefore,
the aim of this paper is to design a sub-connected hybrid analog–digital multi-user linear equalizer
combined with an analog precoder to efficiently remove the multi-user interference. We consider
low complexity user terminals employing pure analog precoders, computed with the knowledge
of a quantized version of the average angles of departure of each cluster. At the base station,
the hybrid multi-user linear equalizer is optimized by using the bit-error-rate (BER) as a metric over
all the subcarriers. The analog domain hardware constraints, together with the assumption of a flat
analog equalizer over the subcarriers, considerably increase the complexity of the corresponding
optimization problem. To simplify the problem at hand, the merit function is first upper bounded,
and by leveraging the specific properties of the resulting problem, we show that the analog equalizer
may be computed iteratively over the radio frequency (RF) chains by assigning the users in an
interleaved fashion to the RF chains. The proposed hybrid sub-connected scheme is compared with a
fully connected counterpart.publishe
Multiple-Description Coding by Dithered Delta-Sigma Quantization
We address the connection between the multiple-description (MD) problem and
Delta-Sigma quantization. The inherent redundancy due to oversampling in
Delta-Sigma quantization, and the simple linear-additive noise model resulting
from dithered lattice quantization, allow us to construct a symmetric and
time-invariant MD coding scheme. We show that the use of a noise shaping filter
makes it possible to trade off central distortion for side distortion.
Asymptotically as the dimension of the lattice vector quantizer and order of
the noise shaping filter approach infinity, the entropy rate of the dithered
Delta-Sigma quantization scheme approaches the symmetric two-channel MD
rate-distortion function for a memoryless Gaussian source and MSE fidelity
criterion, at any side-to-central distortion ratio and any resolution. In the
optimal scheme, the infinite-order noise shaping filter must be minimum phase
and have a piece-wise flat power spectrum with a single jump discontinuity. An
important advantage of the proposed design is that it is symmetric in rate and
distortion by construction, so the coding rates of the descriptions are
identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has
been fixed. Accepted for publication in the IEEE Transactions on Information
Theor
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