586 research outputs found
S-AMP for Non-linear Observation Models
Recently we extended Approximate message passing (AMP) algorithm to be able
to handle general invariant matrix ensembles. In this contribution we extend
our S-AMP approach to non-linear observation models. We obtain generalized AMP
(GAMP) algorithm as the special case when the measurement matrix has zero-mean
iid Gaussian entries. Our derivation is based upon 1) deriving expectation
propagation (EP) like algorithms from the stationary-points equations of the
Gibbs free energy under first- and second-moment constraints and 2) applying
additive free convolution in free probability theory to get low-complexity
updates for the second moment quantities.Comment: 6 page
Capacity Scaling in MIMO Systems with General Unitarily Invariant Random Matrices
We investigate the capacity scaling of MIMO systems with the system
dimensions. To that end, we quantify how the mutual information varies when the
number of antennas (at either the receiver or transmitter side) is altered. For
a system comprising receive and transmit antennas with , we find
the following: By removing as many receive antennas as needed to obtain a
square system (provided the channel matrices before and after the removal have
full rank) the maximum resulting loss of mutual information over all
signal-to-noise ratios (SNRs) depends only on , and the matrix of
left-singular vectors of the initial channel matrix, but not on its singular
values. In particular, if the latter matrix is Haar distributed the ergodic
rate loss is given by nats. Under
the same assumption, if with the ratio
fixed, the rate loss normalized by converges almost surely to
bits with denoting the binary entropy function. We also quantify and
study how the mutual information as a function of the system dimensions
deviates from the traditionally assumed linear growth in the minimum of the
system dimensions at high SNR.Comment: Accepted for publication in the IEEE Transactions on Information
Theor
Recommended from our members
A comparative study of the philosophies of education of John Dewey and Jacques Maritain.
Variational Bayesian Inference of Line Spectra
In this paper, we address the fundamental problem of line spectral estimation
in a Bayesian framework. We target model order and parameter estimation via
variational inference in a probabilistic model in which the frequencies are
continuous-valued, i.e., not restricted to a grid; and the coefficients are
governed by a Bernoulli-Gaussian prior model turning model order selection into
binary sequence detection. Unlike earlier works which retain only point
estimates of the frequencies, we undertake a more complete Bayesian treatment
by estimating the posterior probability density functions (pdfs) of the
frequencies and computing expectations over them. Thus, we additionally capture
and operate with the uncertainty of the frequency estimates. Aiming to maximize
the model evidence, variational optimization provides analytic approximations
of the posterior pdfs and also gives estimates of the additional parameters. We
propose an accurate representation of the pdfs of the frequencies by mixtures
of von Mises pdfs, which yields closed-form expectations. We define the
algorithm VALSE in which the estimates of the pdfs and parameters are
iteratively updated. VALSE is a gridless, convergent method, does not require
parameter tuning, can easily include prior knowledge about the frequencies and
provides approximate posterior pdfs based on which the uncertainty in line
spectral estimation can be quantified. Simulation results show that accounting
for the uncertainty of frequency estimates, rather than computing just point
estimates, significantly improves the performance. The performance of VALSE is
superior to that of state-of-the-art methods and closely approaches the
Cram\'er-Rao bound computed for the true model order.Comment: 15 pages, 8 figures, accepted for publication in IEEE Transactions on
Signal Processin
Dynamical Functional Theory for Compressed Sensing
We introduce a theoretical approach for designing generalizations of the
approximate message passing (AMP) algorithm for compressed sensing which are
valid for large observation matrices that are drawn from an invariant random
matrix ensemble. By design, the fixed points of the algorithm obey the
Thouless-Anderson-Palmer (TAP) equations corresponding to the ensemble. Using a
dynamical functional approach we are able to derive an effective stochastic
process for the marginal statistics of a single component of the dynamics. This
allows us to design memory terms in the algorithm in such a way that the
resulting fields become Gaussian random variables allowing for an explicit
analysis. The asymptotic statistics of these fields are consistent with the
replica ansatz of the compressed sensing problem.Comment: 5 pages, accepted for ISIT 201
Recommended from our members
A study of factors relevant to the development of applied educational research training programs.
Superfast Line Spectral Estimation
A number of recent works have proposed to solve the line spectral estimation
problem by applying off-the-grid extensions of sparse estimation techniques.
These methods are preferable over classical line spectral estimation algorithms
because they inherently estimate the model order. However, they all have
computation times which grow at least cubically in the problem size, thus
limiting their practical applicability in cases with large dimensions. To
alleviate this issue, we propose a low-complexity method for line spectral
estimation, which also draws on ideas from sparse estimation. Our method is
based on a Bayesian view of the problem. The signal covariance matrix is shown
to have Toeplitz structure, allowing superfast Toeplitz inversion to be used.
We demonstrate that our method achieves estimation accuracy at least as good as
current methods and that it does so while being orders of magnitudes faster.Comment: 16 pages, 7 figures, accepted for IEEE Transactions on Signal
Processin
Nitrogen isotopic fractionation during abiotic synthesis of organic solid particles
The formation of organic compounds is generally assumed to result from
abiotic processes in the Solar System, with the exception of biogenic organics
on Earth. Nitrogen-bearing organics are of particular interest, notably for
prebiotic perspectives but also for overall comprehension of organic formation
in the young solar system and in planetary atmospheres. We have investigated
abiotic synthesis of organics upon plasma discharge, with special attention to
N isotope fractionation. Organic aerosols were synthesized from N2-CH4 and
N2-CO gaseous mixtures using low-pressure plasma discharge experiments, aimed
at simulating chemistry occurring in Titan s atmosphere and in the protosolar
nebula, respectively. Nitrogen is efficiently incorporated into the synthesized
solids, independently of the oxidation degree, of the N2 content of the
starting gas mixture, and of the nitrogen speciation in the aerosols. The
aerosols are depleted in 15N by 15-25 permil relative to the initial N2 gas,
whatever the experimental setup is. Such an isotopic fractionation is
attributed to mass-dependent kinetic effect(s). Nitrogen isotope fractionation
upon electric discharge cannot account for the large N isotope variations
observed among solar system objects and reservoirs. Extreme N isotope
signatures in the solar system are more likely the result of self-shielding
during N2 photodissociation, exotic effect during photodissociation of N2
and/or low temperature ion-molecule isotope exchange. Kinetic N isotope
fractionation may play a significant role in the Titan s atmosphere. We also
suggest that the low delta15N values of Archaean organic matter are partly the
result of abiotic synthesis of organics that occurred at that time
- …