19,485 research outputs found
A kepstrum approach to filtering, smoothing and prediction
The kepstrum (or complex cepstrum) method is revisited and applied to the problem of spectral factorization
where the spectrum is directly estimated from observations. The solution to this problem in turn leads to a new
approach to optimal filtering, smoothing and prediction using the Wiener theory. Unlike previous approaches to
adaptive and self-tuning filtering, the technique, when implemented, does not require a priori information on the
type or order of the signal generating model. And unlike other approaches - with the exception of spectral
subtraction - no state-space or polynomial model is necessary. In this first paper results are restricted to
stationary signal and additive white noise
The velocity distribution of nearby stars from Hipparcos data I. The significance of the moving groups
We present a three-dimensional reconstruction of the velocity distribution of
nearby stars (<~ 100 pc) using a maximum likelihood density estimation
technique applied to the two-dimensional tangential velocities of stars. The
underlying distribution is modeled as a mixture of Gaussian components. The
algorithm reconstructs the error-deconvolved distribution function, even when
the individual stars have unique error and missing-data properties. We apply
this technique to the tangential velocity measurements from a kinematically
unbiased sample of 11,865 main sequence stars observed by the Hipparcos
satellite. We explore various methods for validating the complexity of the
resulting velocity distribution function, including criteria based on Bayesian
model selection and how accurately our reconstruction predicts the radial
velocities of a sample of stars from the Geneva-Copenhagen survey (GCS). Using
this very conservative external validation test based on the GCS, we find that
there is little evidence for structure in the distribution function beyond the
moving groups established prior to the Hipparcos mission. This is in sharp
contrast with internal tests performed here and in previous analyses, which
point consistently to maximal structure in the velocity distribution. We
quantify the information content of the radial velocity measurements and find
that the mean amount of new information gained from a radial velocity
measurement of a single star is significant. This argues for complementary
radial velocity surveys to upcoming astrometric surveys
A mean field method with correlations determined by linear response
We introduce a new mean-field approximation based on the reconciliation of
maximum entropy and linear response for correlations in the cluster variation
method. Within a general formalism that includes previous mean-field methods,
we derive formulas improving upon, e.g., the Bethe approximation and the
Sessak-Monasson result at high temperature. Applying the method to direct and
inverse Ising problems, we find improvements over standard implementations.Comment: 15 pages, 8 figures, 9 appendices, significant expansion on versions
v1 and v
On the Fundamental Limits of Random Non-orthogonal Multiple Access in Cellular Massive IoT
Machine-to-machine (M2M) constitutes the communication paradigm at the basis
of Internet of Things (IoT) vision. M2M solutions allow billions of multi-role
devices to communicate with each other or with the underlying data transport
infrastructure without, or with minimal, human intervention. Current solutions
for wireless transmissions originally designed for human-based applications
thus require a substantial shift to cope with the capacity issues in managing a
huge amount of M2M devices. In this paper, we consider the multiple access
techniques as promising solutions to support a large number of devices in
cellular systems with limited radio resources. We focus on non-orthogonal
multiple access (NOMA) where, with the aim to increase the channel efficiency,
the devices share the same radio resources for their data transmission. This
has been shown to provide optimal throughput from an information theoretic
point of view.We consider a realistic system model and characterise the system
performance in terms of throughput and energy efficiency in a NOMA scenario
with a random packet arrival model, where we also derive the stability
condition for the system to guarantee the performance.Comment: To appear in IEEE JSAC Special Issue on Non-Orthogonal Multiple
Access for 5G System
Inference in particle tracking experiments by passing messages between images
Methods to extract information from the tracking of mobile objects/particles
have broad interest in biological and physical sciences. Techniques based on
simple criteria of proximity in time-consecutive snapshots are useful to
identify the trajectories of the particles. However, they become problematic as
the motility and/or the density of the particles increases due to uncertainties
on the trajectories that particles followed during the images' acquisition
time. Here, we report an efficient method for learning parameters of the
dynamics of the particles from their positions in time-consecutive images. Our
algorithm belongs to the class of message-passing algorithms, known in computer
science, information theory and statistical physics as Belief Propagation (BP).
The algorithm is distributed, thus allowing parallel implementation suitable
for computations on multiple machines without significant inter-machine
overhead. We test our method on the model example of particle tracking in
turbulent flows, which is particularly challenging due to the strong transport
that those flows produce. Our numerical experiments show that the BP algorithm
compares in quality with exact Markov Chain Monte-Carlo algorithms, yet BP is
far superior in speed. We also suggest and analyze a random-distance model that
provides theoretical justification for BP accuracy. Methods developed here
systematically formulate the problem of particle tracking and provide fast and
reliable tools for its extensive range of applications.Comment: 18 pages, 9 figure
Throughput-based Design for Polar Coded-Modulation
Typically, forward error correction (FEC) codes are designed based on the
minimization of the error rate for a given code rate. However, for applications
that incorporate hybrid automatic repeat request (HARQ) protocol and adaptive
modulation and coding, the throughput is a more important performance metric
than the error rate. Polar codes, a new class of FEC codes with simple rate
matching, can be optimized efficiently for maximization of the throughput. In
this paper, we aim to design HARQ schemes using multilevel polar
coded-modulation (MLPCM). Thus, we first develop a method to determine a
set-partitioning based bit-to-symbol mapping for high order QAM constellations.
We simplify the LLR estimation of set-partitioned QAM constellations for a
multistage decoder, and we introduce a set of algorithms to design
throughput-maximizing MLPCM for the successive cancellation decoding (SCD).
These codes are specifically useful for non-combining (NC) and Chase-combining
(CC) HARQ protocols. Furthermore, since optimized codes for SCD are not optimal
for SC list decoders (SCLD), we propose a rate matching algorithm to find the
best rate for SCLD while using the polar codes optimized for SCD. The resulting
codes provide throughput close to the capacity with low decoding complexity
when used with NC or CC HARQ
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