10,313 research outputs found
Colored-Gaussian Multiple Descriptions: Spectral and Time-Domain Forms
It is well known that Shannon's rate-distortion function (RDF) in the colored
quadratic Gaussian (QG) case can be parametrized via a single Lagrangian
variable (the "water level" in the reverse water filling solution). In this
work, we show that the symmetric colored QG multiple-description (MD) RDF in
the case of two descriptions can be parametrized in the spectral domain via two
Lagrangian variables, which control the trade-off between the side distortion,
the central distortion, and the coding rate. This spectral-domain analysis is
complemented by a time-domain scheme-design approach: we show that the
symmetric colored QG MD RDF can be achieved by combining ideas of delta-sigma
modulation and differential pulse-code modulation. Specifically, two source
prediction loops, one for each description, are embedded within a common noise
shaping loop, whose parameters are explicitly found from the spectral-domain
characterization.Comment: Accepted for publications in the IEEE Transactions on Information
Theory. Title have been shortened, abstract clarified, and paper
significantly restructure
Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources
We improve the existing achievable rate regions for causal and for zero-delay
source coding of stationary Gaussian sources under an average mean squared
error (MSE) distortion measure. To begin with, we find a closed-form expression
for the information-theoretic causal rate-distortion function (RDF) under such
distortion measure, denoted by , for first-order Gauss-Markov
processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically
attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that,
for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq
Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze
for arbitrary zero-mean Gaussian stationary sources, we
introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the
reconstruction error is jointly stationary with the source. Based upon
\bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate
loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two
of these bounds are strictly smaller than 0.5 bits/sample at all rates. These
bounds differ from one another in their tightness and ease of evaluation; the
tighter the bound, the more involved its evaluation. We then show that, for any
source spectral density and any positive distortion D\leq \sigma_{x}^{2},
\bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set
of causal pre-, post-, and feedback filters. We show that finding such filters
constitutes a convex optimization problem. In order to solve the latter, we
propose an iterative optimization procedure that yields the optimal filters and
is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a
connection to feedback quantization we design a causal and a zero-delay coding
scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor
One-shot lossy quantum data compression
We provide a framework for one-shot quantum rate distortion coding, in which
the goal is to determine the minimum number of qubits required to compress
quantum information as a function of the probability that the distortion
incurred upon decompression exceeds some specified level. We obtain a one-shot
characterization of the minimum qubit compression size for an
entanglement-assisted quantum rate-distortion code in terms of the smooth
max-information, a quantity previously employed in the one-shot quantum reverse
Shannon theorem. Next, we show how this characterization converges to the known
expression for the entanglement-assisted quantum rate distortion function for
asymptotically many copies of a memoryless quantum information source. Finally,
we give a tight, finite blocklength characterization for the
entanglement-assisted minimum qubit compression size of a memoryless isotropic
qubit source subject to an average symbol-wise distortion constraint.Comment: 36 page
CMB at 2x2 order: the dissipation of primordial acoustic waves and the observable part of the associated energy release
Silk damping of primordial small-scale perturbations in the photon-baryon
fluid due to diffusion of photons inevitably creates spectral distortions in
the CMB. With the proposed CMB experiment PIXIE it might become possible to
measure these distortions and thereby constrain the primordial power spectrum
at comoving wavenumbers 50 Mpc^{-1} < k < 10^4 Mpc^{-1}. Since primordial
fluctuations in the CMB on these scales are completely erased by Silk damping,
these distortions may provide the only way to shed light on otherwise
unobservable aspects of inflationary physics. A consistent treatment of the
primordial dissipation problem requires going to second order in perturbation
theory, while thermalization of these distortions necessitates consideration of
second order in Compton scattering energy transfer. Here we give a full 2x2
treatment for the creation and evolution of spectral distortions due to the
acoustic dissipation process, consistently including the effect of polarization
and photon mixing in the free streaming regime. We show that 1/3 of the total
energy (9/4 larger than previous estimates) stored in small-scale temperature
perturbations imprints observable spectral distortions, while the remaining 2/3
only raises the average CMB temperature, an effect that is unobservable. At
high redshift dissipation is mainly mediated through the quadrupole
anisotropies, while after recombination peculiar motions are most important.
During recombination the damping of the higher multipoles is also significant.
We compute the average distortion for several examples using CosmoTherm,
analyzing their dependence on parameters of the primordial power spectrum. For
one of the best fit WMAP7 cosmologies, with n_S=1.027 and n_run=-0.034, the
cooling of baryonic matter practically compensates the heating from acoustic
dissipation in the mu-era. (abridged)Comment: 40 pages, 17 figures, accepted by MNRA
Centroid-Based Clustering with ab-Divergences
Centroid-based clustering is a widely used technique within unsupervised learning
algorithms in many research fields. The success of any centroid-based clustering relies on the
choice of the similarity measure under use. In recent years, most studies focused on including several
divergence measures in the traditional hard k-means algorithm. In this article, we consider the
problem of centroid-based clustering using the family of ab-divergences, which is governed by two
parameters, a and b. We propose a new iterative algorithm, ab-k-means, giving closed-form solutions
for the computation of the sided centroids. The algorithm can be fine-tuned by means of this pair of
values, yielding a wide range of the most frequently used divergences. Moreover, it is guaranteed to
converge to local minima for a wide range of values of the pair (a, b). Our theoretical contribution
has been validated by several experiments performed with synthetic and real data and exploring the
(a, b) plane. The numerical results obtained confirm the quality of the algorithm and its suitability to
be used in several practical applications.MINECO TEC2017-82807-
Optimal Kullback-Leibler Aggregation via Information Bottleneck
In this paper, we present a method for reducing a regular, discrete-time
Markov chain (DTMC) to another DTMC with a given, typically much smaller number
of states. The cost of reduction is defined as the Kullback-Leibler divergence
rate between a projection of the original process through a partition function
and a DTMC on the correspondingly partitioned state space. Finding the reduced
model with minimal cost is computationally expensive, as it requires an
exhaustive search among all state space partitions, and an exact evaluation of
the reduction cost for each candidate partition. Our approach deals with the
latter problem by minimizing an upper bound on the reduction cost instead of
minimizing the exact cost; The proposed upper bound is easy to compute and it
is tight if the original chain is lumpable with respect to the partition. Then,
we express the problem in the form of information bottleneck optimization, and
propose using the agglomerative information bottleneck algorithm for searching
a sub-optimal partition greedily, rather than exhaustively. The theory is
illustrated with examples and one application scenario in the context of
modeling bio-molecular interactions.Comment: 13 pages, 4 figure
- …