201 research outputs found
A new sufficient condition for sum-rate tightness in quadratic Gaussian multiterminal source coding
This work considers the quadratic Gaussian multiterminal (MT) source coding
problem and provides a new sufficient condition for the Berger-Tung sum-rate
bound to be tight. The converse proof utilizes a set of virtual remote sources
given which the MT sources are block independent with a maximum block size of
two. The given MT source coding problem is then related to a set of
two-terminal problems with matrix-distortion constraints, for which a new lower
bound on the sum-rate is given. Finally, a convex optimization problem is
formulated and a sufficient condition derived for the optimal BT scheme to
satisfy the subgradient based Karush-Kuhn-Tucker condition. The set of sum-rate
tightness problems defined by our new sufficient condition subsumes all
previously known tight cases, and opens new direction for a more general
partial solution
The Non-Regular CEO Problem
We consider the CEO problem for non-regular source distributions (such as
uniform or truncated Gaussian). A group of agents observe independently
corrupted versions of data and transmit coded versions over rate-limited links
to a CEO. The CEO then estimates the underlying data based on the received
coded observations. Agents are not allowed to convene before transmitting their
observations. This formulation is motivated by the practical problem of a
firm's CEO estimating (non-regular) beliefs about a sequence of events, before
acting on them. Agents' observations are modeled as jointly distributed with
the underlying data through a given conditional probability density function.
We study the asymptotic behavior of the minimum achievable mean squared error
distortion at the CEO in the limit when the number of agents and the sum
rate tend to infinity. We establish a convergence of the
distortion, an intermediate regime of performance between the exponential
behavior in discrete CEO problems [Berger, Zhang, and Viswanathan (1996)], and
the behavior in Gaussian CEO problems [Viswanathan and Berger (1997)].
Achievability is proved by a layered architecture with scalar quantization,
distributed entropy coding, and midrange estimation. The converse is proved
using the Bayesian Chazan-Zakai-Ziv bound.Comment: 18 pages, 1 figur
Distributed Source Coding of Correlated Gaussian Sources
We consider the distributed source coding system of correlated Gaussian
sources which are noisy observations of correlated Gaussian
remote sources . We assume that
is an observation of the source vector , having the form , where is a matrix and
is a vector of independent Gaussian
random variables also independent of . In this system correlated
Gaussian observations are separately compressed by encoders and sent to the
information processing center. We study the remote source coding problem where
the decoder at the center attempts to reconstruct the remote source . We
consider three distortion criteria based on the covariance matrix of the
estimation error on . For each of those three criteria we derive explicit
inner and outer bounds of the rate distortion region. Next, in the case of
and , we study the multiterminal source coding problem where the
decoder wishes to reconstruct the observation . To investigate
this problem we shall establish a result which provides a strong connection
between the remote source coding problem and the multiterminal source coding
problem. Using this result, we drive several new partial solutions to the
multiterminal source coding problem.Comment: 30 pages 4 figure
Vector Gaussian CEO Problem Under Logarithmic Loss and Applications
We study the vector Gaussian Chief Executive Officer (CEO) problem under
logarithmic loss distortion measure. Specifically, agents observe
independently corrupted Gaussian noisy versions of a remote vector Gaussian
source, and communicate independently with a decoder or CEO over
rate-constrained noise-free links. The CEO also has its own Gaussian noisy
observation of the source and wants to reconstruct the remote source to within
some prescribed distortion level where the incurred distortion is measured
under the logarithmic loss penalty criterion. We find an explicit
characterization of the rate-distortion region of this model. The result can be
seen as the counterpart to the vector Gaussian setting of that by
Courtade-Weissman which provides the rate-distortion region of the model in the
discrete memoryless setting. For the proof of this result, we obtain an outer
bound by means of a technique that relies on the de Bruijn identity and the
properties of Fisher information. The approach is similar to Ekrem-Ulukus outer
bounding technique for the vector Gaussian CEO problem under quadratic
distortion measure, for which it was there found generally non-tight; but it is
shown here to yield a complete characterization of the region for the case of
logarithmic loss measure. Also, we show that Gaussian test channels with
time-sharing exhaust the Berger-Tung inner bound, which is optimal.
Furthermore, application of our results allows us to find the complete
solutions of two related problems: a quadratic vector Gaussian CEO problem with
determinant constraint and the vector Gaussian distributed Information
Bottleneck problem. Finally, we develop Blahut-Arimoto type algorithms that
allow to compute numerically the regions provided in this paper, for both
discrete and Gaussian models. We illustrate the efficiency of our algorithms
through some numerical examples.Comment: accepted for publication in IEEE Transactions on Information Theor
Rate Region of the Quadratic Gaussian Two-Encoder Source-Coding Problem
We determine the rate region of the quadratic Gaussian two-encoder
source-coding problem. This rate region is achieved by a simple architecture
that separates the analog and digital aspects of the compression. Furthermore,
this architecture requires higher rates to send a Gaussian source than it does
to send any other source with the same covariance. Our techniques can also be
used to determine the sum rate of some generalizations of this classical
problem. Our approach involves coupling the problem to a quadratic Gaussian
``CEO problem.''Comment: Contains additional results. To appear in IEEE Trans. Inf. Theor
Robust Distributed Source Coding
We consider a distributed source coding system in which several observations
are communicated to the decoder using limited transmission rate. The
observations must be separately coded. We introduce a robust distributed coding
scheme which flexibly trades off between system robustness and compression
efficiency. The optimality of this coding scheme is proved for various special
cases.Comment: 40 pages, submitted to the IEEE Transactions on Information Theor
An Infeasibility Result for the Multiterminal Source-Coding Problem
We prove a new outer bound on the rate-distortion region for the
multiterminal source-coding problem. This bound subsumes the best outer bound
in the literature and improves upon it strictly in some cases. The improved
bound enables us to obtain a new, conclusive result for the binary erasure
version of the "CEO problem." The bound recovers many of the converse results
that have been established for special cases of the problem, including the
recent one for the Gaussian version of the CEO problem.Comment: 42 pages; submitted to IEEE Trans. Inf. Theor
On the Vacationing CEO Problem: Achievable Rates and Outer Bounds
This paper studies a class of source coding problems that combines elements
of the CEO problem with the multiple description problem. In this setting,
noisy versions of one remote source are observed by two nodes with encoders
(which is similar to the CEO problem). However, it differs from the CEO problem
in that each node must generate multiple descriptions of the source. This
problem is of interest in multiple scenarios in efficient communication over
networks. In this paper, an achievable region and an outer bound are presented
for this problem, which is shown to be sum rate optimal for a class of
distortion constraints.Comment: 19 pages, 1 figure, ISIT 201
The CEO Problem with th Power of Difference and Logarithmic Distortions
The CEO problem has received much attention since first introduced by Berger
et al., but there are limited results on non-Gaussian models with non-quadratic
distortion measures. In this work, we extend the quadratic Gaussian CEO problem
to two continuous alphabet settings with general th power of difference
distortion, and study asymptotics of distortion decay as the number of agents
and sum rate, , grow without bound, while individual rates
vanish. The first setting is a regular source-observation model, such as
jointly Gaussian, with difference distortion and we establish that the
distortion decays at when . We
use sample median estimation after the Berger-Tung scheme for achievability.
The other setting is a non-regular source-observation model, such as copula or
uniform additive noise models, with difference distortion for which
estimation-theoretic regularity conditions do not hold. The decay
when is obtained for the
non-regular model by midrange estimator following the Berger-Tung scheme. We
also provide converses based on the Shannon lower bound for the regular model,
and the Chazan-Zakai-Ziv bound for the non-regular model. Interestingly, the
regular model converse when recovers the Viswanathan-Berger converse and
is thus tight. Lastly, we provide a sufficient condition for the regular model,
under which quadratic and logarithmic distortions are asymptotically equivalent
by an entropy power relationship as the number of agents grows. This proof
relies on the Bernstein-von Mises theorem
Distributed Source Coding of Correlated Gaussian Remote Sources
We consider the distributed source coding system for correlated Gaussian
observations . Let be correlated
Gaussian random variables and be independent additive
Gaussian noises also independent of . We consider the case
where for each , is a noisy observation of , that is,
. On this coding system the determination problem of the rate
distortion region remains open. In this paper, we derive explicit outer and
inner bounds of the rate distortion region. We further find an explicit
sufficient condition for those two to match. We also study the sum rate part of
the rate distortion region when the correlation has some symmetrical property
and derive a new lower bound of the sum rate part. We derive a sufficient
condition for this lower bound to be tight. The derived sufficient condition
depends only on the correlation property of the sources and their observations.Comment: 20 pages,3 figre
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