1,776 research outputs found
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
OPE Convergence in Conformal Field Theory
We clarify questions related to the convergence of the OPE and conformal
block decomposition in unitary Conformal Field Theories (for any number of
spacetime dimensions). In particular, we explain why these expansions are
convergent in a finite region. We also show that the convergence is
exponentially fast, in the sense that the operators of dimension above Delta
contribute to correlation functions at most exp(-a Delta). Here the constant
a>0 depends on the positions of operator insertions and we compute it
explicitly.Comment: 26 pages, 6 figures; v2: a clarifying note and two refs added; v3:
note added concerning an extra constant factor in the main error estimate,
misprint correcte
Uncertainty Principles and Vector Quantization
Given a frame in C^n which satisfies a form of the uncertainty principle (as
introduced by Candes and Tao), it is shown how to quickly convert the frame
representation of every vector into a more robust Kashin's representation whose
coefficients all have the smallest possible dynamic range O(1/\sqrt{n}). The
information tends to spread evenly among these coefficients. As a consequence,
Kashin's representations have a great power for reduction of errors in their
coefficients, including coefficient losses and distortions.Comment: Final version, to appear in IEEE Trans. Information Theory.
Introduction updated, minor inaccuracies corrected
High-resolution product quantization for Gaussian processes under sup-norm distortion
We derive high-resolution upper bounds for optimal product quantization of
pathwise contionuous Gaussian processes respective to the supremum norm on
[0,T]^d. Moreover, we describe a product quantization design which attains this
bound. This is achieved under very general assumptions on random series
expansions of the process. It turns out that product quantization is
asymptotically only slightly worse than optimal functional quantization. The
results are applied e.g. to fractional Brownian sheets and the
Ornstein-Uhlenbeck process.Comment: Version publi\'ee dans la revue Bernoulli, 13(3), 653-67
One-bit Distributed Sensing and Coding for Field Estimation in Sensor Networks
This paper formulates and studies a general distributed field reconstruction
problem using a dense network of noisy one-bit randomized scalar quantizers in
the presence of additive observation noise of unknown distribution. A
constructive quantization, coding, and field reconstruction scheme is developed
and an upper-bound to the associated mean squared error (MSE) at any point and
any snapshot is derived in terms of the local spatio-temporal smoothness
properties of the underlying field. It is shown that when the noise, sensor
placement pattern, and the sensor schedule satisfy certain weak technical
requirements, it is possible to drive the MSE to zero with increasing sensor
density at points of field continuity while ensuring that the per-sensor
bitrate and sensing-related network overhead rate simultaneously go to zero.
The proposed scheme achieves the order-optimal MSE versus sensor density
scaling behavior for the class of spatially constant spatio-temporal fields.Comment: Fixed typos, otherwise same as V2. 27 pages (in one column review
format), 4 figures. Submitted to IEEE Transactions on Signal Processing.
Current version is updated for journal submission: revised author list,
modified formulation and framework. Previous version appeared in Proceedings
of Allerton Conference On Communication, Control, and Computing 200
Interference Mitigation Through Limited Receiver Cooperation
Interference is a major issue limiting the performance in wireless networks.
Cooperation among receivers can help mitigate interference by forming
distributed MIMO systems. The rate at which receivers cooperate, however, is
limited in most scenarios. How much interference can one bit of receiver
cooperation mitigate? In this paper, we study the two-user Gaussian
interference channel with conferencing decoders to answer this question in a
simple setting. We identify two regions regarding the gain from receiver
cooperation: linear and saturation regions. In the linear region receiver
cooperation is efficient and provides a degrees-of-freedom gain, which is
either one cooperation bit buys one more bit or two cooperation bits buy one
more bit until saturation. In the saturation region receiver cooperation is
inefficient and provides a power gain, which is at most a constant regardless
of the rate at which receivers cooperate. The conclusion is drawn from the
characterization of capacity region to within two bits. The proposed strategy
consists of two parts: (1) the transmission scheme, where superposition
encoding with a simple power split is employed, and (2) the cooperative
protocol, where one receiver quantize-bin-and-forwards its received signal, and
the other after receiving the side information decode-bin-and-forwards its
received signal.Comment: Submitted to IEEE Transactions on Information Theory. 69 pages, 14
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