783 research outputs found
Multiple Description Quantization via Gram-Schmidt Orthogonalization
The multiple description (MD) problem has received considerable attention as
a model of information transmission over unreliable channels. A general
framework for designing efficient multiple description quantization schemes is
proposed in this paper. We provide a systematic treatment of the El Gamal-Cover
(EGC) achievable MD rate-distortion region, and show that any point in the EGC
region can be achieved via a successive quantization scheme along with
quantization splitting. For the quadratic Gaussian case, the proposed scheme
has an intrinsic connection with the Gram-Schmidt orthogonalization, which
implies that the whole Gaussian MD rate-distortion region is achievable with a
sequential dithered lattice-based quantization scheme as the dimension of the
(optimal) lattice quantizers becomes large. Moreover, this scheme is shown to
be universal for all i.i.d. smooth sources with performance no worse than that
for an i.i.d. Gaussian source with the same variance and asymptotically optimal
at high resolution. A class of low-complexity MD scalar quantizers in the
proposed general framework also is constructed and is illustrated
geometrically; the performance is analyzed in the high resolution regime, which
exhibits a noticeable improvement over the existing MD scalar quantization
schemes.Comment: 48 pages; submitted to IEEE Transactions on Information Theor
Optimal Quantization for Compressive Sensing under Message Passing Reconstruction
We consider the optimal quantization of compressive sensing measurements
following the work on generalization of relaxed belief propagation (BP) for
arbitrary measurement channels. Relaxed BP is an iterative reconstruction
scheme inspired by message passing algorithms on bipartite graphs. Its
asymptotic error performance can be accurately predicted and tracked through
the state evolution formalism. We utilize these results to design mean-square
optimal scalar quantizers for relaxed BP signal reconstruction and empirically
demonstrate the superior error performance of the resulting quantizers.Comment: 5 pages, 3 figures, submitted to IEEE International Symposium on
Information Theory (ISIT) 2011; minor corrections in v
Asymptotic Task-Based Quantization with Application to Massive MIMO
Quantizers take part in nearly every digital signal processing system which
operates on physical signals. They are commonly designed to accurately
represent the underlying signal, regardless of the specific task to be
performed on the quantized data. In systems working with high-dimensional
signals, such as massive multiple-input multiple-output (MIMO) systems, it is
beneficial to utilize low-resolution quantizers, due to cost, power, and memory
constraints. In this work we study quantization of high-dimensional inputs,
aiming at improving performance under resolution constraints by accounting for
the system task in the quantizers design. We focus on the task of recovering a
desired signal statistically related to the high-dimensional input, and analyze
two quantization approaches: We first consider vector quantization, which is
typically computationally infeasible, and characterize the optimal performance
achievable with this approach. Next, we focus on practical systems which
utilize hardware-limited scalar uniform analog-to-digital converters (ADCs),
and design a task-based quantizer under this model. The resulting system
accounts for the task by linearly combining the observed signal into a lower
dimension prior to quantization. We then apply our proposed technique to
channel estimation in massive MIMO networks. Our results demonstrate that a
system utilizing low-resolution scalar ADCs can approach the optimal channel
estimation performance by properly accounting for the task in the system
design
On Distributed Linear Estimation With Observation Model Uncertainties
We consider distributed estimation of a Gaussian source in a heterogenous
bandwidth constrained sensor network, where the source is corrupted by
independent multiplicative and additive observation noises, with incomplete
statistical knowledge of the multiplicative noise. For multi-bit quantizers, we
derive the closed-form mean-square-error (MSE) expression for the linear
minimum MSE (LMMSE) estimator at the FC. For both error-free and erroneous
communication channels, we propose several rate allocation methods named as
longest root to leaf path, greedy and integer relaxation to (i) minimize the
MSE given a network bandwidth constraint, and (ii) minimize the required
network bandwidth given a target MSE. We also derive the Bayesian Cramer-Rao
lower bound (CRLB) and compare the MSE performance of our proposed methods
against the CRLB. Our results corroborate that, for low power multiplicative
observation noises and adequate network bandwidth, the gaps between the MSE of
our proposed methods and the CRLB are negligible, while the performance of
other methods like individual rate allocation and uniform is not satisfactory
- …