288 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
Source Coding Optimization for Distributed Average Consensus
Consensus is a common method for computing a function of the data distributed
among the nodes of a network. Of particular interest is distributed average
consensus, whereby the nodes iteratively compute the sample average of the data
stored at all the nodes of the network using only near-neighbor communications.
In real-world scenarios, these communications must undergo quantization, which
introduces distortion to the internode messages. In this thesis, a model for
the evolution of the network state statistics at each iteration is developed
under the assumptions of Gaussian data and additive quantization error. It is
shown that minimization of the communication load in terms of aggregate source
coding rate can be posed as a generalized geometric program, for which an
equivalent convex optimization can efficiently solve for the global minimum.
Optimization procedures are developed for rate-distortion-optimal vector
quantization, uniform entropy-coded scalar quantization, and fixed-rate uniform
quantization. Numerical results demonstrate the performance of these
approaches. For small numbers of iterations, the fixed-rate optimizations are
verified using exhaustive search. Comparison to the prior art suggests
competitive performance under certain circumstances but strongly motivates the
incorporation of more sophisticated coding strategies, such as differential,
predictive, or Wyner-Ziv coding.Comment: Master's Thesis, Electrical Engineering, North Carolina State
Universit
Message-Passing Estimation from Quantized Samples
Estimation of a vector from quantized linear measurements is a common problem
for which simple linear techniques are suboptimal -- sometimes greatly so. This
paper develops generalized approximate message passing (GAMP) algorithms for
minimum mean-squared error estimation of a random vector from quantized linear
measurements, notably allowing the linear expansion to be overcomplete or
undercomplete and the scalar quantization to be regular or non-regular. GAMP is
a recently-developed class of algorithms that uses Gaussian approximations in
belief propagation and allows arbitrary separable input and output channels.
Scalar quantization of measurements is incorporated into the output channel
formalism, leading to the first tractable and effective method for
high-dimensional estimation problems involving non-regular scalar quantization.
Non-regular quantization is empirically demonstrated to greatly improve
rate-distortion performance in some problems with oversampling or with
undersampling combined with a sparsity-inducing prior. Under the assumption of
a Gaussian measurement matrix with i.i.d. entries, the asymptotic error
performance of GAMP can be accurately predicted and tracked through the state
evolution formalism. We additionally use state evolution to design MSE-optimal
scalar quantizers for GAMP signal reconstruction and empirically demonstrate
the superior error performance of the resulting quantizers.Comment: 12 pages, 8 figure
Frame Permutation Quantization
Frame permutation quantization (FPQ) is a new vector quantization technique
using finite frames. In FPQ, a vector is encoded using a permutation source
code to quantize its frame expansion. This means that the encoding is a partial
ordering of the frame expansion coefficients. Compared to ordinary permutation
source coding, FPQ produces a greater number of possible quantization rates and
a higher maximum rate. Various representations for the partitions induced by
FPQ are presented, and reconstruction algorithms based on linear programming,
quadratic programming, and recursive orthogonal projection are derived.
Implementations of the linear and quadratic programming algorithms for uniform
and Gaussian sources show performance improvements over entropy-constrained
scalar quantization for certain combinations of vector dimension and coding
rate. Monte Carlo evaluation of the recursive algorithm shows that mean-squared
error (MSE) decays as 1/M^4 for an M-element frame, which is consistent with
previous results on optimal decay of MSE. Reconstruction using the canonical
dual frame is also studied, and several results relate properties of the
analysis frame to whether linear reconstruction techniques provide consistent
reconstructions.Comment: 29 pages, 5 figures; detailed added to proof of Theorem 4.3 and a few
minor correction
New Directions in Subband Coding
Two very different subband coders are described. The first is a modified dynamic bit-allocation-subband coder (D-SBC) designed for variable rate coding situations and easily adaptable to noisy channel environments. It can operate at rates as low as 12 kb/s and still give good quality speech. The second coder is a 16-kb/s waveform coder, based on a combination of subband coding and vector quantization (VQ-SBC). The key feature of this coder is its short coding delay, which makes it suitable for real-time communication networks. The speech quality of both coders has been enhanced by adaptive postfiltering. The coders have been implemented on a single AT&T DSP32 signal processo
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