3,817 research outputs found
n-Channel Asymmetric Multiple-Description Lattice Vector Quantization
We present analytical expressions for optimal entropy-constrained
multiple-description lattice vector quantizers which, under high-resolutions
assumptions, minimize the expected distortion for given packet-loss
probabilities. We consider the asymmetric case where packet-loss probabilities
and side entropies are allowed to be unequal and find optimal quantizers for
any number of descriptions in any dimension. We show that the normalized second
moments of the side-quantizers are given by that of an -dimensional sphere
independent of the choice of lattices. Furthermore, we show that the optimal
bit-distribution among the descriptions is not unique. In fact, within certain
limits, bits can be arbitrarily distributed.Comment: To appear in the proceedings of the 2005 IEEE International Symposium
on Information Theory, Adelaide, Australia, September 4-9, 200
n-Channel Asymmetric Entropy-Constrained Multiple-Description Lattice Vector Quantization
This paper is about the design and analysis of an index-assignment (IA) based
multiple-description coding scheme for the n-channel asymmetric case. We use
entropy constrained lattice vector quantization and restrict attention to
simple reconstruction functions, which are given by the inverse IA function
when all descriptions are received or otherwise by a weighted average of the
received descriptions. We consider smooth sources with finite differential
entropy rate and MSE fidelity criterion. As in previous designs, our
construction is based on nested lattices which are combined through a single IA
function. The results are exact under high-resolution conditions and
asymptotically as the nesting ratios of the lattices approach infinity. For any
n, the design is asymptotically optimal within the class of IA-based schemes.
Moreover, in the case of two descriptions and finite lattice vector dimensions
greater than one, the performance is strictly better than that of existing
designs. In the case of three descriptions, we show that in the limit of large
lattice vector dimensions, points on the inner bound of Pradhan et al. can be
achieved. Furthermore, for three descriptions and finite lattice vector
dimensions, we show that the IA-based approach yields, in the symmetric case, a
smaller rate loss than the recently proposed source-splitting approach.Comment: 49 pages, 4 figures. Accepted for publication in IEEE Transactions on
Information Theory, 201
Multiple-Description Coding by Dithered Delta-Sigma Quantization
We address the connection between the multiple-description (MD) problem and
Delta-Sigma quantization. The inherent redundancy due to oversampling in
Delta-Sigma quantization, and the simple linear-additive noise model resulting
from dithered lattice quantization, allow us to construct a symmetric and
time-invariant MD coding scheme. We show that the use of a noise shaping filter
makes it possible to trade off central distortion for side distortion.
Asymptotically as the dimension of the lattice vector quantizer and order of
the noise shaping filter approach infinity, the entropy rate of the dithered
Delta-Sigma quantization scheme approaches the symmetric two-channel MD
rate-distortion function for a memoryless Gaussian source and MSE fidelity
criterion, at any side-to-central distortion ratio and any resolution. In the
optimal scheme, the infinite-order noise shaping filter must be minimum phase
and have a piece-wise flat power spectrum with a single jump discontinuity. An
important advantage of the proposed design is that it is symmetric in rate and
distortion by construction, so the coding rates of the descriptions are
identical and there is therefore no need for source splitting.Comment: Revised, restructured, significantly shortened and minor typos has
been fixed. Accepted for publication in the IEEE Transactions on Information
Theor
Integer-Forcing Source Coding
Integer-Forcing (IF) is a new framework, based on compute-and-forward, for
decoding multiple integer linear combinations from the output of a Gaussian
multiple-input multiple-output channel. This work applies the IF approach to
arrive at a new low-complexity scheme, IF source coding, for distributed lossy
compression of correlated Gaussian sources under a minimum mean squared error
distortion measure. All encoders use the same nested lattice codebook. Each
encoder quantizes its observation using the fine lattice as a quantizer and
reduces the result modulo the coarse lattice, which plays the role of binning.
Rather than directly recovering the individual quantized signals, the decoder
first recovers a full-rank set of judiciously chosen integer linear
combinations of the quantized signals, and then inverts it. In general, the
linear combinations have smaller average powers than the original signals. This
allows to increase the density of the coarse lattice, which in turn translates
to smaller compression rates. We also propose and analyze a one-shot version of
IF source coding, that is simple enough to potentially lead to a new design
principle for analog-to-digital converters that can exploit spatial
correlations between the sampled signals.Comment: Submitted to IEEE Transactions on Information Theor
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 Design of Multiple Description Lattice Vector Quantizers
In the design of multiple description lattice vector quantizers (MDLVQ),
index assignment plays a critical role. In addition, one also needs to choose
the Voronoi cell size of the central lattice v, the sublattice index N, and the
number of side descriptions K to minimize the expected MDLVQ distortion, given
the total entropy rate of all side descriptions Rt and description loss
probability p. In this paper we propose a linear-time MDLVQ index assignment
algorithm for any K >= 2 balanced descriptions in any dimensions, based on a
new construction of so-called K-fraction lattice. The algorithm is greedy in
nature but is proven to be asymptotically (N -> infinity) optimal for any K >=
2 balanced descriptions in any dimensions, given Rt and p. The result is
stronger when K = 2: the optimality holds for finite N as well, under some mild
conditions. For K > 2, a local adjustment algorithm is developed to augment the
greedy index assignment, and conjectured to be optimal for finite N.
Our algorithmic study also leads to better understanding of v, N and K in
optimal MDLVQ design. For K = 2 we derive, for the first time, a
non-asymptotical closed form expression of the expected distortion of optimal
MDLVQ in p, Rt, N. For K > 2, we tighten the current asymptotic formula of the
expected distortion, relating the optimal values of N and K to p and Rt more
precisely.Comment: Submitted to IEEE Trans. on Information Theory, Sep 2006 (30 pages, 7
figures
Achievable Rate Regions for Two-Way Relay Channel using Nested Lattice Coding
This paper studies Gaussian Two-Way Relay Channel where two communication
nodes exchange messages with each other via a relay. It is assumed that all
nodes operate in half duplex mode without any direct link between the
communication nodes. A compress-and-forward relaying strategy using nested
lattice codes is first proposed. Then, the proposed scheme is improved by
performing a layered coding : a common layer is decoded by both receivers and a
refinement layer is recovered only by the receiver which has the best channel
conditions. The achievable rates of the new scheme are characterized and are
shown to be higher than those provided by the decode-and-forward strategy in
some regions.Comment: 27 pages, 13 figures, Submitted to IEEE Transactions on Wireless
Communications (October 2013
Multiple Description Vector Quantization with Lattice Codebooks: Design and Analysis
The problem of designing a multiple description vector quantizer with lattice
codebook Lambda is considered. A general solution is given to a labeling
problem which plays a crucial role in the design of such quantizers. Numerical
performance results are obtained for quantizers based on the lattices A_2 and
Z^i, i=1,2,4,8, that make use of this labeling algorithm. The high-rate
squared-error distortions for this family of L-dimensional vector quantizers
are then analyzed for a memoryless source with probability density function p
and differential entropy h(p) < infty. For any a in (0,1) and rate pair (R,R),
it is shown that the two-channel distortion d_0 and the channel 1 (or channel
2) distortions d_s satisfy lim_{R -> infty} d_0 2^(2R(1+a)) = (1/4) G(Lambda)
2^{2h(p)} and lim_{R -> infty} d_s 2^(2R(1-a)) = G(S_L) 2^2h(p), where
G(Lambda) is the normalized second moment of a Voronoi cell of the lattice
Lambda and G(S_L) is the normalized second moment of a sphere in L dimensions.Comment: 46 pages, 14 figure
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
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