9 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
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
Zero-Delay Multiple Descriptions of Stationary Scalar Gauss-Markov Sources
In this paper, we introduce the zero-delay multiple-description problem, where an encoder constructs two descriptions and the decoders receive a subset of these descriptions. The encoder and decoders are causal and operate under the restriction of zero delay, which implies that at each time instance, the encoder must generate codewords that can be decoded by the decoders using only the current and past codewords. For the case of discrete-time stationary scalar Gauss—Markov sources and quadratic distortion constraints, we present information-theoretic lower bounds on the average sum-rate in terms of the directed and mutual information rate between the source and the decoder reproductions. Furthermore, we show that the optimum test channel is in this case Gaussian, and it can be realized by a feedback coding scheme that utilizes prediction and correlated Gaussian noises. Operational achievable results are considered in the high-rate scenario using a simple differential pulse code modulation scheme with staggered quantizers. Using this scheme, we achieve operational rates within 0.415 bits / sample / description of the theoretical lower bounds for varying description rates
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
Incremental Refinements and Multiple Descriptions with Feedback
It is well known that independent (separate) encoding of K correlated sources
may incur some rate loss compared to joint encoding, even if the decoding is
done jointly. This loss is particularly evident in the multiple descriptions
problem, where the sources are repetitions of the same source, but each
description must be individually good. We observe that under mild conditions
about the source and distortion measure, the rate ratio Rindependent(K)/Rjoint
goes to one in the limit of small rate/high distortion. Moreover, we consider
the excess rate with respect to the rate-distortion function, Rindependent(K,
M) - R(D), in M rounds of K independent encodings with a final distortion level
D. We provide two examples - a Gaussian source with mean-squared error and an
exponential source with one-sided error - for which the excess rate vanishes in
the limit as the number of rounds M goes to infinity, for any fixed D and K.
This result has an interesting interpretation for a multi-round variant of the
multiple descriptions problem, where after each round the encoder gets a
(block) feedback regarding which of the descriptions arrived: In the limit as
the number of rounds M goes to infinity (i.e., many incremental rounds), the
total rate of received descriptions approaches the rate-distortion function. We
provide theoretical and experimental evidence showing that this phenomenon is
in fact more general than in the two examples above.Comment: 62 pages. Accepted in the IEEE Transactions on Information Theor
Multiple Description Coding: Proposed Methods And Video Application
Multiple description (MD) coding and quantization has received a lot of attention recently, and has been studied extensively and extended to many demanding appli-cations such as speech and video. We propose two multiple description quantization schemes in order to design the codebooks and partitions of side and central quantiz-ers. The applied framework originates in the multiple description quantization via Gram-Schmidt orthogonalization approach which provides systematic treatment of the achievable rate-distortion region by subtractive dithering and successive quanti-zation along with quantization splitting. The basic idea of our proposed MD quanti-zation schemes is to minimize a Lagrangian cost function (defined as the weighted sum of the central and side distortions) by an iterative technique which jointly designs side codebooks and consequently forms associated partitions. In the first scheme, multiple description vector quantization with weighted sum central decoder (MDVQ-WSC), the central decoder is formed by a linear combination (weighted sum) of the side codebooks. The parameters of this linear combination are also found to minimiz