305 research outputs found
Multiuser Successive Refinement and Multiple Description Coding
We consider the multiuser successive refinement (MSR) problem, where the
users are connected to a central server via links with different noiseless
capacities, and each user wishes to reconstruct in a successive-refinement
fashion. An achievable region is given for the two-user two-layer case and it
provides the complete rate-distortion region for the Gaussian source under the
MSE distortion measure. The key observation is that this problem includes the
multiple description (MD) problem (with two descriptions) as a subsystem, and
the techniques useful in the MD problem can be extended to this case. We show
that the coding scheme based on the universality of random binning is
sub-optimal, because multiple Gaussian side informations only at the decoders
do incur performance loss, in contrast to the case of single side information
at the decoder. We further show that unlike the single user case, when there
are multiple users, the loss of performance by a multistage coding approach can
be unbounded for the Gaussian source. The result suggests that in such a
setting, the benefit of using successive refinement is not likely to justify
the accompanying performance loss. The MSR problem is also related to the
source coding problem where each decoder has its individual side information,
while the encoder has the complete set of the side informations. The MSR
problem further includes several variations of the MD problem, for which the
specialization of the general result is investigated and the implication is
discussed.Comment: 10 pages, 5 figures. To appear in IEEE Transaction on Information
Theory. References updated and typos correcte
Network vector quantization
We present an algorithm for designing locally optimal vector quantizers for general networks. We discuss the algorithm's implementation and compare the performance of the resulting "network vector quantizers" to traditional vector quantizers (VQs) and to rate-distortion (R-D) bounds where available. While some special cases of network codes (e.g., multiresolution (MR) and multiple description (MD) codes) have been studied in the literature, we here present a unifying approach that both includes these existing solutions as special cases and provides solutions to previously unsolved examples
Erasure Multiple Descriptions
We consider a binary erasure version of the n-channel multiple descriptions
problem with symmetric descriptions, i.e., the rates of the n descriptions are
the same and the distortion constraint depends only on the number of messages
received. We consider the case where there is no excess rate for every k out of
n descriptions. Our goal is to characterize the achievable distortions D_1,
D_2,...,D_n. We measure the fidelity of reconstruction using two distortion
criteria: an average-case distortion criterion, under which distortion is
measured by taking the average of the per-letter distortion over all source
sequences, and a worst-case distortion criterion, under which distortion is
measured by taking the maximum of the per-letter distortion over all source
sequences. We present achievability schemes, based on random binning for
average-case distortion and systematic MDS (maximum distance separable) codes
for worst-case distortion, and prove optimality results for the corresponding
achievable distortion regions. We then use the binary erasure multiple
descriptions setup to propose a layered coding framework for multiple
descriptions, which we then apply to vector Gaussian multiple descriptions and
prove its optimality for symmetric scalar Gaussian multiple descriptions with
two levels of receivers and no excess rate for the central receiver. We also
prove a new outer bound for the general multi-terminal source coding problem
and use it to prove an optimality result for the robust binary erasure CEO
problem. For the latter, we provide a tight lower bound on the distortion for
\ell messages for any coding scheme that achieves the minimum achievable
distortion for k messages where k is less than or equal to \ell.Comment: 48 pages, 2 figures, submitted to IEEE Trans. Inf. Theor
Lecture Notes on Network Information Theory
These lecture notes have been converted to a book titled Network Information
Theory published recently by Cambridge University Press. This book provides a
significantly expanded exposition of the material in the lecture notes as well
as problems and bibliographic notes at the end of each chapter. The authors are
currently preparing a set of slides based on the book that will be posted in
the second half of 2012. More information about the book can be found at
http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of
the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/
The Three-Terminal Interactive Lossy Source Coding Problem
The three-node multiterminal lossy source coding problem is investigated. We
derive an inner bound to the general rate-distortion region of this problem
which is a natural extension of the seminal work by Kaspi'85 on the interactive
two-terminal source coding problem. It is shown that this (rather involved)
inner bound contains several rate-distortion regions of some relevant source
coding settings. In this way, besides the non-trivial extension of the
interactive two terminal problem, our results can be seen as a generalization
and hence unification of several previous works in the field. Specializing to
particular cases we obtain novel rate-distortion regions for several lossy
source coding problems. We finish by describing some of the open problems and
challenges. However, the general three-node multiterminal lossy source coding
problem seems to offer a formidable mathematical complexity.Comment: New version with changes suggested by reviewers.Revised and
resubmitted to IEEE Transactions on Information Theory. 92 pages, 11 figures,
1 tabl
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
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