3,855 research outputs found
Rate-Distortion with Side-Information at Many Decoders
We present a new inner bound for the rate region of the -stage
successive-refinement problem with side-information. We also present a new
upper bound for the rate-distortion function for lossy-source coding with
multiple decoders and side-information. Characterising this rate-distortion
function is a long-standing open problem, and it is widely believed that the
tightest upper bound is provided by Theorem 2 of Heegard and Berger's paper
"Rate Distortion when Side Information may be Absent", \emph{IEEE Trans.
Inform. Theory}, 1985. We give a counterexample to Heegard and Berger's result.Comment: 36 pages. Submitted to IEEE Transactions on Information Theory. In
proc. ISIT 2010
Rate-Distortion Function for a Heegard-Berger Problem with Two Sources and Degraded Reconstruction sets
In this work, we investigate an instance of the Heegard-Berger problem with
two sources and arbitrarily correlated side information sequences at two
decoders, in which the reconstruction sets at the decoders are degraded.
Specifically, two sources are to be encoded in a manner that one of the two is
reproduced losslessly by both decoders, and the other is reproduced to within
some prescribed distortion level at one of the two decoders. We establish a
single-letter characterization of the rate-distortion function for this model.
The investigation of this result in some special cases also sheds light on the
utility of joint compression of the two sources. Furthermore, we also
generalize our result to the setting in which the source component that is to
be recovered by both users is reconstructed in a lossy fashion, under the
requirement that all terminals (i.e., the encoder and both decoders) can share
an exact copy of the compressed version of this source component, i.e., a
common encoder-decoders reconstruction constraint. For this model as well, we
establish a single-letter characterization of the associated rate-distortion
function.Comment: Submitted to IEEE Trans. on Information Theor
A Rate-Distortion Approach to Index Coding
We approach index coding as a special case of rate-distortion with multiple
receivers, each with some side information about the source. Specifically,
using techniques developed for the rate-distortion problem, we provide two
upper bounds and one lower bound on the optimal index coding rate. The upper
bounds involve specific choices of the auxiliary random variables in the best
existing scheme for the rate-distortion problem. The lower bound is based on a
new lower bound for the general rate-distortion problem. The bounds are shown
to coincide for a number of (groupcast) index coding instances, including all
instances for which the number of decoders does not exceed three.Comment: Substantially extended version. Submitted to IEEE Transactions on
Information Theor
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
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
Secure Lossy Source Coding with Side Information at the Decoders
This paper investigates the problem of secure lossy source coding in the
presence of an eavesdropper with arbitrary correlated side informations at the
legitimate decoder (referred to as Bob) and the eavesdropper (referred to as
Eve). This scenario consists of an encoder that wishes to compress a source to
satisfy the desired requirements on: (i) the distortion level at Bob and (ii)
the equivocation rate at Eve. It is assumed that the decoders have access to
correlated sources as side information. For instance, this problem can be seen
as a generalization of the well-known Wyner-Ziv problem taking into account the
security requirements. A complete characterization of the
rate-distortion-equivocation region for the case of arbitrary correlated side
informations at the decoders is derived. Several special cases of interest and
an application example to secure lossy source coding of binary sources in the
presence of binary and ternary side informations are also considered. It is
shown that the statistical differences between the side information at the
decoders and the presence of non-zero distortion at the legitimate decoder can
be useful in terms of secrecy. Applications of these results arise in a variety
of distributed sensor network scenarios.Comment: 7 pages, 5 figures, 1 table, to be presented at Allerton 201
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