19 research outputs found
On Multistage Successive Refinement for Wyner-Ziv Source Coding with Degraded Side Informations
We provide a complete characterization of the rate-distortion region for the
multistage successive refinement of the Wyner-Ziv source coding problem with
degraded side informations at the decoder. Necessary and sufficient conditions
for a source to be successively refinable along a distortion vector are
subsequently derived. A source-channel separation theorem is provided when the
descriptions are sent over independent channels for the multistage case.
Furthermore, we introduce the notion of generalized successive refinability
with multiple degraded side informations. This notion captures whether
progressive encoding to satisfy multiple distortion constraints for different
side informations is as good as encoding without progressive requirement.
Necessary and sufficient conditions for generalized successive refinability are
given. It is shown that the following two sources are generalized successively
refinable: (1) the Gaussian source with degraded Gaussian side informations,
(2) the doubly symmetric binary source when the worse side information is a
constant. Thus for both cases, the failure of being successively refinable is
only due to the inherent uncertainty on which side information will occur at
the decoder, but not the progressive encoding requirement.Comment: Submitted to IEEE Trans. Information Theory Apr. 200
Side-information Scalable Source Coding
The problem of side-information scalable (SI-scalable) source coding is
considered in this work, where the encoder constructs a progressive
description, such that the receiver with high quality side information will be
able to truncate the bitstream and reconstruct in the rate distortion sense,
while the receiver with low quality side information will have to receive
further data in order to decode. We provide inner and outer bounds for general
discrete memoryless sources. The achievable region is shown to be tight for the
case that either of the decoders requires a lossless reconstruction, as well as
the case with degraded deterministic distortion measures. Furthermore we show
that the gap between the achievable region and the outer bounds can be bounded
by a constant when square error distortion measure is used. The notion of
perfectly scalable coding is introduced as both the stages operate on the
Wyner-Ziv bound, and necessary and sufficient conditions are given for sources
satisfying a mild support condition. Using SI-scalable coding and successive
refinement Wyner-Ziv coding as basic building blocks, a complete
characterization is provided for the important quadratic Gaussian source with
multiple jointly Gaussian side-informations, where the side information quality
does not have to be monotonic along the scalable coding order. Partial result
is provided for the doubly symmetric binary source with Hamming distortion when
the worse side information is a constant, for which one of the outer bound is
strictly tighter than the other one.Comment: 35 pages, submitted to IEEE Transaction on Information Theor
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
Source Coding Problems with Conditionally Less Noisy Side Information
A computable expression for the rate-distortion (RD) function proposed by
Heegard and Berger has eluded information theory for nearly three decades.
Heegard and Berger's single-letter achievability bound is well known to be
optimal for \emph{physically degraded} side information; however, it is not
known whether the bound is optimal for arbitrarily correlated side information
(general discrete memoryless sources). In this paper, we consider a new setup
in which the side information at one receiver is \emph{conditionally less
noisy} than the side information at the other. The new setup includes degraded
side information as a special case, and it is motivated by the literature on
degraded and less noisy broadcast channels. Our key contribution is a converse
proving the optimality of Heegard and Berger's achievability bound in a new
setting. The converse rests upon a certain \emph{single-letterization} lemma,
which we prove using an information theoretic telescoping identity {recently
presented by Kramer}. We also generalise the above ideas to two different
successive-refinement problems
Successive refinement with conditionally less noisy side information
We consider the successive refinement of information problem with decoder side information. The rate-distortion region is unknown in general; Steinberg & Merhav and Tian & Diggavi solved it in the special case of degraded side information. We extend this special case to a new setup, conditionally less noisy side information, and we give a single-letter solution when one distortion function is deterministic.QC 20140108</p
Wyner-Ziv Coding over Broadcast Channels: Digital Schemes
This paper addresses lossy transmission of a common source over a broadcast
channel when there is correlated side information at the receivers, with
emphasis on the quadratic Gaussian and binary Hamming cases. A digital scheme
that combines ideas from the lossless version of the problem, i.e.,
Slepian-Wolf coding over broadcast channels, and dirty paper coding, is
presented and analyzed. This scheme uses layered coding where the common layer
information is intended for both receivers and the refinement information is
destined only for one receiver. For the quadratic Gaussian case, a quantity
characterizing the overall quality of each receiver is identified in terms of
channel and side information parameters. It is shown that it is more
advantageous to send the refinement information to the receiver with "better"
overall quality. In the case where all receivers have the same overall quality,
the presented scheme becomes optimal. Unlike its lossless counterpart, however,
the problem eludes a complete characterization
Rate-Distortion Region of a Gray–Wyner Model with Side Information
In this work, we establish a full single-letter characterization of the rate-distortion region of an instance of the Gray–Wyner model with side information at the decoders. Specifically, in this model, an encoder observes a pair of memoryless, arbitrarily correlated, sources (Sn1,Sn2) and communicates with two receivers over an error-free rate-limited link of capacity R0 , as well as error-free rate-limited individual links of capacities R1 to the first receiver and R2 to the second receiver. Both receivers reproduce the source component Sn2 losslessly; and Receiver 1 also reproduces the source component Sn1 lossily, to within some prescribed fidelity level D1 . In addition, Receiver 1 and Receiver 2 are equipped, respectively, with memoryless side information sequences Yn1 and Yn2 . Important in this setup, the side information sequences are arbitrarily correlated among them, and with the source pair (Sn1,Sn2) ; and are not assumed to exhibit any particular ordering. Furthermore, by specializing the main result to two Heegard–Berger models with successive refinement and scalable coding, we shed light on the roles of the common and private descriptions that the encoder should produce and the role of each of the common and private links. We develop intuitions by analyzing the developed single-letter rate-distortion regions of these models, and discuss some insightful binary examples