6,152 research outputs found
Vector cross product in n-dimensional vector space
The definition of vector cross product (VCP) introduced by Eckmann only
exists in thethree- and the seven- dimensional vector space. In this paper,
according to the orthogonal completeness, magnitude of basis vector cross
product and all kinds of combinations of basis vector , the
generalized definition of VCP in the odd n-dimensional vector space is given by
introducing a cross term . In addition, the definition is validated by
reducing the generalization definition to the fundamental three- and
seven-dimensional vector space.Comment: 9 pages, 1 figure, comments are welcom
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
Existence and convexity of local solutions to degenerate hessian equations
In this work, we prove the existence of local convex solution to the
degenerate Hessian equationComment: corrections some typos in this versio
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
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