64,284 research outputs found
Linear-Codes-Based Lossless Joint Source-Channel Coding for Multiple-Access Channels
A general lossless joint source-channel coding (JSCC) scheme based on linear
codes and random interleavers for multiple-access channels (MACs) is presented
and then analyzed in this paper. By the information-spectrum approach and the
code-spectrum approach, it is shown that a linear code with a good joint
spectrum can be used to establish limit-approaching lossless JSCC schemes for
correlated general sources and general MACs, where the joint spectrum is a
generalization of the input-output weight distribution. Some properties of
linear codes with good joint spectra are investigated. A formula on the
"distance" property of linear codes with good joint spectra is derived, based
on which, it is further proved that, the rate of any systematic codes with good
joint spectra cannot be larger than the reciprocal of the corresponding
alphabet cardinality, and any sparse generator matrices cannot yield linear
codes with good joint spectra. The problem of designing arbitrary rate coding
schemes is also discussed. A novel idea called "generalized puncturing" is
proposed, which makes it possible that one good low-rate linear code is enough
for the design of coding schemes with multiple rates. Finally, various coding
problems of MACs are reviewed in a unified framework established by the
code-spectrum approach, under which, criteria and candidates of good linear
codes in terms of spectrum requirements for such problems are clearly
presented.Comment: 18 pages, 3 figure
Law of large numbers for branching symmetric Hunt processes with measure-valued branching rates
We establish weak and strong law of large numbers for a class of branching
symmetric Hunt processes with the branching rate being a smooth measure with
respect to the underlying Hunt process, and the branching mechanism being
general and state-dependent. Our work is motivated by recent work on strong law
of large numbers for branching symmetric Markov processes by Chen-Shiozawa [J.
Funct. Anal., 250, 374--399, 2007] and for branching diffusions by
Engl\"ander-Harris-Kyprianou [Ann. Inst. Henri Poincar\'e Probab. Stat., 46,
279--298, 2010]. Our results can be applied to some interesting examples that
are covered by neither of these papers
The 3-rainbow index of a graph
Let be a nontrivial connected graph with an edge-coloring , where adjacent edges may be
colored the same. A tree in is a if no two edges of
receive the same color. For a vertex subset , a tree that
connects in is called an -tree. The minimum number of colors that
are needed in an edge-coloring of such that there is a rainbow -tree for
each -subset of is called -rainbow index, denoted by
. In this paper, we first determine the graphs whose 3-rainbow index
equals 2, , , respectively. We also obtain the exact values of
for regular complete bipartite and multipartite graphs and wheel
graphs. Finally, we give a sharp upper bound for of 2-connected
graphs and 2-edge connected graphs, and graphs whose attains the
upper bound are characterized.Comment: 13 page
High-Order Harmonic Generation and Molecular Orbital Tomography: Characteristics of Molecular Recollision Electronic Wave Packets
We investigate the orientation dependence of molecular high-order harmonic
generation (HHG) both numerically and analytically. We show that the molecular
recollision electronic wave packets (REWPs) in the HHG are closely related to
the ionization potential as well as the particular orbital from which it
ionized. As a result, the spectral amplitude of the molecular REWP can be
significantly different from its reference atom (i.e., with the same ionization
potential as the molecule under study) in some energy regions due to the
interference between the atomic cores of the molecules. This finding is
important for molecular orbital tomography using HHG[Nature \textbf{432},
867(2004)].Comment: 4 pages, 4 figure
- β¦