15,028 research outputs found
Linear Information Coupling Problems
Many network information theory problems face the similar difficulty of
single letterization. We argue that this is due to the lack of a geometric
structure on the space of probability distribution. In this paper, we develop
such a structure by assuming that the distributions of interest are close to
each other. Under this assumption, the K-L divergence is reduced to the squared
Euclidean metric in an Euclidean space. Moreover, we construct the notion of
coordinate and inner product, which will facilitate solving communication
problems. We will also present the application of this approach to the
point-to-point channel and the general broadcast channel, which demonstrates
how our technique simplifies information theory problems.Comment: To appear, IEEE International Symposium on Information Theory, July,
201
The Linear Information Coupling Problems
Many network information theory problems face the similar difficulty of
single-letterization. We argue that this is due to the lack of a geometric
structure on the space of probability distribution. In this paper, we develop
such a structure by assuming that the distributions of interest are close to
each other. Under this assumption, the K-L divergence is reduced to the squared
Euclidean metric in an Euclidean space. In addition, we construct the notion of
coordinate and inner product, which will facilitate solving communication
problems. We will present the application of this approach to the
point-to-point channel, general broadcast channel, and the multiple access
channel (MAC) with the common source. It can be shown that with this approach,
information theory problems, such as the single-letterization, can be reduced
to some linear algebra problems. Moreover, we show that for the general
broadcast channel, transmitting the common message to receivers can be
formulated as the trade-off between linear systems. We also provide an example
to visualize this trade-off in a geometric way. Finally, for the MAC with the
common source, we observe a coherent combining gain due to the cooperation
between transmitters, and this gain can be quantified by applying our
technique.Comment: 27 pages, submitted to IEEE Transactions on Information Theor
Recommended from our members
Study on SPH Viscosity Term Formulations
For viscosity-dominated flows, the viscous effect plays a much more important role. Since the viscosity term in SPH-governing (Smoothed Particle Hydrodynamics) equations involves the discretization of a second-order derivative, its treatment could be much more challenging than that of a first-order derivative, such as the pressure gradient. The present paper summarizes a series of improved methods for modeling the second-order viscosity force term. By using a benchmark patch test, the numerical accuracy and efficiency of different approaches are evaluated under both uniform and non-uniform particle configurations. Then these viscosity force models are used to compute a documented lid-driven cavity flow and its interaction with a cylinder, from which the most recommended viscosity term formulation has been identified
Superfluidity and Stabilities of a Bose-Einstein condensate with periodically modulated interatomic interaction
We study theoretically the superfluidity and stability of a Bose-Einstein
condensate (BEC) whose interatomic scattering length is periodically modulated
with optical Feshbach resonance. Our numerical study finds that the properties
of this periodic BEC are strongly influenced by the modulation strength. When
the modulation strength is small, only the Bloch waves close to the Brillouin
zone edge suffer both Landau and dynamical instabilities. When the modulation
strength is strong enough, all Bloch waves become dynamically unstable. In
other words, the periodic BEC loses its superfluidity completely.Comment: 5 pages, 5 figure
- …