27,538 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
Pointwise convergence of multiple ergodic averages and strictly ergodic models
By building some suitable strictly ergodic models, we prove that for an
ergodic system , , , the averages converge a.e.
Deriving some results from the construction, for distal systems we answer
positively the question if the multiple ergodic averages converge a.e. That is,
we show that if is an ergodic distal system, and , then multiple ergodic averages converge a.e.Comment: 35 pages, revised version following referees' report
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