Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wyner's Common Information: Generalizations and A New Lossy Source
  Coding Interpretation   Wyner's common information was originally defined for a pair of dependent
discrete random variables. Its significance is largely reflected in, hence also
confined to, several existing interpretations in various source coding
problems. This paper attempts to both generalize its definition and to expand
its practical significance by providing a new operational interpretation. The
generalization is two-folded: the number of dependent variables can be
arbitrary, so are the alphabet of those random variables. New properties are
determined for the generalized Wyner's common information of N dependent
variables. More importantly, a lossy source coding interpretation of Wyner's
common information is developed using the Gray-Wyner network. In particular, it
is established that the common information equals to the smallest common
message rate when the total rate is arbitrarily close to the rate distortion
function with joint decoding. A surprising observation is that such equality
holds independent of the values of distortion constraints as long as the
distortions are within some distortion region. Examples about the computation
of common information are given, including that of a pair of dependent Gaussian
random variables.

34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: hep-th