173 research outputs found
On the Continuity of Achievable Rate Regions for Source Coding over Networks
The continuity property of achievable rate regions for source coding over networks is considered. We show rate- distortion regions are continuous with respect to distortion vectors. Then we focus on the continuity of lossless rate regions with respect to source distribution: First, the proof of continuity for general networks with independent sources is given; then, for the case of dependent sources, continuity is proven both in examples where one-letter characterizations are known and in examples where one-letter characterizations are not known; the proofs in the latter case rely on the concavity of the rate regions for those networks
On the Concavity of Rate Regions for Lossless Source Coding in Networks
For a family of network source coding problems, we prove that the lossless rate region is concave in the distribution of sources. While the proof of concavity is straightforward for the few examples where a single-letter characterization of the lossless source coding region is known, it is more difficult for the vast majority of networks where the lossless source coding region remains unsolved. The class of networks that we investigate includes both solved and unsolved examples. We further conjecture that the same property applies more widely and sketch an avenue for investigating that conjecture
On Source Coding with Coded Side Information for a Binary Source with Binary Side Information
The lossless rate region for the coded side information problem is "solved," but its solution is expressed in terms of an auxiliary random variable. As a result, finding the rate region for any fixed example requires an optimization over a family of allowed auxiliary random variables. While intuitive constructions are easy to come by and optimal solutions are known under some special conditions, proving the optimal solution is surprisingly difficult even for examples as basic as a binary source with binary side information. We derive the optimal auxiliary random variables and corresponding achievable rate regions for a family of problems where both the source and side information are binary. Our solution involves first tightening known bounds on the alphabet size of the auxiliary random variable and then optimizing the auxiliary random variable subject to this constraint. The technique used to tighten the bound on the alphabet size applies to a variety of problems beyond the one studied here
Cores of Cooperative Games in Information Theory
Cores of cooperative games are ubiquitous in information theory, and arise
most frequently in the characterization of fundamental limits in various
scenarios involving multiple users. Examples include classical settings in
network information theory such as Slepian-Wolf source coding and multiple
access channels, classical settings in statistics such as robust hypothesis
testing, and new settings at the intersection of networking and statistics such
as distributed estimation problems for sensor networks. Cooperative game theory
allows one to understand aspects of all of these problems from a fresh and
unifying perspective that treats users as players in a game, sometimes leading
to new insights. At the heart of these analyses are fundamental dualities that
have been long studied in the context of cooperative games; for information
theoretic purposes, these are dualities between information inequalities on the
one hand and properties of rate, capacity or other resource allocation regions
on the other.Comment: 12 pages, published at
http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/318704 in EURASIP
Journal on Wireless Communications and Networking, Special Issue on "Theory
and Applications in Multiuser/Multiterminal Communications", April 200
Can Negligible Cooperation Increase Network Capacity? The Average-Error Case
In communication networks, cooperative strategies are coding schemes where
network nodes work together to improve network performance metrics such as
sum-rate. This work studies encoder cooperation in the setting of a discrete
multiple access channel with two encoders and a single decoder. A node in the
network that is connected to both encoders via rate-limited links, referred to
as the cooperation facilitator (CF), enables the cooperation strategy.
Previously, the authors presented a class of multiple access channels where the
average-error sum-capacity has an infinite derivative in the limit where CF
output link capacities approach zero. The authors also demonstrated that for
some channels, the maximal-error sum-capacity is not continuous at the point
where the output link capacities of the CF equal zero. This work shows that the
the average-error sum-capacity is continuous when CF output link capacities
converge to zero; that is, the infinite derivative of the average-error
sum-capacity is not a result of its discontinuity as in the maximal-error case.Comment: 20 pages, 1 figure. To be submitted to ISIT '1
Lecture Notes on Network Information Theory
These lecture notes have been converted to a book titled Network Information
Theory published recently by Cambridge University Press. This book provides a
significantly expanded exposition of the material in the lecture notes as well
as problems and bibliographic notes at the end of each chapter. The authors are
currently preparing a set of slides based on the book that will be posted in
the second half of 2012. More information about the book can be found at
http://www.cambridge.org/9781107008731/. The previous (and obsolete) version of
the lecture notes can be found at http://arxiv.org/abs/1001.3404v4/
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