CaltechAUTHORS
  A Caltech Library Service

Entropy Vectors, Network Information Theory and Wireless Networks

Hassibi, Babak (2007) Entropy Vectors, Network Information Theory and Wireless Networks. In: 5th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks and Workshops, 2007. WiOpt 2007. IEEE , Piscataway, NJ, pp. 1-2. ISBN 978-1-4244-0960-0. https://resolver.caltech.edu/CaltechAUTHORS:20150302-164022192

[img] PDF - Published Version
See Usage Policy.

78kB

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20150302-164022192

Abstract

Information theory is well poised to have an impact on the manner in which future networks are designed and maintained, both because wired networks are ripe for applications such as network coding and also because wireless networks cannot be satisfactorily dealt with using conventional networking tools. The challenge is that most network information theory problems are notoriously difficult and so the barriers that must be overcome are often quite high. In particular, there are only a limited number of tools available and so fresh approaches are quite welcome. We describe an approach based on the definition of the space of "normalized" entropic vectors. In this framework, for a large class of acyclic memoryless networks, the capacity region for an arbitrary set of sources and destinations can be found by maximization of a linear function over the set of channel-constrained normalized entropic vectors and some linear constraints. The key point is that the closure of this set is convex and compact. While this may not necessarily make the problem simpler, it certainly circumvents the "infinite-letter characterization" issue, as well as the nonconvexity of earlier formulations. It also exposes the core of the problem as that of determining the space of normalized entropic vectors. The approach has several interesting consequences: it allows one to obtain the classical cutset bounds via a duality argument; for wired networks, it shows one need only consider the space of unconstrained normalized entropic vectors, thus separating channel and network coding---a result very recently recognized in the community. Outer bounds to the space of normalized entropic vectors are known to be related to non-Shannon inequalities. We develop inner bounds on this space using lattice-generated distributions and show how they can be used to compute inner bounds on the capacity region of networks using linear programming.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1109/WIOPT.2007.4480016DOIAbstract
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=4480016PublisherAbstract
Additional Information:© 2007 IEEE. Keynote Speaker.
DOI:10.1109/WIOPT.2007.4480016
Record Number:CaltechAUTHORS:20150302-164022192
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20150302-164022192
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:55441
Collection:CaltechAUTHORS
Deposited By: Shirley Slattery
Deposited On:03 Mar 2015 01:45
Last Modified:10 Nov 2021 20:45

Repository Staff Only: item control page