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S

Series in Communication Theory
Edited by Helmut Bölcskei
Vol. 13:
David Stotz,
Fractal Dimension in Information Theory
1st edition 2016. XX, 172 pages; € 64.00.
ISBN 9783866285613
In this work,
we apply concepts from fractal geometry to establish new results on informationtheoretic
problems. For interference channels we identify explicit and almost surely
satisfied conditions on the channel matrix to admit full degrees of freedom. We
establish a formal connection between additive combinatorics and the characterization
of degrees of freedom. Furthermore, we extend the framework to vector
interference channels allowing for a unified treatment of different
interference alignment schemes. Moreover, we study the separation of random
signals with arbirtrary distributions for which we
present general achievability results based on a theory of probabilistic
uncertainty relations.
About the author:
David Stotz was born in Breisach,
Germany, in 1986. He recieved the MASt in Mathematics in 2009 from the Universtity
of Cambridge, United Kingdom, and the Dipl.Math. degree
in 2010 from the University of Freiburg, Germany. In 2011 he joined the
Communication Technology Laboratory at ETH Zurich, where he graduated with the
Dr. sc. degree in 2015.
Keywords: fractal dimension, information dimension, Minkowski
dimension, interference channel, degrees of freedom, additive combinatorics,
signal separation, uncertainty relations
Series in Communication
Theory
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