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Series in Communication Theory
Edited by Helmut Bölcskei
Fractal Dimension in Information Theory
1st edition 2016. XX, 172 pages; € 64.00.
In this work, we apply concepts from fractal geometry to establish new results on information-theoretic 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
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