Fractal dimension in information theory

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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.