Re-proving Channel Polarization Theorems: An Extremality and Robustness Analysis

The general subject considered in this thesis is a recently discovered coding technique, polar coding, which is used to construct a class of error correction codes with unique properties. In his ground-breaking work, Ar{\i}kan proved that this class of codes, called polar codes, achieve the symmetric capacity --- the mutual information evaluated at the uniform input distribution ---of any stationary binary discrete memoryless channel with low complexity encoders and decoders requiring in the order of $O(N\log N)$ operations in the block-length $N$. This discovery settled the long standing open problem left by Shannon of finding low complexity codes achieving the channel capacity. Polar coding settled an open problem in information theory, yet opened plenty of challenging problems that need to be addressed. A significant part of this thesis is dedicated to advancing the knowledge about this technique in two directions. The first one provides a better understanding of polar coding by generalizing some of the existing results and discussing their implications, and the second one studies the robustness of the theory over communication models introducing various forms of uncertainty or variations into the probabilistic model of the channel.Comment: Preview of my PhD Thesis, EPFL, Lausanne, 2014. For the full version, see http://people.epfl.ch/mine.alsan/publication

Covert channel detection using Information Theory

This paper presents an information theory based detection framework for covert channels. We first show that the usual notion of interference does not characterize the notion of deliberate information flow of covert channels. We then show that even an enhanced notion of "iterated multivalued interference" can not capture flows with capacity lower than one bit of information per channel use. We then characterize and compute the capacity of covert channels that use control flows for a class of systems.Comment: In Proceedings SecCo 2010, arXiv:1102.516