Security in the context of future communication challenges and compressive sensing

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The present proposal suggests a continuing concerted effort to tackle and resolve key challenges in the development of communication technologies - examining physical layers of security in future mobile phone and quantum technologies that offer the perspective of unconditionally secure communication. Compressed sensing is the main tool to be exploited here: In fact, in the first two years, it has become clear that notions of compressed sensing and security are even much more closely intertwined than originally anticipated, in a "dichotomy" that will be laid out in the proposal. It brings together significant expertise from electrical engineering and mobile phone communication, quantum information science, and applied mathematics collaboratively; with both principal investigators having a substantial track record in research on modern signal processing and specifically compressed sensing. At the heart of the proposal is significant mathematical method development of hierarchical structures, structured problems beyond low-rank and sparse situations and novel instances of bi-linear problems, in a commutative reading as well as in non-commutative analogs that naturally arise in the quantum settings. Algorithmically, new fast and memory-economical methods will be in the focus of attention.