Algorithmic Polarization for Hidden Markov Models

Using a mild variant of polar codes we design linear compression schemes compressing Hidden Markov sources (where the source is a Markov chain, but whose state is not necessarily observable from its output), and to decode from Hidden Markov channels (where the channel has a state and the error introduced depends on the state). We give the first polynomial time algorithms that manage to compress and decompress (or encode and decode) at input lengths that are polynomial both in the gap to capacity and the mixing time of the Markov chain. Prior work achieved capacity only asymptotically in the limit of large lengths, and polynomial bounds were not available with respect to either the gap to capacity or mixing time. Our results operate in the setting where the source (or the channel) is known. If the source is unknown then compression at such short lengths would lead to effective algorithms for learning parity with noise - thus our results are the first to suggest a separation between the complexity of the problem when the source is known versus when it is unknown

Computer Aided ECG Analysis - State of the Art and Upcoming Challenges

In this paper we present current achievements in computer aided ECG analysis and their applicability in real world medical diagnosis process. Most of the current work is covering problems of removing noise, detecting heartbeats and rhythm-based analysis. There are some advancements in particular ECG segments detection and beat classifications but with limited evaluations and without clinical approvals. This paper presents state of the art advancements in those areas till present day. Besides this short computer science and signal processing literature review, paper covers future challenges regarding the ECG signal morphology analysis deriving from the medical literature review. Paper is concluded with identified gaps in current advancements and testing, upcoming challenges for future research and a bullseye test is suggested for morphology analysis evaluation.Comment: 7 pages, 3 figures, IEEE EUROCON 2013 International conference on computer as a tool, 1-4 July 2013, Zagreb, Croati

Quantum walks: a comprehensive review

Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a solid field of research of quantum computation full of exciting open problems for physicists, computer scientists, mathematicians and engineers. In this paper we review theoretical advances on the foundations of both discrete- and continuous-time quantum walks, together with the role that randomness plays in quantum walks, the connections between the mathematical models of coined discrete quantum walks and continuous quantum walks, the quantumness of quantum walks, a summary of papers published on discrete quantum walks and entanglement as well as a succinct review of experimental proposals and realizations of discrete-time quantum walks. Furthermore, we have reviewed several algorithms based on both discrete- and continuous-time quantum walks as well as a most important result: the computational universality of both continuous- and discrete- time quantum walks.Comment: Paper accepted for publication in Quantum Information Processing Journa