On graphical models for communications and machine learning: algorithms, bounds, and analog implementation

This dissertation is about a specific problem and about general methods. The specific problem is carrier-phase synchronization, which appears in the context of digital communications. The general methods are messagepassing algorithms operating on graphical models, in particular, factor graphs. We consider applications of such algorithms in the context of statistical inference (as in communications, signal processing, and machine learning), statistics, information theory, and the theory of dynamical systems (such as analog electronic circuits). The primary motivation for this work was (1) to analyze the degradation of digital communications systems due to oscillator non-idealities; (2) the development of synchronization algorithms that minimize this performance degradation. Clocks are ubiquitous in digital communications systems; real-life clocks are noisy, i.e., their signals are not perfectly periodic, which often leads to a significant degradation of the performance of communications systems. In the early days of communications, this source of degradation was only of secondary concern. Communications systems used to operate far from the ultimate performance bound, i.e., channel capacity. The main concern was therefore to develop error-correcting techniques that could close the gap between the performance of practical communications systems and channel capacity. With the recent advent of iterative decoding techniques, communications systems nowadays most often operate close to the ultimate performance limits; issues such as synchronization, which were earlier only of secondary importance, have now become the mayor (remaining) bottlenecks