New Model and Methodology for Signal Estimation and Decoding

点击翻译按钮获取中文摘要

This project aims to apply nonlinear dynamics to the study of (iterative) statistical inference, an important class of algorithms with well-proven applications in communications, signal processing and artificial intelligence. Existing models and methodologies for iterative analysis, coming largely from an information theoretical perspective, are inadequate in predicting and controlling the individual (rather than the ensemble-average) time-evolution behavior of a large-dimension and highly-dynamic signal sequence. On the other hand, estimating nonlinear dynamical systems, especially the challenging case of chaos, has not taken advantage of the powerful tool of statistical inference nearly as much as it could have. A wide spectrum of activities are planned to bring together the important ideas and tools from these two fields, to supply each other with new perspectives and new approaches, and to hopefully generate a whole new engineering methodology for unifying classical signals and chaotic signals. Specific focus will be set on understanding the cause and impact of chaotic behavior in statistical inference, developing ways to control chaos and transient chaos, and using statistical inference on appropriate models, such as Markov random fields and factor graphs, to predict and synchronize chaotic systems. In view of the very pervasive scope of the practical applications associated with statistical inference algorithms and nonlinear dynamical theory, the research work in the proposed direction will have significant societal and scientific impacts. The potential application is broad, including many communication systems and discrete dynamical systems, such as cellular networks, wireless sensor and ad-hoc networks, digital data recording systems, radar systems, weather and tornado prediction, ecology, and population estimation. The proposed research also integrates a meaningful education and outreach component, which includes opening a series of seminars, supplying undergraduate and graduate students with theses projects, developing a new graduate level course, and engaging under-represented students in research.