Research
My main research interests target the design and analysis of wireless networked control systems. In such systems the control loops are closed via a communication network. As a result, its study necessitates the interplay between dynamical systems and their communication aspects. Toward this end, my research can be characterized as interdisciplinary because it combines tools from control and estimation theories, communications, signal processing and optimization. Specifically, my research spans the areas of: i) information theory, ii) stochastic control and estimation theory, iii) signal processing.
Properties of information measures in systems with memory and feedback
In this research we investigate functional and topological properties of directed information and its variants that is known to be a handy information measure that quantifies the information rate in systems with memory and feedback. Directed information from an input process to an output process captures the uncertainty of the latter due to the causal knowledge of the former. In information theory, directed information or its variants are used to characterize capacity of channels with memory and feedback and lossy data compression of causal and zerodelay codes. Moreover, it can be used in network communication systems as a metric for evaluating the capacity of special types of networks, such as, the twoway channel, the multiple access channel, etc. Furthermore, directed information has found usage in a variety of problems subject to causality constraints, such as, gambling, portfolio theory, data compression and hypothesis testing, in biology as an alternative to Granger's measure of causality, and in communication for networked control systems.
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Causal and zerodelay processing of information in systems with memory and feedback
In this research we investigate the rate performance and the coding aspects of causal and zerodelay codes (i.e., a zerodelay code is a causal code but not the other way around) in systems with memory and possibly feedback. This research is unfolded using an information theoretic measure called nonanticipative or sequential rate distortion function that is a lower bound to the operational causal and zerodelay rate distortion functions. A natural question that arise in this case is why not using the operational causal or zerodelay rate distortion functions instead of using this lower bound? The answer is because the operational causal or zerodelay rate distortion functions are highly nonconvex optimization problems. Therefore, it is extremely difficult these to be solved optimally. On the other hand, information nonanticipative rate distortion is a convex optimization problem which is often tractable and can be solved explicitly for a variety of systems which are designed to include memory and/or feedback. In such systems, the fundamental question is how close one can get to the operational causal or zerodelay rate distortion functions by means of this lower bound. This research aims to give meaningful answers to this fundamental question.
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Lowdelay joint sourcechannel coding
In this research we investigate the rate performance and the coding aspects of the fundamental communication setup, that of merging the source dynamics and the channel dynamics in a unified framework. In such joint sourcechannel communication systems the goal is to find sourcechannel codes where the source and the channel statistics, in addition to the distortion measure of the source with the input cost function of the channel are favorably matched. If not matched, then of interest is to investigate certain schemes that achieve a nearoptimal or satisfactory performance. Of particular interest in the recent state of the art systems like, for instance, in 5G communication systems, is the requirement for reliable transmission of information using short data packets whereas the system is forced to operate under stringent delay requirements.
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Feedback capacity of channels with memory
In this research we investigate the feedback capacity for a class of channels with memory with or without transmission cost constraints. Computing feedback capacity for any class of channel distributions with memory, with or without transmission cost constraints, computing the optimal probabilistic strategies that achieves feedback capacity, and determining whether feedback increases capacity, are fundamental and challenging open problems in information and communication theories for half a century. This research aims into determining the closed form expressions of the optimal strategies for a class of channels with memory without assuming a priori any assumptions of stationarity or ergodicity on the given channel.
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Communication and Coding for Networked Control Systems
In this research we investigate the communication aspects of a simple closed loop control system. In particular, we are interested in the source coding aspects of the realistic possibility that the channel connecting the observer to the controller might be noisy or noiseless. In the case where the controller is separated from the purely communication part of the closed loop system, we wish to design lowdelay communication strategies so that at the output of the feedback system, the estimated process obtained based on an optimal linear least squares estimator (Kalman filter) satisfies an endtoend average fidelity or distortion criterion.
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