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, and convex optimization. Specifically, my research span the areas of: i) information theory, ii) stochastic control and estimation theory.
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 feedback. This investigation is established using information nonanticipative or sequential rate distortion function which is an achievable lower bound to the operational causal rate distortion function. A natural question that arise in this case is why not using the operational causal rate distortion function itself to quantify the rate performance and construct efficient achievable coding schemes that convey reliably information instead of using this lower bound? The answer is immediate since by definition the operational causal rate distortion function can be cast as a nonconvex optimization problem. As a result, it is extremely difficult to be solved explicitly. 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 including memory and feedback. In such systems, the question of interest is as follows. Using nonanticipative rate distortion function how close we can get to the operational causal rate distortion function? This research aims to providing insights to this question.
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Lowdelay joint sourcechannel coding
In this research we investigate the rate performance and the coding aspects of the ultimate communication scenario, that of merging the source dynamics and the channel dynamics in a unified framework. In such joint sourcechannel communication systems we aim into finding sourcechannel codes where the source and channel probability distributions, and the distortion measure of the source with the input cost function of the channel are favorably matched. Of particular interest in the recent technological advancements like for example in 5G communication systems is the requirement for transmission of information in short data packets reliably with lowlatency. This is another target of this research.
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Feedback capacity of channels with memory
In this research we investigate 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. Here we aim 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 networked 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 a lowdelay optimal communication strategy so that at the output of this 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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