Research
My main research targets the study of fundamental performance limitations of networked control systems and the privacy aspects of such systems or other dynamical systems. The study of such complex systems can be characterized as interdisciplinary because it combines tools from control and estimation theories, communication and information theories, signal processing and optimization. My ongoing expertise span the areas of: i) information theory, ii) stochastic control and estimation theory, iii) signal processing, iv) convex optimization.
Properties of information measures
In this research, we study various functional and topological properties of information measures, such as, directed information, causally condition directed information or its variants. In information theory, directed information or its variants was primarily used to characterize the capacity of channels with feedback, some lossy compression problems and in network information theory. However, the last decade such information measures are widely used to characterize the fundamental performance limitations of delay constrained dynamical systems, like for instance, in networked control systems. This is because by definition, such measures can take into account the dynamics in systems where the components are modeled by (stochastic or deterministic) processes. The utility of directed information is not exhaustive to the previous research directions. Instead, it can be used in an anthology of problems like gambling, portfolio theory, or in biology as an alternative to Granger's measure of causality.
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Source coding and rate distortion theory
In this research direction, we study generalizations of classical source coding and Shannon's rate distortion theory but we are not limited to such problems. On the contrary, we ask the question how source coding and rate distortion theory can be applied to delayconstrained dynamical systems. Our question is motivated by the utility need of the next generation systems to process information as quick as possible and as reliably as possible. Those standards are the epitomy of the next generation of engineering systems, such as, cyberphysical systems or networked control systems. Our study is focued in identifying the fundamental performance limitations of systems that operate using causal and/or instantaneous codes, and in understanding practical coding schemes that can support such frameworks.
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Joint sourcechannel coding
In this research direction, we study sourcechannel codes which combined can achieve optimal or nearoptimal performance within a pointtopoint system or a network. We are primarily interested in delay constrained dynamical systems although we are not limited to those. Our motivation is partly to understand if such coding paradigms can be applied to the next generation of engineering systems hence providing meaningful answers related to the performance of such systems. Another key aspect that triggers our research interest herein, is that the high level joint construction of a transmitter, the (realworld) channel and the receiver that model a communication system is shown to be very hard to achieve even for simple networks.
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Feedback capacity of channels with memory
In this research direction, we are interested in computing the (ergodic) channel capacity of channels with memory and/or feedback. Ergodic feedback capacity is one of the fundamental characterizations in communication theory because it gives theoretical limitations on the least upper bound of allowable rate conveyed through a communication channel. However, characterizing the ergodic channel capacity of a communication system that is often expressed as an intractable optimization problem is not an easy task, let alone finding analytical expressions to such characterizations. In information theory, ergodic channel capacity is computed in closed form expressions for simple memoryless channels (defined either on finite alphabet or continuous alphabet spaces) For these simple channel models it is wellknown that the presence of noiseless feedback often makes the coding much simpler but it cannot outperform the ergodic channel capacity without noiseless feedback. Unfortunately, this is not the case for channels with memory and, thus, to arrive to similar conclusions as those deduced for the class of memoryless channels, one has to characterize and then find analytical or computable expressions for specific classes of channels with memory. The previous challenging task is the motivation behind this study.
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Communication and Coding for Networked Control Systems
In this research direction, we are interested in identifying fundamental performance limitations and practical coding schemes for simple networked control systems, for instance, a closed loop control system where the information plant conveys information via a communication channel (noisy or noiseless) that in turn connects the observer to the controller. In the case where the controller is fully or weakly separated from the communication part of the closed loop system, we wish to design lowdelay communication strategies which ensure that at the decoder of the communication system, the estimated process obtained based on an optimal minimum mean squared estimator (a la Kalman filter) satisfies an endtoend average fidelity or distortion criterion.
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