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

MapReduce
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 zero-delay 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 two-way 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.

Selected Publications
Book Chapters:
[3] C. D. Charalambous, P. A. Stavrou, and C. K. Kourtellaris, "Directed information on abstract spaces: Properties and extremum Problems," Coordination Control of Distributed Systems (Edt. by Jan Van Schuppen and Tiziano Villa) in ser. Lecture Notes in Control and Information Sciences, Vol. 456, pp. 307-315, November 2014.
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Journal papers:
[2] C. D. Charalambous, and P. A. Stavrou, "Directed information on abstract spaces: properties and variational equalities," IEEE Transactions on Information Theory, vol. 62, Issue 11, pp. 6019-6052, November 2016.
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Conference papers:
[10] P. A. Stavrou and C. D. Charalambous, "Variational equalities of directed information and applications " in proceedings of IEEE International Symposium on Information Theory (ISIT), 2013.
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[7] C. D. Charalambous and P. A. Stavrou, "Directed information on abstract Alphabets: properties and extremum problems," in proceedings of IEEE International Symposium on Information Theory (ISIT), 2012.
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Causal and zero-delay processing of information in systems with memory and feedback

In this research we investigate the rate performance and the coding aspects of causal and zero-delay codes (i.e., a zero-delay 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 zero-delay rate distortion functions. A natural question that arise in this case is why not using the operational causal or zero-delay rate distortion functions instead of using this lower bound? The answer is because the operational causal or zero-delay rate distortion functions are highly non-convex 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 zero-delay rate distortion functions by means of this lower bound. This research aims to give meaningful answers to this fundamental question.

Zero-delay source coding system
Fig. An example of zero-delay processing of a Gauss-Markov source using variable-length coding.

Selected Publications
Book Chapters:
[2] P. A. Stavrou, C. K. Kourtellaris, and C. D. Charalambous, "Information nonanticipative rate distortion function and its applications," Coordination Control of Distributed Systems (Edt. by Jan Van Schuppen and Tiziano Villa) in ser. Lecture Notes in Control and Information Sciences, Vol. 456, pp. 317-324, November 2014.
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Journal papers:
[6] P. A. Stavrou, T. Charalambous, and C. D. Charalambous, "Optimal estimation via nonanticipative rate distortion function and applications to time-varying Gauss-Markov processes," SIAM Journal on Control and Optimization, Vol. 56, Issue 5, pp. 3731-3765, 2018.
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[5] P. A. Stavrou, J. Østergaard, and C. D. Charalambous, "Zero-delay rate distortion via filtering for vector-valued Gaussian sources," IEEE Journal of Selected Topics in Signal Processing , Vol. 12, Issue 5, pp. 841-856, October 2018.
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[4] P. A. Stavrou, T. Charalambous and C. D. Charalambous, "Finite-time nonanticipative rate distortion function for time-varying scalar-valued Gauss-Markov sources," IEEE Control Systems Letters, Vol. 2, Issue 1, pp. 175-180, January 2018.
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Conference papers:
[22] P. A. Stavrou, T. Charalambous, C. D. Charalambous, S. Loyka and M. Skoglund, Asymptotic reverse-waterfilling solution of nonanticipative rate distortion function for vector-valued Gauss-Markov sources, in proceedings of IEEE 57th Conference on Decision and Control (CDC), 2018 (accepted).
[20] P. A. Stavrou, J. Østergaard, and M. Skoglund, "On zero-delay source coding of LTI Gauss-Markov systems with covariance matrix distortion constraints," in proceedings of European Control Conference (ECC), 2018 (accepted).
[19] P. A. Stavrou and J. Østergaard, "Fixed-rate zero-delay source coding for stationary vector-valued Gauss-Markov sources," in proceedings of Data Compression Conference (DCC), 2018.
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[18] P. A. Stavrou, J. Østergaard, C. D. Charalambous, and M. Derpich, "An upper bound to zero-delay rate distortion via Kalman filtering for Vector Gaussian sources," in proceedings of IEEE Information Theory Workshop (ITW), 2017.
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[16] P. A. Stavrou and J. Østergaard, "A lower bound on causal and zero-delay rate distortion for scalar Gaussian autoregressive sources," in proceedings of International Symposium on Information Theory and Signal Processing in Benelux (SITB), 2017.
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[12] P. A. Stavrou, C. K. Kourtellaris, and C. D. Charalambous, "Applications of information nonanticipative rate distortion function," in proceedings of IEEE International Symposium on Information Theory (ISIT), 2014.
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Low-delay joint source-channel 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 source-channel communication systems the goal is to find source-channel 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 near-optimal 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.

Realization
Fig. Probabilistic low-delay lossy joint source-channel coding for sources with memory with respect to average distortion or excess distortion probability.

Selected Publications
Book Chapters:
[4] C. D. Charalambous, C. K. Kourtellaris, and P. A. Stavrou, "On Shannon's duality of a source and a channel and nonanticipative communication and communication for control," Coordination Control of Distributed Systems (Edt. by Jan Van Schuppen and Tiziano Villa) in ser. Lecture Notes in Control and Information Sciences, Vol. 456, pp. 291-305, November 2014.
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[1] C. K. Kourtellaris, C. D. Charalambous, and P. A. Stavrou, "Nonanticipative duality of sources and channels with memory and feedback," Coordination Control of Distributed Systems (Edt. by Jan Van Schuppen and Tiziano Villa) in ser. Lecture Notes in Control and Information Sciences, Vol. 456, pp. 325-335, November 2014.
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Conference papers:
[12] P. A. Stavrou, C. K. Kourtellaris, and C. D. Charalambous, "Applications of information nonanticipative rate distortion function," in proceedings of IEEE International Symposium on Information Theory (ISIT), 2014.
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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.

Feedback Capacity
Fig. Convergence of the binary erasure channel with memory to its feedback capacity after a finite number of transmissions.

Selected Publications
Journal papers:
[3] P. A. Stavrou, C. D. Charalambous and C. K. Kourtellaris, "Sequential necessary and sufficient conditions for capacity achieving distributions of channels with memory and feedback," IEEE Transactions on Information Theory, Vol. 63, Issue 11, pp. 7095-7115, November 2017.
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Conference papers:
[14] P. A. Stavrou, C. D. Charalambous, and C. K. Kourtellaris, "Sequential necessary and sufficient conditions for optimal channel input distributions of channels with memory and feedback," in proceedings of IEEE International Symposium on Information Theory (ISIT), 2016.
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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 low-delay 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 end-to-end average fidelity or distortion criterion.

Filtering
Fig. Communicating a possibly unstable source over a noisy channel via a feedback realization scheme.

Selected Publications
Book Chapters:
[4] C. D. Charalambous, C. K. Kourtellaris, and P. A. Stavrou, "On Shannon's duality of a source and a channel and nonanticipative communication and communication for control," Coordination Control of Distributed Systems (Edt. by Jan Van Schuppen and Tiziano Villa) in ser. Lecture Notes in Control and Information Sciences, Vol. 456, pp. 291-305, November 2014.
Full Text

Journals:
[6] P. A. Stavrou, T. Charalambous, and C. D. Charalambous, "Optimal estimation via nonanticipative rate distortion function and applications to time-varying Gauss-Markov processes," SIAM Journal on Control and Optimization, Vol. 56, Issue 5, pp. 3731-3765, 2018.
Full Text
[5] P. A. Stavrou, J. Østergaard, and C. D. Charalambous, "Zero-delay rate distortion via filtering for vector-valued Gaussian sources," IEEE Journal of Selected Topics in Signal Processing, Vol. 12, Issue 5, pp. 841-856, October 2018.
Full Text
[1] C. D. Charalambous, P. A. Stavrou, and N. U. Ahmed, "Nonanticipative rate distortion function and relations to filtering theory," IEEE Transactions on Automatic Control, Vol. 59, Issue 4, pp. 937-952, April 2014.
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Conference papers:
[22] P. A. Stavrou, T. Charalambous, C. D. Charalambous, S. Loyka and M. Skoglund, Asymptotic reverse-waterfilling solution of nonanticipative rate distortion function for vector-valued Gauss-Markov sources, in proceedings of IEEE 57th Conference on Decision and Control (CDC), 2018 (accepted).
[21] C. D. Charalambous, P. A. Stavrou, C. K. Kourtellaris and I. Tzortzis, "Directed Information subject to a fidelity: applications to conditionally Gaussian processes," in proceedings of European Control Conference (ECC), 2018 (accepted).
[17] M. Barforooshan, J. Østergaard, and P. A. Stavrou, "Achievable performance of zero-delay variable-rate coding in rate constrained networked control systems with channel delay," in proceedings of IEEE Conference on Decision and Control (CDC), 2017.
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[15] P. A. Stavrou, T. Charalambous, and C. D. Charalambous, "Filtering with fidelity for time-varying Gauss-Markov processes," in proceedings of IEEE 55th Conference on Decision and Control (CDC), 2016.
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[11] C. D. Charalambous and P. A. Stavrou, "Optimization of directed information and relations to filtering theory," in proceedings of 13th European Control Conference (ECC), 2014.
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[9] C. D. Charalambous and P. A. Stavrou, "On the relation of nonanticipative rate distortion function and filtering theory," in proceedings of 12th Biannual European Control Conference (ECC), 2013.
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