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Charalambos D. Charalambous - One of the best experts on this subject based on the ideXlab platform.
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joint nonanticipative rate Distortion Function for a tuple of random processes with individual fidelity criteria
arXiv: Information Theory, 2021Co-Authors: Charalambos D. Charalambous, Evagoras StylianouAbstract:The joint nonanticipative rate Distortion Function (NRDF) for a tuple of random processes with individual fidelity criteria is considered. Structural properties of optimal test channel distributions are derived. Further, for the application example of the joint NRDF of a tuple of jointly multivariate Gaussian Markov processes with individual square-error fidelity criteria, a realization of the reproduction processes which induces the optimal test channel distribution is derived, and the corresponding joint NRDF is characterized. The analysis of the simplest example, of a tuple of scalar correlated Markov processes, illustrates many of the challenging aspects of such problems.
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joint rate Distortion Function of a tuple of correlated multivariate gaussian sources with individual fidelity criteria
arXiv: Information Theory, 2021Co-Authors: Evagoras Stylianou, Charalambos D. Charalambous, Themistoklis CharalambousAbstract:In this paper we analyze the joint rate Distortion Function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual Distortion criteria. First, we derive structural properties of the realizations of the reproduction Random Variables (RVs), which induce the corresponding optimal test channel distributions of the joint RDF. Second, we consider a tuple of correlated multivariate jointly Gaussian RVs, $X_1 : \Omega \rightarrow {\mathbb R}^{p_1}, X_2 : \Omega \rightarrow {\mathbb R}^{p_2}$ with two square-error fidelity criteria, and we derive additional structural properties of the optimal realizations, and use these to characterize the RDF as a convex optimization problem with respect to the parameters of the realizations. We show that the computation of the joint RDF can be performed by semidefinite programming. Further, we derive closed-form expressions of the joint RDF, such that Gray's [1] lower bounds hold with equality, and verify their consistency with the semidefinite programming computations.
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Generalizations of Nonanticipative Rate Distortion Function to Multivariate Nonstationary Gaussian Autoregressive Processes
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Co-Authors: Charalambos D. Charalambous, Themistoklis Charalambous, Christos Kourtellaris, Jan H. Van SchuppenAbstract:The characterizations of nonanticipative rate Distortion Function (NRDF) on a finite horizon are generalized to nonstationary multivariate Gaussian order L autoregressive, AR(L), source processes, with respect to mean square error (MSE) Distortion Functions. It is shown that the optimal reproduction distributions are induced by a reproduction process, which is a linear Function of the state of the source, its best mean-square error estimate, and a Gaussian random process.
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asymptotic reverse waterfilling characterization of nonanticipative rate Distortion Function of vector valued gauss markov processes with mse Distortion
Conference on Decision and Control, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey Loyka, Mikael SkoglundAbstract:We analyze the asymptotic nonanticipative rate Distortion Function (NRDF) of vector-valued Gauss-Markov processes subject to a mean-squared error (MSE) Distortion Function. We derive a parametric characterization in terms of a reverse-waterfilling algorithm, that requires the solution of a matrix Riccati algebraic equation (RAE). Further, we develop an algorithm reminiscent of the classical reverse-waterfilling algorithm that provides an upper bound to the optimal solution of the reverse-waterfilling optimization problem, and under certain cases, it operates at the NRDF. Moreover, using the characterization of the reverse-waterfilling algorithm, we derive the analytical solution of the NRDF, for a simple two-dimensional parallel Gauss-Markov process. The efficacy of our proposed algorithm is demonstrated via an example.
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optimal estimation via nonanticipative rate Distortion Function and applications to time varying gauss markov processes
Siam Journal on Control and Optimization, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey LoykaAbstract:In this paper, we develop finite-time horizon causal filters for general processes taking values in Polish spaces using the nonanticipative rate Distortion Function ($NRDF$). Subsequently, we apply...
Photios A Stavrou - One of the best experts on this subject based on the ideXlab platform.
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asymptotic reverse waterfilling characterization of nonanticipative rate Distortion Function of vector valued gauss markov processes with mse Distortion
Conference on Decision and Control, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey Loyka, Mikael SkoglundAbstract:We analyze the asymptotic nonanticipative rate Distortion Function (NRDF) of vector-valued Gauss-Markov processes subject to a mean-squared error (MSE) Distortion Function. We derive a parametric characterization in terms of a reverse-waterfilling algorithm, that requires the solution of a matrix Riccati algebraic equation (RAE). Further, we develop an algorithm reminiscent of the classical reverse-waterfilling algorithm that provides an upper bound to the optimal solution of the reverse-waterfilling optimization problem, and under certain cases, it operates at the NRDF. Moreover, using the characterization of the reverse-waterfilling algorithm, we derive the analytical solution of the NRDF, for a simple two-dimensional parallel Gauss-Markov process. The efficacy of our proposed algorithm is demonstrated via an example.
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optimal estimation via nonanticipative rate Distortion Function and applications to time varying gauss markov processes
Siam Journal on Control and Optimization, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey LoykaAbstract:In this paper, we develop finite-time horizon causal filters for general processes taking values in Polish spaces using the nonanticipative rate Distortion Function ($NRDF$). Subsequently, we apply...
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finite time nonanticipative rate Distortion Function for time varying scalar valued gauss markov sources
IEEE Control Systems Letters, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. CharalambousAbstract:We derive the finite-time horizon nonanticipative rate Distortion Function (NRDF) of time-varying scalar Gauss–Markov sources under an average mean squared-error (MSE) Distortion fidelity. Further, we show that a conditionally Gaussian reproduction process realizes the optimal reproduction distribution, and this is determined from the solution of a dynamic reverse-waterfilling optimization problem. We provide an iterative algorithm that approximates the solution of the dynamic reverse-waterfilling problem. From the above results, we also obtain, as a special case, the NRDF under a per-letter or pointwise MSE Distortion fidelity, and we draw connections to the classical RDF of Gaussian processes. Our results are corroborated with illustrative examples.
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information nonanticipative rate Distortion Function and its applications
arXiv: Information Theory, 2015Co-Authors: Photios A Stavrou, Christos K Kourtellaris, Charalambos D. CharalambousAbstract:In this chapter, we introduce the information nonanticipative rate Distortion Function (RDF), and we compare it with the classical information RDF, identifying certain limitations of the later, with respect to nonanticipative or real-time transmission for delay-sensitive applications. Then, we proceed further to describe applications of nonanticipative RDF in (1) joint source-channel coding (JSCC) using nonanticipative (delayless) transmission, and in (2) bounding the optimal performance theoretically attainable (OPTA) by noncausal and causal codes for general sources. Finally, to facilitate the application of the information nonanticipative RDF in computing the aforementioned bounds and in applying it to JSCC based on nonanticipative transmission, we proceed further to present the expression of the optimal reproduction distribution for nonstationary sources.
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applications of information nonanticipative rate Distortion Function
International Symposium on Information Theory, 2014Co-Authors: Photios A Stavrou, Christos K Kourtellaris, Charalambos D. CharalambousAbstract:The objective of this paper is to further investigate various applications of information Nonanticipative Rate Distortion Function (NRDF) by discussing two working examples, the Binary Symmetric Markov Source with parameter p (BSMS(p)) with Hamming distance Distortion, and the multidimensional partially observed Gaussian-Markov source. For the BSMS(p), we give the solution to the NRDF, and we use it to compute the Rate Loss (RL) of causal codes with respect to noncausal codes. For the multidimensional Gaussian-Markov source, we also give the solution to the NRDF, we show its operational meaning via joint source-channel matching over a vector of parallel Gaussian channels, and we compute the RL of causal and zero-delay codes with respect to noncausal codes.
Themistoklis Charalambous - One of the best experts on this subject based on the ideXlab platform.
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joint rate Distortion Function of a tuple of correlated multivariate gaussian sources with individual fidelity criteria
arXiv: Information Theory, 2021Co-Authors: Evagoras Stylianou, Charalambos D. Charalambous, Themistoklis CharalambousAbstract:In this paper we analyze the joint rate Distortion Function (RDF), for a tuple of correlated sources taking values in abstract alphabet spaces (i.e., continuous) subject to two individual Distortion criteria. First, we derive structural properties of the realizations of the reproduction Random Variables (RVs), which induce the corresponding optimal test channel distributions of the joint RDF. Second, we consider a tuple of correlated multivariate jointly Gaussian RVs, $X_1 : \Omega \rightarrow {\mathbb R}^{p_1}, X_2 : \Omega \rightarrow {\mathbb R}^{p_2}$ with two square-error fidelity criteria, and we derive additional structural properties of the optimal realizations, and use these to characterize the RDF as a convex optimization problem with respect to the parameters of the realizations. We show that the computation of the joint RDF can be performed by semidefinite programming. Further, we derive closed-form expressions of the joint RDF, such that Gray's [1] lower bounds hold with equality, and verify their consistency with the semidefinite programming computations.
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Generalizations of Nonanticipative Rate Distortion Function to Multivariate Nonstationary Gaussian Autoregressive Processes
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Co-Authors: Charalambos D. Charalambous, Themistoklis Charalambous, Christos Kourtellaris, Jan H. Van SchuppenAbstract:The characterizations of nonanticipative rate Distortion Function (NRDF) on a finite horizon are generalized to nonstationary multivariate Gaussian order L autoregressive, AR(L), source processes, with respect to mean square error (MSE) Distortion Functions. It is shown that the optimal reproduction distributions are induced by a reproduction process, which is a linear Function of the state of the source, its best mean-square error estimate, and a Gaussian random process.
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asymptotic reverse waterfilling characterization of nonanticipative rate Distortion Function of vector valued gauss markov processes with mse Distortion
Conference on Decision and Control, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey Loyka, Mikael SkoglundAbstract:We analyze the asymptotic nonanticipative rate Distortion Function (NRDF) of vector-valued Gauss-Markov processes subject to a mean-squared error (MSE) Distortion Function. We derive a parametric characterization in terms of a reverse-waterfilling algorithm, that requires the solution of a matrix Riccati algebraic equation (RAE). Further, we develop an algorithm reminiscent of the classical reverse-waterfilling algorithm that provides an upper bound to the optimal solution of the reverse-waterfilling optimization problem, and under certain cases, it operates at the NRDF. Moreover, using the characterization of the reverse-waterfilling algorithm, we derive the analytical solution of the NRDF, for a simple two-dimensional parallel Gauss-Markov process. The efficacy of our proposed algorithm is demonstrated via an example.
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optimal estimation via nonanticipative rate Distortion Function and applications to time varying gauss markov processes
Siam Journal on Control and Optimization, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. Charalambous, Sergey LoykaAbstract:In this paper, we develop finite-time horizon causal filters for general processes taking values in Polish spaces using the nonanticipative rate Distortion Function ($NRDF$). Subsequently, we apply...
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finite time nonanticipative rate Distortion Function for time varying scalar valued gauss markov sources
IEEE Control Systems Letters, 2018Co-Authors: Photios A Stavrou, Themistoklis Charalambous, Charalambos D. CharalambousAbstract:We derive the finite-time horizon nonanticipative rate Distortion Function (NRDF) of time-varying scalar Gauss–Markov sources under an average mean squared-error (MSE) Distortion fidelity. Further, we show that a conditionally Gaussian reproduction process realizes the optimal reproduction distribution, and this is determined from the solution of a dynamic reverse-waterfilling optimization problem. We provide an iterative algorithm that approximates the solution of the dynamic reverse-waterfilling problem. From the above results, we also obtain, as a special case, the NRDF under a per-letter or pointwise MSE Distortion fidelity, and we draw connections to the classical RDF of Gaussian processes. Our results are corroborated with illustrative examples.
Ram Zamir - One of the best experts on this subject based on the ideXlab platform.
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High-resolution source coding for nondifference Distortion measures: The rate Distortion Function,” this issue
2016Co-Authors: Ram Zamir, Kenneth Zeger, Senior MemberAbstract:Abstract—Entropy-coded vector quantization is studied using high-resolution multidimensional companding over a class of non-difference Distortion measures. For Distortion measures which are “locally quadratic ” a rigorous derivation of the asymptotic Distortion and entropy-coded rate of multidimensional compan-ders is given along with conditions for the optimal choice of the compressor Function. This optimum compressor, when it exists, depends on the Distortion measure but not on the source distribution. The rate-Distortion performance of the companding scheme is studied using a recently obtained asymptotic expression for the rate-Distortion Function which parallels the Shannon lower bound for difference Distortion measures. It is proved that the high-resolution performance of the scheme is arbitrarily close to the rate-Distortion limit for large quantizer dimensions if the compressor Function and the lattice quantizer used in the companding scheme are optimal, extending an analogous state-ment for entropy-coded lattice quantization and MSE Distortion. The companding approach is applied to obtain a high-resolution quantizing scheme for noisy sources. Index Terms—Asymptotic quantization theory, entropy coding, lattice quantizers, multidimensional companding, non-difference Distortion measures, rate-Distortion Function. I
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achieving the gaussian rate Distortion Function by prediction
IEEE Transactions on Information Theory, 2008Co-Authors: Ram Zamir, Yuval Kochman, Uri ErezAbstract:The ldquowater-fillingrdquo solution for the quadratic rate-Distortion Function of a stationary Gaussian source is given in terms of its power spectrum. This formula naturally lends itself to a frequency domain ldquotest-channelrdquo realization. We provide an alternative time-domain realization for the rate-Distortion Function, based on linear prediction. The predictive test channel has some interesting implications, including the optimality at all Distortion levels of pre/post filtered vector-quantized differential pulse-code modulation (DPCM), and a duality relationship with decision-feedback equalization (DFE) for intersymbol interference (ISI) channels.
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Achieving the Gaussian Rate-Distortion Function by Prediction
arXiv: Information Theory, 2007Co-Authors: Ram Zamir, Yuval Kochman, Uri ErezAbstract:The "water-filling" solution for the quadratic rate-Distortion Function of a stationary Gaussian source is given in terms of its power spectrum. This formula naturally lends itself to a frequency domain "test-channel" realization. We provide an alternative time-domain realization for the rate-Distortion Function, based on linear prediction. This solution has some interesting implications, including the optimality at all Distortion levels of pre/post filtered vector-quantized differential pulse code modulation (DPCM), and a duality relationship with decision-feedback equalization (DFE) for inter-symbol interference (ISI) channels.
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High-resolution source coding for non-difference Distortion measures: the rate Distortion Function
IEEE Transactions on Information Theory, 1999Co-Authors: Tamas Linder, Ram ZamirAbstract:The problem of asymptotic (i,e., low-Distortion) behavior of the rate-Distortion Function of a random vector is investigated for a class of non-difference Distortion measures. The main result is an asymptotically tight expression which parallels the Shannon lower bound for difference Distortion measures. For example, for an input-weighted squared error Distortion measure d(x,y)=/spl par/W(x)(y-x)/spl par//sup 2/,y,x/spl isin/R/sup n/, the asymptotic expression for the rate-Distortion Function of X/spl isin/R/sup n/ at Distortion level D equals h(X)-/sub 2///sup n/log(2/spl pi/eD/n)+Elog|detW(X)| where h(X) is the differential entropy of X. Extensions to stationary sources and to high-resolution remote ("noisy") source coding are also given.
Jan H. Van Schuppen - One of the best experts on this subject based on the ideXlab platform.
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Generalizations of Nonanticipative Rate Distortion Function to Multivariate Nonstationary Gaussian Autoregressive Processes
2019 IEEE 58th Conference on Decision and Control (CDC), 2019Co-Authors: Charalambos D. Charalambous, Themistoklis Charalambous, Christos Kourtellaris, Jan H. Van SchuppenAbstract:The characterizations of nonanticipative rate Distortion Function (NRDF) on a finite horizon are generalized to nonstationary multivariate Gaussian order L autoregressive, AR(L), source processes, with respect to mean square error (MSE) Distortion Functions. It is shown that the optimal reproduction distributions are induced by a reproduction process, which is a linear Function of the state of the source, its best mean-square error estimate, and a Gaussian random process.