Journals:
F. Rezaei and N.U. Ahmed and C.D. Charalambous, “Rate Distortion Theory for Abstract Sources with Potential Applications to Image Compression,” International Journal of Applied Mathematics, pages 141-165, Vol.3, No.2, 2006
Abstract
This paper introduces a general framework for dealing with the subject of rate distortion or source coding with fidelity criterion, in Polish spaces. Pre- vious well known results for abstract alphabets are extended to the more general case in which marginal measures on the reproduction space may not be absolutely continuous with respect to the optimal marginal measure. In this situation, the chain rule for Radon-Nikodym derivatives does not hold and hence standard techniques do not apply. This problem is resolved by developing a variational approach on the space of measure valued functions. It is also shown that the compactness assumption on the reproduction space can be relaxed. Moreover, the question of existence of a solution to the im- plicit equation of optimal distribution is addressed by proving a fixed point theorem. In the discrete alphabet case, the existence of such a solution follows from the Blahut algorithm. However in the abstract alphabet case, more analysis is needed. This is formulated as a fixed point problem on a suitable locally convex topological vector space. Existence of solution of the original problem is proved by establishing the existence of a fixed point.
Conferences:
C.D. Charalambous and Christos Kourtellaris “Rate Distortion with Causal Decoding,” in Proceeding of the 49th IEEE Conference on Decision and Control, Atlanta, Georgia, December 15-17, 2010
Abstract
This paper considers source coding of general sources with memory, when causal feedback is available at the decoder. The rate distortion function is defined as the infimum of the so-called directed information over causal data compression channels which satisfy a distortion fidelity constraint. The expression of the optimal causal data compression is derived. Further a tight lower bound on the rate distortion bound is derived. These are variants of the classical non-causal rate distortion function, and associate Shannon lower bound. Generalization of the results to controlled sources is also discussed.
F. Rezaei, C.D. Charalambous, and Photios A. Stavrou “Rate Distortion Function for a Class of Relative Entropy Sources,” ,” in 19th International Symposium on Network and Systems, Budapest, Hungary, July 5-July 9, 2010
Abstract
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and a nominal distribution. The rate distortion problem for the class is thus formulated and solved using minimax strategies, which result in robust source coding with fidelity criterion. It is shown that minimax and maxmin strategies can be computed explicitly, and they are generalizations of the classical solution. Finally, for discrete memoryless uncertain sources, the rate distortion theorem is stated for the class omitting the derivations while the converse is derived.
F. Rezaei, C.D. Charalambous and Photios Stavrou “Minimax Rate Distortion for a Class of Sources,” in 4th International Symposium on Communication, Control and Signal Processing, Limassol, Cyprus, March 3-March 5, 2010
Abstract
This paper deals with rate distortion or source coding with fidelity criterion, in measure spaces, for a class of source distributions. The class of source distributions is described by a relative entropy constraint set between the true and a nominal distribution. The rate distortion problem for the class is thus formulated and solved using minimax strategies, which result in robust source coding with fidelity criterion.
F. Rezaei and N.U. Ahmed and C.D. Charalambous, “On the Fixed Point Problem in the Abstract Rate Distortion Theory,” Forty-Four Annual Allerton Conference, Allerton House, University of Illinois-Urbana Champagne, Illinois, U.S.A., September 27-29, 2006
Abstract
This paper introduces a general framework for dealing with the subject of rate distortion or source coding with fidelity criterion, in Polish spaces. The problem is ad-dressed using a variational approach on the space of measure valued functions. Due to the implicit form of the optimal solution, the question of existence of solution is crucial. This is formulated as a fixed point problem on a suitable locally convex topological vector space (consisting of functions with values in the space of finitely additive measures). Existence of solution of the original problem is proved by establishing the existence of a fixed point.
