On the fixed point problem in the abstract rate distortion theory
Date
2006ISBN
978-1-60423-792-4Publisher
University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical EngineeringSource
44th Annual Allerton Conference on Communication, Control, and Computing 200644th Annual Allerton Conference on Communication, Control, and Computing 2006
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1Pages
408-412Google Scholar check
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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.
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