Successive refinement of vector sources under individual distortion criteria

  • Authors:

  • Jayanth Nayak;Ertem Tuncel;Deniz Gündüz;Elza Erkip

  • Affiliations:

  • Mayachitra Inc., Santa Barbara, CA and University of California, Riverside, CA;Department of Electrical Engineering, University of California, Riverside, CA;Centre Tecnológic de Telecomunicacions de Catalunya, Castelldefels, Barcelona, Spain and Department of Electrical Engineering, Princeton University, Princeton, NJ and Department of Electrical ...;Polytechnic Institute of New York University, Brooklyn, NY

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2010

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Abstract

The successive refinement problem is extended to vector sources where individual distortion constraints are posed on each vector component. For vector Gaussian sources with squared-error distortion, a single-letter rate-distortion characterization is inherited from the previously studied Gaussian multiple descriptions problem with covariance distortion constraints. Though this characterization is amenable to well-known numerical convex optimization techniques, an analytical solution is difficult to obtain in full generality even for 2-D sources. In this work, the special case of successive refinability is addressed analytically. Specifically, vector Gaussian sources are shown to be not successively refinable everywhere unlike scalar Gaussian sources. It is also shown that, for 2-D Gaussian sources, the rate loss at the second stage can be as high as 0.5 b/sample in a "degenerate" scenario corresponding to what is known as sequential coding of correlated sources. Finally, analysis of 2-D binary symmetric sources with Hamming distortion reveals that the behavior of these sources with respect to successive refinability exhibits remarkable similarity to their 2-D Gaussian counterparts.