On the uniform quantization of a class of sparse sources

Authors:
Aurélia Fraysse;Béatrice Pesquet-Popescu;Jean-Christophe Pesquet
Affiliations:
Laboratoire des Signaux et Systèmes, CNRS, Université Paris-Sud, Supélec, Gif Sur Yvette, France;Signal and Image Processing Department, Telecom ParisTech, Paris Cédex 13, France;Institut Gaspard Monge and CNRS, Université Paris-Est, Marne-la-Vallée Cedex 2, France
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

We consider the uniform scalar quantization of a class of mixed distributed memoryless sources, namely sources having a Bernoulli Generalized Gaussian (BGG) distribution. Both for low and high resolutions, asymptotic expressions of the distortion for a pth-order moment error measure, and close approximations of the entropy are provided for these sources. Operational rate-distortion functions at high bit rate and their slope factors at low bit rate are derived. The dependence of these results on p and the distribution parameters as well as the relation to the Shannon optimal rate-distortion bound are then discussed. The application of these results to transform coding in two simple cases is finally high-lighted.