On the Uniform Quantization of a Class of Sparse Sources

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 highlighted.