High-resolution quantization and entropy coding for fractional Brownian motion

Details High-resolution quantization and entropy coding for fractional Brownian motion High-resolution quantization and entropy coding for fractional Brownian motion

2005-04-23

arxiv.org/abs/math/0504480v1

Mathematics

Probability

25 pages

Scientific paper

We derive a high-resolution formula for the quantization and entropy coding approximation quantities for fractional Brownian motion, respective to the supremum norm and L^p[0,1]-norm distortions. We show that all moments in the quantization problem lead to the same asymptotics. Using a general principle, we conclude that entropy coding and quantization coincide asymptotically. Under supremum-norm distortion, our proof uses an explicit construction of efficient codebooks based on a particular entropy constrained coding scheme. This procedure can be used to construct close to optimal high resolution quantizers.

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