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Uniform quantization of random processes

Quantization of a continuous-value signal into discrete form (or discretization of amplitude) is a standard task in all analog/digital devices. We consider quantization of a signal (or random process) in a probabilistic framework. The quantization method presented in this paper can be applied to signal coding and storage capacity problems. In order to demonstrate the general approach, the uniform quantization of a Gaussian process is studied in more detail. We investigate asymptotic properties of some accuracy characteristics, such as rate and distortion, in terms of correlation structure of the original random process when quantization cellwidth tends to zero. Some examples and numerical experiments are presented.