The compressibility of stationary random processes

There are two types of inefficiencies in the time domain representation of a digitized random process. One is the time correlation between samples that causes one sample to be predictable based on the previous samples. Another is the non-uniform distribution of sample amplitudes. Maximum lossless compression of a stationary random process occurs when a sequence is completely decorrelated without loss and the decorrelated sequence is encoded at its entropy rate. This paper presents a mathematical description of theoretical limit of the compressibility of Gaussian stationary random processes.