Asymptotics of the Epsilon-Entropy of Discrete Stationary Processes

The aim of the article is to obtain upper and lower asymptotic bounds for e-entropy of stationary sources and discrete time, with a finite number of states, and with a criterion of reproduction accuracy specified in terms of an additive loss function. In general the estimates obtained by us may be in asymptotic disagreement. They necessarily agree in the case of Markov sources. In § 1 we define concepts needed in formulating the problems and we introduce some notation. In § 2 we formulate the results; proofs of the results are contained in §§ 3, 4, and 5.