A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. II: Applications. (English) Zbl 0533.94001

This is Part II of a two-part paper and applies the results of Part I [Kybernetika 18, 361-375 (1982; Zbl 0504.94021)] to determine a complete set of invariants for the class of all conditionally Bernoulli sources, with respect to both metric and finitary isomorphisms. The results extend Ornstein and Keane-Smorodinsky isomorphism theorems. A generalization of Krieger’s finite generator theorem is proved in a form which exhibits a close connection between generator problems of ergodic theory and noiseless source coding. A finitary version of it yields an extension of an almost topological generator theorem of Denker and Keane. A result of Kieffer on zero-error transmission of ergodic sources over stationary channels is generalized to the transmission of aperiodic non-ergodic sources. A sufficient condition for \(\epsilon\)-transmissibility is derived which offers a new interpretation of \(\epsilon\)-rates.
Reviewer: G.Longo


94A29 Source coding
28D20 Entropy and other invariants


Zbl 0504.94021
Full Text: EuDML


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