×

zbMATH — the first resource for mathematics

A local structure of stationary perfectly noiseless codes between stationary non-ergodic sources. I: General considerations. (English) Zbl 0504.94021

MSC:
94A29 Source coding
PDF BibTeX XML Cite
Full Text: EuDML
References:
[1] P. Billingsley: Ergodic Theory and Information. Wiley, New York 1965. · Zbl 0141.16702
[2] R. Bowen: Equilibrium States and the ErgodicTheory of Anosov Diffeomorphisms. (Lecture Notes in Mathematics 470.) Springer - Verlag, Berlin-Heidelberg-New York 1975. · Zbl 0308.28010
[3] M. Denker: Finite generators for ergodic, measure-preserving transformations. Z. Wahrsch. verw. Gebiete 29 (1974), 45-55. · Zbl 0278.28006
[4] M. Denker, Ch. Grillenberger, and K. Sigmund: Ergodic Theory on Compact Spaces. (Lecture Notes in Mathematics 527.) Springer - Verlag, Berlin -Heidelberg-New York 1976. · Zbl 0328.28008
[5] M. Denker, M. Keane: Almost topological dynamical systems. Israel J. Math. 34 (1979), 139-160. · Zbl 0441.28008
[6] P. R. Halmos: Measure Theory. D. Van Nostrand, Princeton, N. J. 1950. · Zbl 0040.16802
[7] M. Keane, M. Smorodinsky: Bernoulli schemes of the same entropy are finitarily isomorphic. Ann. of Math. 109 (1979), 387-406. · Zbl 0405.28017
[8] J. C. Kieffer: Zero-error stationary coding over stationary channels. Z. Wahrsch. verw. Gebiete 56 (1981), 113-126. · Zbl 0444.94007
[9] J. C. Kieffer, M. Rahe: Selecting universal partitions in ergodic theory. Ann. Probab. 9 (1981), 705-709. · Zbl 0464.60036
[10] W. Krieger: On entropy and generators of measure-preservirg transformations. Trans. Amer. Math. Soc. 149 (1970), 453-464, Erratum, ibid. 168 (1972), 519. · Zbl 0204.07904
[11] D. S. Ornstein: Bernoulli shifts with the same entropy are isomorphic. Adv. in Math. 4 (1970), 337-352. · Zbl 0197.33502
[12] D. S. Ornstein: Ergodic Theory, Randomness, and Dynamical Systems. Yale Univ. Press, New Haven and London 1974. · Zbl 0296.28016
[13] J. C. Oxtoby: Ergodic sets. Bull. Amer. Math. Soc. 55 (1952), 116-136. · Zbl 0046.11504
[14] W. Parry: Entropy and Generators in Ergodic Theory. W. A. Benjamin, New York -Amsterdam 1969. · Zbl 0175.34001
[15] V. A. Rohlin: On the basic concepts of measure theory. (in Russian). Matem. Sborn. 25 (67) (1949), 107-150.
[16] P. C. Shields: Stationary coding of processes. IEEE Trans. Inform. Theory IT-25 (1979), 293-291. · Zbl 0401.94018
[17] M. Smorodinsky: Ergodic Theory, Entropy. (Lecture Notes in Mathematics 214.) Springer -Verlag, Berlin-Heidelberg-New York 1971. · Zbl 0213.07502
[18] K. Winkelbauer: On the asymptotic rate of non-ergodic information sources. Kybernetika 6 (1970), 127-148. · Zbl 0245.94013
[19] K. Winkelbauer: On the existence of finite generators for invertible measure-preserving transformations. Comment. Math. Univ. Carolinae 18 (1977), 789-812. · Zbl 0368.28020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.