@article{KYB_1983_19_Suppl_a0,
author = {\v{S}ujan, \v{S}tefan},
title = {Ergodic theory, entropy, and coding problems of information theory},
journal = {Kybernetika},
pages = {1--66},
year = {1983},
volume = {19},
number = {Suppl},
mrnumber = {0902063},
zbl = {0542.94006},
language = {en},
url = {http://geodesic.mathdoc.fr/item/KYB_1983_19_Suppl_a0/}
}
Šujan, Štefan. Ergodic theory, entropy, and coding problems of information theory. Kybernetika, Tome 19 (1983), pp. 1-66. http://geodesic.mathdoc.fr/item/KYB_1983_19_Suppl_a0/
[1] M. A. Ackoglu A. del Junco, and M. Rahe: Finitary codes between Markov processes. Z. Wahrsch. verw. Gebiete 47 (1979), 305-314. | MR
[2] R. L. Adler W. Goodwyn, and B. Weiss: Equivalence of topological Markov shifts. Israel J. Math. 27 (1977), 49-63. | MR
[3] R. L. Adler A. G. Konheim, and M. H. McAndrew: Topological entropy. Trans. Amer. Math. Soc. 114 (1965), 309-319. | MR
[4] R. L. Adler, B. Marcus: Topological entropy and equivalence of dynamical systems. Memoirs Amer. Math. Soc. 219 (1979). | MR | Zbl
[5] R. L. Adler, B. Weiss: Similarity of the automorphisms of the torus. Memoirs Amer. Math. Soc. 98 (1970). | MR
[6] V. M. Alekseev: Symbolic Dynamics. (in Russian). Math. Institute, AN USSR, Kiev 1976. | MR
[7] V. M. Alekseev, M. V. Jakobson: Symbolic dynamics and hyperbolic dynamical systems. (in Russian). Supplement to R. Bowen: Methods of Symbolic Dynamics (in Russian). Mir, Moskva 1979, pp. 196-240.
[8] R. B. Ash: Information Theory. J. Wiley, New York 1965. | MR | Zbl
[9] T. Berger: Rate Distortion Theory. Prentice Hall, Englewood Cliff's 1971. | MR
[10] T. Berger: Information singular processes. IEEE Trans. Inform. Theory IT-20 (1975), 502-511.. | MR
[11] P. Billingsley: Ergodic Theory and Information. J. Wiley, New York-London-Sydney 1965. | MR | Zbl
[12] P. Billingsley: Convergence of Probability Measures. J. Wiley, New York-London-Sydney-Toronto 1968. | MR | Zbl
[13] R. E. Blahut: Computation of channel capacity and rate-distortion functions. IEEE Trans. Inform. Theory IT-18 (1972), 460-473. | MR | Zbl
[14] H. Blasbalg, R. van Blerkom: Message compression. IRE Trans. Space Electron. Telemech. 1962, 228-338.
[15] J. R. Blum, D. L. Hanson: On invariant probability measures I. Pacific J. Math. 10 (1960), 1125-1240.
[16] J. R. Blum, D. L. Hanson: On the isomorphism problem for Bernoulli schemes. Bull. Amer. Math. Soc. 63 (1963), 221-223. | MR | Zbl
[17] R. Bowen: Symbolic dynamics for hyperbolic systems. Amer. J. Math. 95 (1973), 429-459. | MR | Zbl
[18] R. Bowen: Topological entropy for non-compact sets. Trans. Amer. Math. Soc. 184 (1973), 413-423. | MR
[19] R. Bowen: Smooth partitions of Anosov diffeomorphisms are weak Bernoulli. Israel J. Math. 27(1975), 95-100. | MR | Zbl
[20] R. Bowen: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. (Lecture Notes in Mathematics 470.) Springer-Verlag, Berlin-Heidelberg-New York 1975. | MR | Zbl
[21] R. Bowen, D. Ruelle: The ergodic theory of Axiom A flows. Invent. Mathematicae 29 (1975), 181-202. | MR | Zbl
[22] R. C. Bradley, Jr.: On the strong mixing and weak Bernoulli conditions. Z. Wahrsch. verw. Gebiete 51 (1980), 49-54. | MR | Zbl
[23] A. A. Brudno: Entropy and algorithmic complexity of trajectories of a dynamical system. (in Russian). Preprint, VNIISI, Moskva 1980.
[24] E. Coven, M. Paul: Endomorphisms of irreducible shifts of finite type. Math. Systems Theory 8(1974), 165-175. | MR
[25] L. D. Davisson: Universal noiseless coding. IEEE Trans. Inform. Theory IT-19 (1973), 783-795. | MR | Zbl
[26] L. D. Davisson, R. M. Gray: A simplified proof of the sliding-block source coding theorem and its universal extension. Proc. Int. Conf. on Communication, Vol. 2, pp. 34.4.1 - 34.4.5. Toronto, Canada 1978. | MR
[27] A. del Junco, M. Rahe: Finitary codings and weak Bernoulli partitions. Proc. Amer. Math. Soc. 75 (1979), 259-364. | MR | Zbl
[28] M. Denker: Finite generators for ergodic measure-preserving transformations. Z. Wahrsch. verw. Gebiete 29 (1974), 45-55. | MR
[29] M. Denker: Generators and almost topological isomorphisms. Astérisque 59 (1977), 23-35. | MR
[30] M. Denker C. Grillenberger, and K. Sigmund: Ergodic Theory on Compact Spaces. (Lecture Notes in Mathematics 527.) Springer-Verlag, Berlin-Heidelberg-New York 1976. | MR
[31] M. Denker, M. Keane: Almost topological dynamical systems. Israel J. Math. 34 (1979), 139-160. | MR | Zbl
[32] M. Denker, M. Keane: Finitary codes and the law of the iterated logarithm. Z. Wahrsch. verw. Gebiete 52 (1980), 321-331. | MR | Zbl
[33] J. G. Dunham: Abstract alphabet sliding-block entropy compression coding with a fidelity criterion. Ann. Probab. 8 (1980), 1085-1092. | MR | Zbl
[34] R. Fellgett, W. Parry: Endomorphisms of a Lebesgue space II. Israel J. Math. 21 (1975), 167-172. | MR | Zbl
[35] B. M. Fitingoff: Optimal coding in case of unknown and changing message statistics. (in Russian). Problemy Peredachi Informacii 2 (1966), 3-11. | MR
[36] B. M. Fitingoff: The compression of discrete information. (in Russian). Problemy Peredachi Informacii 3 (1967), 28-36. | MR
[37] R. J. Fontana R. M. Gray, and J. C. Kieffer: Asymptotically mean stationary channels. IEEE Trans. Inform. Theory IT-27 (1981), 308-316. | MR
[38] N. Friedman, D. S. Ornstein: On the isomorphism of weak Bernoulli transformations. Adv. in Math. 5 (1970), 365-394. | MR
[39] R. G. Gallager: Information Theory and Reliable Communication. J. Wiley, New York 1968. | Zbl
[40] F. R. Gantmacher: The Theory of Matrices. Vols. I and II. Chelsea, New York 1959. | Zbl
[41] R. M. Gray: Sliding-block source coding. IEEE Trans. Inform. Theory IT-21 (1975), 357-368. | MR | Zbl
[42] R. M. Gray, L. D. Davisson: The ergodic decomposition of stationary discrete random processes. IEEE Trans. Inform. Theory IT-20 (1974), 625 - 636. | MR | Zbl
[43] R. M. Gray, L. D. Davisson: Source coding theorems without the ergodic assumption. IEEE Trans. Inform. Theory IT-20 (1974), 502-516. | MR | Zbl
[44] R. M. Gray, J. C. Kieffer: Mutual information rate, distortion, and quantization in metric spaces. IEEE Trans. Inform. Theory IT-26 (1980), 412-422. | MR | Zbl
[45] R. M. Gray, J. C. Kieffer: Asymptotically mean stationary measures. Ann. Probab. (1980), 962-973. | MR | Zbl
[46] R. M. Gray D. L. Neuhoff, and J. K. Omura: Process definitions of distortion-rate function and source coding theorems. IEEE Trans. Inform. Theory IT-21 (1975), 524-532. | MR
[47] R. M. Gray D. L. Neuhoff, and D. S. Ornstein: Non block source coding with a fidelity criterion. Ann. Probab. 3 (1975), 478-491. | MR
[48] R. M. Gray D. L. Neuhoff, and P. C. Shields: A generalization of Ornstein's d-distance with applications to information theory. Ann. Probab. 3 (1975), 315 - 328. | MR
[49] R. M. Gray, D. S. Ornstein: Sliding-block joint source/noisy channel coding theorems. IEEE Trans. Inform. Theory IT-22 (1976), 683-690. | MR | Zbl
[50] R. M. Gray, D. S. Ornstein: Block coding for discrete stationary d-continuous noisy channels. IEEE Trans. Inform. Theory IT-25 (1979), 292-306. | MR
[51] R. M. Gray D. S. Ornstein, and R. L. Dobrushin: Block synchronization, sliding-block coding, invulnerable sources, and zero-error codes for discrete noisy channels. Ann. Probab. 8 (1980), 639-674. | MR
[52] C. Grillenberger, U. Krengel: On marginaldistributionsandisomorphisms of stationary processes. Math. Z. 149, (1976), 131-154. | MR
[53] B. Hajek: Information-singularity and recoverability of random processes. IEEE Trans. Inform. Theory IT-28 (1983), 422-429. | MR
[54] P. R. Halmos: Measure Theory. D. Van Nostrand, Princeton N. J. 1950. | MR | Zbl
[55] P. R. Halmos: Lectures on Ergodic Theory. Chelsea, New York 1953.
[56] G. Hansel, J. P. Raoult: Ergodicité, uniformité et unique ergodicité. Indiana Univ. Math. J. 23 (1973), 221-237. | MR
[57] R. Heim: On the algorithmic foundations of information theory. IEEETrans. Inform. Theory 1T-25 (1979), 557-566. | MR
[58] R. I. Jewett: The prevalence of uniquely ergodic systems. J. Math. and Mech. 19 (1970), 717-729. | MR | Zbl
[59] M. Keane: Coding problems in ergodic theory. Proc. Int. Conf. on Math. Physics. Camerino, Italy, 1974.
[60] M. Keane, M. Smorodinsky: A class of finitary codes. Israel J. Math. 26 (1977), 352-371. | MR | Zbl
[61] M. Keane, M. Smorodinsky: Bernoulli schemes of the same entropy are finitarily isomorphic. Ann. Math. 109 (1979). 397-406. | MR | Zbl
[62] M. Keane, M. Smorodinsky: The finitary isomorphism theorem for Markov shifts. Bull. (New Series) Amer. Math. Soc. 1 (1979), 436-438. | MR | Zbl
[63] A. I. Khinchine: Mathematical Foundations of Information Theory. Dover, New York 1957. | MR
[64] J. C. Kieffer: On approximation of stationary measures by periodic and ergodic measures. Ann. Probab. 2 (1974), 530-534. | MR
[65] J. C. Kieffer: A generalized Shannon-McMillan theorem for the action of an amenable group on a probability space. Ann. Probab. 3 (1975), 1031 - 1037. | MR
[66] J. C. Kieffer: Block coding for an ergodic source relative to a zero-one valued fidelity criterion. IEEE Trans. Inform. Theory IT-24 (1978), 432-438. | MR | Zbl
[67] J. C. Kieffer: A unified approach to weak universal source coding. IEEE Trans. Inform. Theory IT-24 (1978), 674-682. | MR | Zbl
[68] J. C. Kieffer: On the minimum rate for strong universal block coding of a class of ergodic sources. IEEE Trans. Inform. Theory IT-26 (1980), 693-702. | MR | Zbl
[69] J. C. Kieffer: On the transmission of Bernoulli sources over stationary channels. Ann. Probab. 8 (1980), 942-961. | MR | Zbl
[70] J. C. Kieffer: On coding a stationary process to achieve a given marginal distribution. Ann. Probab. 8 (1980), 131-141. | MR
[71] J. C. Kieffer: Extensions of source codirig theorems for block codes to sliding-block codes. IEEE Trans. Inform. Theory IT-26 (1970), 679-692. | MR
[72] J. C. Kieffer: Stationary coding over stationary channels. Z. Wahrsch. verw. Gebiete 56 (1981), 113-136. | MR | Zbl
[73] J. C. Kieffer: Block coding for weakly continuous channels. IEEE Trans. Inform. Theory IT-27 (1981), 721-727. | MR | Zbl
[74] J. C. Kieffer: Perfect transmission over a discrete memoryless channel requires infinite expected coding time. J. Combin. Inform. System Sci. 5 (1980), 317-322. | MR | Zbl
[75] J. C. Kieffer: Sliding-Ыock coding for weakly continuous channels. IEEE Trans. Inform. Theory IT-28 (1982), 2-10. | MR
[76] J. C. Kieffer: Characterizations of d-total boundedness for classes of B sources. IEEE Trans. Inform. Theory IT-28 (1982), 26-35. | MR | Zbl
[77] J. C. Kieffer: On obtaining a stationary process isomorphic to a given process with a desired distribution. Preprint, Univ. of Missouri at Rolla, 1982. | MR
[78] J. C. Kieffer: Generators with prescribed marginals for nonergodic automorphisms. Lecture presented at the 9th Prague Conf. Inform. Theory, Prague, June 1982. | MR
[79] J. C. Kieffer, M. Rahe: Selecting universal partitions in ergodic theory. Ann. Probab. 9 (1981), 705-709. | MR | Zbl
[80] A. N. Kolmogorov: A new metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces. (in Russian). Doklady AN SSSR 119 (1958), 862-864. | MR
[81] A. N. Kolmogorov: The three approaches to the definition of the concept "amount of information". (in Russian). Problemy Peredachi Informacii 5 (1965), 3 - 7. | MR
[82] I. P. Kornfeľd, Ya. G. Sinai, and S. V. Fomin: Ergodic Theory. (in Russian). Nauka, Moskva 1980. | MR
[83] U. Krengel: Recent results on generators in ergodic theory. Trans. бth Conf. Inform. Theory etc, Academia, Prague 1973, 465 - 482. | MR | Zbl
[84] U. Krengel: Discussion of Professor's Ornstein's paper. (see [45]). Ann. Probab. 1 (1973).
[85] W. Krieger: On entropy and generators of measure-preserving transformations. Trans. Amer. Math. Soc. 119 (1970), 453-464. Erratum: ibid. 168 (1972), 519. | MR | Zbl
[86] W. Krieger: On unique ergodicity. Proc. бth Berkeley Symp. Math. Stat. Prob., Vol. I. University of California Press, Los Angeles 1972, 327-346. | MR | Zbl
[87] N. Kryloff, N. Bogoliouboff: La théorie générale de la mesure dans son application à ľétude des systémes dynamiques de la mécanique non linéaire. Ann. Math. 38 (1937), 65-113. | MR
[88] A. G. Kushnirenko: On metric invariants of entropy type. (in Russian). Uspehi Mat. Nauk 22 (1967), 57-65. | MR | Zbl
[89] A. Leon-Garcia L. D. Davisson, and D. L. Neuhoff: New results on coding of stationary nonergodic sources. IEEE Trans. Inform. Theory IT-25 (1979), 137-144. | MR
[90] K. M. Mackenthun, M. B. Pursley: Variable-rate universal block source coding subject to a fidelity criterion. IEEE Trans. Inform. Theory IT-24 (1978), 349 - 360. | MR
[91] B. Marcus: Factors and extensions of full shifts. Monatsh. Math. 88 (1979), 239-247. | MR | Zbl
[92] B. McMillan: The basic theorems of information theory. Ann. Math. Statist. 24 (1953), 196-219. | MR | Zbl
[93] L. D. Meshalkin: One particular case of isomorphism of Bernoulli schemes. (in Russian). Doklady AN SSR 141 (1959), 41-44.
[94] M. Morse: Symbolic Dynamics. (lecture notes). Institute for Advanced Study, Princeton 1966. | Zbl
[95] D. L. Neuhoff R. M. Gray.and L. D. Davisson: Fixed-rate universal block source coding with a fidelity criterion. IEEE Trans. Inform. Theory IT-22 (1975), 524-532. | MR
[96] D. L. Neuhoff, P. C. Shields: Fixed-rate universal codes for Markov sources. IEEE Trans. Inform. Theory IT-24 (1978), 360-367. | MR | Zbl
[97] D. L. Neuhoff, P. C. Shields: Channels with almost finite memory. IEEE Trans. Inform. Theory 1T-25 (1979), 440-447. | MR | Zbl
[98] D. L. Neuhoff, P. C. Shields: Indecomposable finite state channels and primitive approximation. IEEE Trans. Inform. Theory IT-28 (1982), 11-18. | MR | Zbl
[99] D. S. Ornstein: Bernoulli shifts with the same entropy are isomorphic. Adv. in Math. 4 (1970), 338-352. | MR | Zbl
[100] D. S. Ornstein: Factors of Bernoulli shifts are Bernoulli. Adv. in Math. 5 (1970), 349-364. | MR
[101] D. S. Ornstein: Imbedding Bernoulli shifts in flows. Contributions to Ergodic Theory and Probability. (Lecture Notes in Mathematics 160.) Springer-Verlag, Berlin-Heidelberg-New York 1970, 178-218. | MR | Zbl
[102] D. S. Ornstein: An application of ergodic theory to probability theory. Ann. Probab. 1 (1973), 43-65. | MR | Zbl
[103] D. S. Ornstein: Ergodic Theory, Randomness, and Dynamical Systems. Yale Univ. Press, New Haven-London 1974. | MR | Zbl
[104] D. S. Ornstein, B. Weiss: Ergodic theory of amenable group actions. I: The Rohlin lemma. Bull. (New Series) Amer. Math. Soc. 2 (1980), 161-164. | MR | Zbl
[105] J. C. Oxtoby: Ergodic sets. Bull. Amer. Math. Soc. 58 (1952), 116-136. | MR | Zbl
[106] W. Parry: Intrinsic Markov chains. Trans. Amer. Math. Soc. 112 (1964), 55 - 66. | MR | Zbl
[107] W. Parry: Entropy and Generators in Ergodic Theory. W. A. Benjamin, New York-Amsterdam 1969. | MR | Zbl
[108] W. Parry: A finitary classification of topological Markov chains and sofic systems. Bull. London Math. Soc. 9 (1977), 86-92. | MR | Zbl
[109] W. Parry: Endomorphisms of a Lebesgue space III. Israel J. Math. 21 (1975), 167-172. | MR | Zbl
[110] W. Parry: The information cocycle and $\epsilon$-bounded codes. Israel J. Math. 29 (1978), 205-230. | MR
[111] W. Parry: An information obstruction to finite expected coding length. Ergodic Theory. Proceedings, Oberwolfach. (Lecture Notes in Mathematics 729.) Springer-Verlag, Berlin-Heidelberg-New York 1979, 163-168. | MR | Zbl
[112] W. Parry: Finitary isomorphisms with finite expected code-length. Bull. London Math. Soc. 11 (1979), 170- 176. | MR
[113] W. Parry: Topics in Ergodic Theory. (Cambridge Tracts in Mathematics 75.) Cambridge Univ. Press, Cambridge 1981. | MR | Zbl
[114] W. Parry, K. Schmidt: A note on cocycles of unitary representations. Proc. Amer. Math. Soc. 55 (1976), 185-190. | MR | Zbl
[115] W. Parry, S. Tuncel: On the classification of Markov chains by finite equivalence. Preprint. Warwick Univ., Math. Institute, March 1981. | MR | Zbl
[116] K. R. Parthasarathy: Probability Measures on Metric Spaces. Academic Press, New York 1967. | MR | Zbl
[117] M. B. Pursley, L. D. Davisson: Variable-rate coding for nonergodic sources and classes of sources subject to a fìdelity constraint. IEEE Trans. Inform. Theory IT-22 (1976), 324-337. | MR
[118] M. B. Pursley, K. M. Mackenthun: Variable-rate coding for classes of sources with generalized alphabets. IEEE Trans. Inform. Theory IT-23 (1977), 592-597. | MR | Zbl
[119] V. A. Rohlin: On basic concepts of measure theory. (in Russian). Mat. Sbornik 67 (1949), 107-150. | MR
[120] V.A. Rohlin: Selected problems of the metric theory of dynamical systems. (in Russian). Uspehi Mat. Nauk 30 (1949), 57-128. | MR
[121] V. A. Rohlin: On the decomposition of a dynamical system into transitive components. (in Russian). Mat. Sbornik 67 (1949), 235-249. | MR
[122] V. A. Rohlin, Ya. G. Sinai: Construction and properties of invariant measurable partitions. (in Russian). Doklady AN SSSR 141 (1961), 1038 - 1041. | MR
[123] D. J. Rudolph: A characterization of those processes finitarily isomorphic to a Bernoulli shift. Ergodic Theory and Dynamical Systems I. Progress in Mathematics, Vol. 10. Birkhäuser, Boston, Mass. 1981, 1 - 64. | MR | Zbl
[124] D. J. Sakrison: The rate distortion function of a class of sources. Inform. and Control 15 (1969), 165-195. | MR
[125] C. E. Shannon: A mathematical theory of communication. Bell. System Techn. J. 27 (1948), 379-432, 623-656. | MR | Zbl
[126] C. E. Shannon: Coding theorems for discrete source with a fidelity criterion. IRE Nat. Conv. Rec, part 4 (1959), 142-163.
[127] C. E. Shannon: The zero-error capacity of a noisy channel. IRE Trans. 3 (1056), 8 - 32. | MR
[128] P. C. Shields: The Theory of Bernoulli Shifts. Univ. of Chicago Press, Chicago 1973. | MR | Zbl
[129] P. C. Shields: Stationary coding of processes. IEEE Trans. Inform. Theory IT-25 (1979), 283-291. | MR | Zbl
[130] P. C. Shields: Almost block independence. Z. Wahrsch. verw. Gebiete 49 (1979), 119-123. | MR | Zbl
[131] P. C. Shields, D. L. Neuhoff: Block and sliding-block source coding. IEEE Trans. Inform. Theory 1T-23 (1977), 211-215. | MR | Zbl
[132] K. Sigmund: On the prevalence of zero entropy. Israel J. Math. 10 (1971), 281-288. | MR | Zbl
[133] Ya. G. Sinai: On the notion of entropy of a dynamical system. (in Russian). Doklady AN SSSR 124 (1959), 768-771. | MR
[134] Ya. G. Sinai: On weak isomorphism of transformations with an invariant measure. (in Russian). Mat. Sbornik 63 (1964), 23-42. | MR
[135] S. Smale: Differentiable dynamical systems. Bull. Amer. Math. Soc. 73 (1967), 747-817. | MR | Zbl
[136] M. Smorodinsky: Ergodic Theory, Entropy. (Lecture Notes in Mathematics 214.) Springer-Verlag, Berlin- Heidelberg- New York 1971. | MR | Zbl
[137] M. Smorodinsky: A partition on a Bernoulli shift which is not weak Bernoulli. Math. Systems Theory 5 (1971), 201-203. | MR
[138] Š. Šujan: Generators of an abelian group of invertible measure-preserving transformations. Monatsh. Math. 90 (1980), 68-79. | MR
[139] Š. Šujan: Epsilon-rates, epsilon-quantiles, and group coding theorems for firiitely additîve information sources. Kybernetika 16 (1980), 105-119. | MR
[140] Š. Šujan: Existence of asymptotic rate for asymptotically mean stationary sources with countable alphabets. Trans. Зrd Czechosl.-Soviet-Hung. Seminar on Information Theory. ÚTIA ČSAV, Prague 1980, 201-207.
[141] Š. Šujan: Channels with additive asymptotically mean stationary noise. Kybernetika 17 (1981), 1-15. | MR
[142] Š. Šujan: On the capacity of asymptotically mean stationary channels. Kybernetika 17 (1981), 122-233. | MR
[143] Š. Šujan: Continuity and quantization of channels with infinite alphabets. Kybernetika 17 (1981), 465-478. | MR
[144] Š. Šujan: Block transmissibility and quantization. Probability and Statistical Inference. (W. Grossmann et al., eds.), D. Reidel, Dordrecht-Boston-London 1982, 361 - 371. | MR
[145] Š. Šujan: A local structure of stationary perfectly noiseless codes between stationary nonergodic sources. I: General considerations. Kybernetika 18 (1982), 361-376. | MR
[146] Š. Šujan: A local structure of stationary perfectly noiseless codes between stationary nonergodic sources. II: Applications. Kybernetika 18 (1982), 465-484. | MR
[147] Š. Šujan: Codes in ergodic theory and information: Some examples. Proc. Conf. Ergodic Theory and Related Topics, Akademie-Verlag, Berlin 1982 (to appear).
[148] Š. Šujan: Finite generators for amenable group actions. (submitted).
[149] J.-P. Thouvenot: Quelques proprietes des systémes dynamiques qui se decomposent en un produit de deux systémes dont l'un est un schema de Bernoulli. Israel J. Math. 21 (1975), 178-207. | MR | Zbl
[150] S. Tuncel: Conditional pressure and coding. Israel J. Math. 39 (1981), 101 - 112. | MR | Zbl
[151] P. Walters: Ergodic Theory. Introductory Lectures. (Lectures Notes in Mathematics 458.) Springer-Verlag, Berlin -Heidelberg-New York 1975. | MR | Zbl
[152] B. Weiss: The isomorphism problem in ergodic theory. Bull. Amer. Math. Soc. 78 (1972), 668-684. | MR | Zbl
[153] K. Winkelbauer: On discrete information sources. Trans. 3rd Prague Conf. Inform. Theory etc., NČSAV, Prague 1964, 765-830. | MR | Zbl
[154] K. Winkelbauer: On the asymptotic rate of nonergodic information sources. Kybernetika 6 (1970), 128-148. | MR
[155] K. Winkelbauer: On the existence of finite generators for invertible measure-preserving transformations. Comment. Math. Univ. Carolinae 18 (1977), 789 - 812. | MR | Zbl
[156] J. Wolfowitz: Coding Theorems of Information Theory. 2nd ed. Springer-Verlag, New York 1964. | MR | Zbl
[157] G. M. Zaslavskij: On the isomorphism problem for stationary processes. (in Russian). Teoria veroyatnostej i primen. 9 (1964), 241 - 298. | MR | Zbl
[158] J. Ziv: Coding of sources with unknown statistics. Part I: Probability of encoding error; Part II: Distortion relative to a fidelity criterion. IEEE Trans. Inform. Theory IT-18 (1972), 384-394. | MR
[159] J. Ziv: Coding theorems for individual sequences. IEEE Trans. Inform. Theory IT-24 (1978), 405-413. | MR | Zbl
[160] J. Ziv, A. Lempel: Compression of individual sequences via variable-rate coding. IEEE Trans. Inform. Theory IT-24 (1978), 530-536. | MR | Zbl