| Title:
|
Ergodic theory, entropy, and coding problems of information theory (English) |
| Author:
|
Šujan, Štefan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
19 |
| Issue:
|
7 |
| Year:
|
1983 |
| Pages:
|
(1),3-66 |
| . |
| Category:
|
math |
| . |
| MSC:
|
28D20 |
| MSC:
|
28D99 |
| MSC:
|
37A25 |
| MSC:
|
94-02 |
| MSC:
|
94A15 |
| MSC:
|
94A17 |
| idZBL:
|
Zbl 0542.94006 |
| idMR:
|
MR0902063 |
| . |
| Date available:
|
2009-09-24T17:38:17Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/124553 |
| . |
| Reference:
|
[1] M. A. Ackoglu A. del Junco, and M. Rahe: Finitary codes between Markov processes.Z. Wahrsch. verw. Gebiete 47 (1979), 305-314. MR 0525312 |
| Reference:
|
[2] R. L. Adler W. Goodwyn, and B. Weiss: Equivalence of topological Markov shifts.Israel J. Math. 27 (1977), 49-63. MR 0437715 |
| Reference:
|
[3] R. L. Adler A. G. Konheim, and M. H. McAndrew: Topological entropy.Trans. Amer. Math. Soc. 114 (1965), 309-319. MR 0175106 |
| Reference:
|
[4] R. L. Adler, B. Marcus: Topological entropy and equivalence of dynamical systems.Memoirs Amer. Math. Soc. 219 (1979). Zbl 0412.54050, MR 0533691 |
| Reference:
|
[5] R. L. Adler, B. Weiss: Similarity of the automorphisms of the torus.Memoirs Amer. Math. Soc. 98 (1970). MR 0257315 |
| Reference:
|
[6] V. M. Alekseev: Symbolic Dynamics.(in Russian). Math. Institute, AN USSR, Kiev 1976. MR 0464317 |
| Reference:
|
[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. |
| Reference:
|
[8] R. B. Ash: Information Theory.J. Wiley, New York 1965. Zbl 0141.34904, MR 0229475 |
| Reference:
|
[9] T. Berger: Rate Distortion Theory.Prentice Hall, Englewood Cliff's 1971. MR 0408988 |
| Reference:
|
[10] T. Berger: Information singular processes.IEEE Trans. Inform. Theory IT-20 (1975), 502-511.. MR 0398667 |
| Reference:
|
[11] P. Billingsley: Ergodic Theory and Information.J. Wiley, New York-London-Sydney 1965. Zbl 0141.16702, MR 0192027 |
| Reference:
|
[12] P. Billingsley: Convergence of Probability Measures.J. Wiley, New York-London-Sydney-Toronto 1968. Zbl 0172.21201, MR 0233396 |
| Reference:
|
[13] R. E. Blahut: Computation of channel capacity and rate-distortion functions.IEEE Trans. Inform. Theory IT-18 (1972), 460-473. Zbl 0247.94017, MR 0476161 |
| Reference:
|
[14] H. Blasbalg, R. van Blerkom: Message compression.IRE Trans. Space Electron. Telemech. 1962, 228-338. |
| Reference:
|
[15] J. R. Blum, D. L. Hanson: On invariant probability measures I.Pacific J. Math. 10 (1960), 1125-1240. |
| Reference:
|
[16] J. R. Blum, D. L. Hanson: On the isomorphism problem for Bernoulli schemes.Bull. Amer. Math. Soc. 63 (1963), 221-223. Zbl 0121.13601, MR 0143862 |
| Reference:
|
[17] R. Bowen: Symbolic dynamics for hyperbolic systems.Amer. J. Math. 95 (1973), 429-459. Zbl 0257.54042, MR 0339281 |
| Reference:
|
[18] R. Bowen: Topological entropy for non-compact sets.Trans. Amer. Math. Soc. 184 (1973), 413-423. MR 0338317 |
| Reference:
|
[19] R. Bowen: Smooth partitions of Anosov diffeomorphisms are weak Bernoulli.Israel J. Math. 27(1975), 95-100. Zbl 0315.58020, MR 0385927 |
| Reference:
|
[20] R. Bowen: Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms.(Lecture Notes in Mathematics 470.) Springer-Verlag, Berlin-Heidelberg-New York 1975. Zbl 0308.28010, MR 2423393 |
| Reference:
|
[21] R. Bowen, D. Ruelle: The ergodic theory of Axiom A flows.Invent. Mathematicae 29 (1975), 181-202. Zbl 0311.58010, MR 0380889 |
| Reference:
|
[22] R. C. Bradley, Jr.: On the strong mixing and weak Bernoulli conditions.Z. Wahrsch. verw. Gebiete 51 (1980), 49-54. Zbl 0396.60038, MR 0566107 |
| Reference:
|
[23] A. A. Brudno: Entropy and algorithmic complexity of trajectories of a dynamical system.(in Russian). Preprint, VNIISI, Moskva 1980. |
| Reference:
|
[24] E. Coven, M. Paul: Endomorphisms of irreducible shifts of finite type.Math. Systems Theory 8(1974), 165-175. MR 0383378 |
| Reference:
|
[25] L. D. Davisson: Universal noiseless coding.IEEE Trans. Inform. Theory IT-19 (1973), 783-795. Zbl 0283.94005, MR 0465519 |
| Reference:
|
[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 0583948 |
| Reference:
|
[27] A. del Junco, M. Rahe: Finitary codings and weak Bernoulli partitions.Proc. Amer. Math. Soc. 75 (1979), 259-364. Zbl 0417.28011, MR 0532147 |
| Reference:
|
[28] M. Denker: Finite generators for ergodic measure-preserving transformations.Z. Wahrsch. verw. Gebiete 29 (1974), 45-55. MR 0382587 |
| Reference:
|
[29] M. Denker: Generators and almost topological isomorphisms.Astérisque 59 (1977), 23-35. MR 0499073 |
| Reference:
|
[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 0457675 |
| Reference:
|
[31] M. Denker, M. Keane: Almost topological dynamical systems.Israel J. Math. 34 (1979), 139-160. Zbl 0441.28008, MR 0571401 |
| Reference:
|
[32] M. Denker, M. Keane: Finitary codes and the law of the iterated logarithm.Z. Wahrsch. verw. Gebiete 52 (1980), 321-331. Zbl 0417.60040, MR 0576892 |
| Reference:
|
[33] J. G. Dunham: Abstract alphabet sliding-block entropy compression coding with a fidelity criterion.Ann. Probab. 8 (1980), 1085-1092. Zbl 0452.94009, MR 0602382 |
| Reference:
|
[34] R. Fellgett, W. Parry: Endomorphisms of a Lebesgue space II.Israel J. Math. 21 (1975), 167-172. Zbl 0305.28009, MR 0382591 |
| Reference:
|
[35] B. M. Fitingoff: Optimal coding in case of unknown and changing message statistics.(in Russian). Problemy Peredachi Informacii 2 (1966), 3-11. MR 0202498 |
| Reference:
|
[36] B. M. Fitingoff: The compression of discrete information.(in Russian). Problemy Peredachi Informacii 3 (1967), 28-36. MR 0290859 |
| Reference:
|
[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 0619116 |
| Reference:
|
[38] N. Friedman, D. S. Ornstein: On the isomorphism of weak Bernoulli transformations.Adv. in Math. 5 (1970), 365-394. MR 0274718 |
| Reference:
|
[39] R. G. Gallager: Information Theory and Reliable Communication.J. Wiley, New York 1968. Zbl 0198.52201 |
| Reference:
|
[40] F. R. Gantmacher: The Theory of Matrices.Vols. I and II. Chelsea, New York 1959. Zbl 0085.01001 |
| Reference:
|
[41] R. M. Gray: Sliding-block source coding.IEEE Trans. Inform. Theory IT-21 (1975), 357-368. Zbl 0308.94015, MR 0376230 |
| Reference:
|
[42] R. M. Gray, L. D. Davisson: The ergodic decomposition of stationary discrete random processes.IEEE Trans. Inform. Theory IT-20 (1974), 625 - 636. Zbl 0301.94027, MR 0373763 |
| Reference:
|
[43] R. M. Gray, L. D. Davisson: Source coding theorems without the ergodic assumption.IEEE Trans. Inform. Theory IT-20 (1974), 502-516. Zbl 0301.94026, MR 0476163 |
| Reference:
|
[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. Zbl 0452.94010, MR 0581788 |
| Reference:
|
[45] R. M. Gray, J. C. Kieffer: Asymptotically mean stationary measures.Ann. Probab. (1980), 962-973. Zbl 0447.28014, MR 0586779 |
| Reference:
|
[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 0449878 |
| Reference:
|
[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 0376239 |
| Reference:
|
[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 0368127 |
| Reference:
|
[49] R. M. Gray, D. S. Ornstein: Sliding-block joint source/noisy channel coding theorems.IEEE Trans. Inform. Theory IT-22 (1976), 683-690. Zbl 0348.94019, MR 0530088 |
| Reference:
|
[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 0528007 |
| Reference:
|
[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 0577308 |
| Reference:
|
[52] C. Grillenberger, U. Krengel: On marginaldistributionsandisomorphisms of stationary processes.Math. Z. 149, (1976), 131-154. MR 0407237 |
| Reference:
|
[53] B. Hajek: Information-singularity and recoverability of random processes.IEEE Trans. Inform. Theory IT-28 (1983), 422-429. MR 0672878 |
| Reference:
|
[54] P. R. Halmos: Measure Theory.D. Van Nostrand, Princeton N. J. 1950. Zbl 0040.16802, MR 0033869 |
| Reference:
|
[55] P. R. Halmos: Lectures on Ergodic Theory.Chelsea, New York 1953. |
| Reference:
|
[56] G. Hansel, J. P. Raoult: Ergodicité, uniformité et unique ergodicité.Indiana Univ. Math. J. 23 (1973), 221-237. MR 0318449 |
| Reference:
|
[57] R. Heim: On the algorithmic foundations of information theory.IEEETrans. Inform. Theory 1T-25 (1979), 557-566. MR 0545011 |
| Reference:
|
[58] R. I. Jewett: The prevalence of uniquely ergodic systems.J. Math. and Mech. 19 (1970), 717-729. Zbl 0192.40601, MR 0252604 |
| Reference:
|
[59] M. Keane: Coding problems in ergodic theory.Proc. Int. Conf. on Math. Physics. Camerino, Italy, 1974. |
| Reference:
|
[60] M. Keane, M. Smorodinsky: A class of finitary codes.Israel J. Math. 26 (1977), 352-371. Zbl 0357.94012, MR 0450514 |
| Reference:
|
[61] M. Keane, M. Smorodinsky: Bernoulli schemes of the same entropy are finitarily isomorphic.Ann. Math. 109 (1979). 397-406. Zbl 0405.28017, MR 0528969 |
| Reference:
|
[62] M. Keane, M. Smorodinsky: The finitary isomorphism theorem for Markov shifts.Bull. (New Series) Amer. Math. Soc. 1 (1979), 436-438. Zbl 0407.28010, MR 0520082 |
| Reference:
|
[63] A. I. Khinchine: Mathematical Foundations of Information Theory.Dover, New York 1957. MR 0092709 |
| Reference:
|
[64] J. C. Kieffer: On approximation of stationary measures by periodic and ergodic measures.Ann. Probab. 2 (1974), 530-534. MR 0369661 |
| Reference:
|
[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 0393422 |
| Reference:
|
[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. Zbl 0385.94011, MR 0504358 |
| Reference:
|
[67] J. C. Kieffer: A unified approach to weak universal source coding.IEEE Trans. Inform. Theory IT-24 (1978), 674-682. Zbl 0394.94012, MR 0514346 |
| Reference:
|
[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. Zbl 0473.94007, MR 0596278 |
| Reference:
|
[69] J. C. Kieffer: On the transmission of Bernoulli sources over stationary channels.Ann. Probab. 8 (1980), 942-961. Zbl 0452.94012, MR 0586778 |
| Reference:
|
[70] J. C. Kieffer: On coding a stationary process to achieve a given marginal distribution.Ann. Probab. 8 (1980), 131-141. MR 0556419 |
| Reference:
|
[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 0596277 |
| Reference:
|
[72] J. C. Kieffer: Stationary coding over stationary channels.Z. Wahrsch. verw. Gebiete 56 (1981), 113-136. Zbl 0444.94007, MR 0612163 |
| Reference:
|
[73] J. C. Kieffer: Block coding for weakly continuous channels.IEEE Trans. Inform. Theory IT-27 (1981), 721-727. Zbl 0473.94004, MR 0650708 |
| Reference:
|
[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. Zbl 0475.94007, MR 0609819 |
| Reference:
|
[75] J. C. Kieffer: Sliding-Ыock coding for weakly continuous channels.IEEE Trans. Inform. Theory IT-28 (1982), 2-10. MR 0651095 |
| Reference:
|
[76] J. C. Kieffer: Characterizations of d-total boundedness for classes of B sources.IEEE Trans. Inform. Theory IT-28 (1982), 26-35. Zbl 0473.94009, MR 0651098 |
| Reference:
|
[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 0725630 |
| Reference:
|
[78] J. C. Kieffer: Generators with prescribed marginals for nonergodic automorphisms.Lecture presented at the 9th Prague Conf. Inform. Theory, Prague, June 1982. MR 0757901 |
| Reference:
|
[79] J. C. Kieffer, M. Rahe: Selecting universal partitions in ergodic theory.Ann. Probab. 9 (1981), 705-709. Zbl 0464.60036, MR 0624699 |
| Reference:
|
[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 0103254 |
| Reference:
|
[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 0184801 |
| Reference:
|
[82] I. P. Kornfeľd, Ya. G. Sinai, and S. V. Fomin: Ergodic Theory.(in Russian). Nauka, Moskva 1980. MR 0610981 |
| Reference:
|
[83] U. Krengel: Recent results on generators in ergodic theory.Trans. бth Conf. Inform. Theory etc, Academia, Prague 1973, 465 - 482. Zbl 0318.94024, MR 0348078 |
| Reference:
|
[84] U. Krengel: Discussion of Professor's Ornstein's paper.(see [45]). Ann. Probab. 1 (1973). |
| Reference:
|
[85] W. Krieger: On entropy and generators of measure-preserving transformations.Trans. Amer. Math. Soc. 119 (1970), 453-464. Erratum: ibid. 168 (1972), 519. Zbl 0204.07904, MR 0259068 |
| Reference:
|
[86] W. Krieger: On unique ergodicity.Proc. бth Berkeley Symp. Math. Stat. Prob., Vol. I. University of California Press, Los Angeles 1972, 327-346. Zbl 0262.28013, MR 0393402 |
| Reference:
|
[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 1503326 |
| Reference:
|
[88] A. G. Kushnirenko: On metric invariants of entropy type.(in Russian). Uspehi Mat. Nauk 22 (1967), 57-65. Zbl 0169.46101, MR 0217257 |
| Reference:
|
[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 0521306 |
| Reference:
|
[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 0493647 |
| Reference:
|
[91] B. Marcus: Factors and extensions of full shifts.Monatsh. Math. 88 (1979), 239-247. Zbl 0432.54036, MR 0553733 |
| Reference:
|
[92] B. McMillan: The basic theorems of information theory.Ann. Math. Statist. 24 (1953), 196-219. Zbl 0050.35501, MR 0055621 |
| Reference:
|
[93] L. D. Meshalkin: One particular case of isomorphism of Bernoulli schemes.(in Russian). Doklady AN SSR 141 (1959), 41-44. |
| Reference:
|
[94] M. Morse: Symbolic Dynamics.(lecture notes). Institute for Advanced Study, Princeton 1966. Zbl 0164.22201 |
| Reference:
|
[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 0411825 |
| Reference:
|
[96] D. L. Neuhoff, P. C. Shields: Fixed-rate universal codes for Markov sources.IEEE Trans. Inform. Theory IT-24 (1978), 360-367. Zbl 0404.94006, MR 0490453 |
| Reference:
|
[97] D. L. Neuhoff, P. C. Shields: Channels with almost finite memory.IEEE Trans. Inform. Theory 1T-25 (1979), 440-447. Zbl 0409.94011, MR 0536234 |
| Reference:
|
[98] D. L. Neuhoff, P. C. Shields: Indecomposable finite state channels and primitive approximation.IEEE Trans. Inform. Theory IT-28 (1982), 11-18. Zbl 0483.94011, MR 0651096 |
| Reference:
|
[99] D. S. Ornstein: Bernoulli shifts with the same entropy are isomorphic.Adv. in Math. 4 (1970), 338-352. Zbl 0197.33502, MR 0257322 |
| Reference:
|
[100] D. S. Ornstein: Factors of Bernoulli shifts are Bernoulli.Adv. in Math. 5 (1970), 349-364. MR 0274717 |
| Reference:
|
[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. Zbl 0227.28013, MR 0272985 |
| Reference:
|
[102] D. S. Ornstein: An application of ergodic theory to probability theory.Ann. Probab. 1 (1973), 43-65. Zbl 0282.28009, MR 0348831 |
| Reference:
|
[103] D. S. Ornstein: Ergodic Theory, Randomness, and Dynamical Systems.Yale Univ. Press, New Haven-London 1974. Zbl 0296.28016, MR 0447525 |
| Reference:
|
[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. Zbl 0427.28018, MR 0551753 |
| Reference:
|
[105] J. C. Oxtoby: Ergodic sets.Bull. Amer. Math. Soc. 58 (1952), 116-136. Zbl 0046.11504, MR 0047262 |
| Reference:
|
[106] W. Parry: Intrinsic Markov chains.Trans. Amer. Math. Soc. 112 (1964), 55 - 66. Zbl 0127.35301, MR 0161372 |
| Reference:
|
[107] W. Parry: Entropy and Generators in Ergodic Theory.W. A. Benjamin, New York-Amsterdam 1969. Zbl 0175.34001, MR 0262464 |
| Reference:
|
[108] W. Parry: A finitary classification of topological Markov chains and sofic systems.Bull. London Math. Soc. 9 (1977), 86-92. Zbl 0352.60054, MR 0482707 |
| Reference:
|
[109] W. Parry: Endomorphisms of a Lebesgue space III.Israel J. Math. 21 (1975), 167-172. Zbl 0312.28018, MR 0382591 |
| Reference:
|
[110] W. Parry: The information cocycle and $\epsilon$-bounded codes.Israel J. Math. 29 (1978), 205-230. MR 0480943 |
| Reference:
|
[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. Zbl 0414.28016, MR 0550419 |
| Reference:
|
[112] W. Parry: Finitary isomorphisms with finite expected code-length.Bull. London Math. Soc. 11 (1979), 170- 176. MR 0541971 |
| Reference:
|
[113] W. Parry: Topics in Ergodic Theory.(Cambridge Tracts in Mathematics 75.) Cambridge Univ. Press, Cambridge 1981. Zbl 0449.28016, MR 0614142 |
| Reference:
|
[114] W. Parry, K. Schmidt: A note on cocycles of unitary representations.Proc. Amer. Math. Soc. 55 (1976), 185-190. Zbl 0329.22008, MR 0393336 |
| Reference:
|
[115] W. Parry, S. Tuncel: On the classification of Markov chains by finite equivalence.Preprint. Warwick Univ., Math. Institute, March 1981. Zbl 0485.60063, MR 0662472 |
| Reference:
|
[116] K. R. Parthasarathy: Probability Measures on Metric Spaces.Academic Press, New York 1967. Zbl 0153.19101, MR 0226684 |
| Reference:
|
[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 0408991 |
| Reference:
|
[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. Zbl 0364.94026, MR 0469520 |
| Reference:
|
[119] V. A. Rohlin: On basic concepts of measure theory.(in Russian). Mat. Sbornik 67 (1949), 107-150. MR 0030584 |
| Reference:
|
[120] V.A. Rohlin: Selected problems of the metric theory of dynamical systems.(in Russian). Uspehi Mat. Nauk 30 (1949), 57-128. MR 0030710 |
| Reference:
|
[121] V. A. Rohlin: On the decomposition of a dynamical system into transitive components.(in Russian). Mat. Sbornik 67 (1949), 235-249. MR 0032958 |
| Reference:
|
[122] V. A. Rohlin, Ya. G. Sinai: Construction and properties of invariant measurable partitions.(in Russian). Doklady AN SSSR 141 (1961), 1038 - 1041. MR 0152629 |
| Reference:
|
[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. Zbl 0483.28015, MR 0633760 |
| Reference:
|
[124] D. J. Sakrison: The rate distortion function of a class of sources.Inform. and Control 15 (1969), 165-195. MR 0262005 |
| Reference:
|
[125] C. E. Shannon: A mathematical theory of communication.Bell. System Techn. J. 27 (1948), 379-432, 623-656. Zbl 1154.94303, MR 0026286 |
| Reference:
|
[126] C. E. Shannon: Coding theorems for discrete source with a fidelity criterion.IRE Nat. Conv. Rec, part 4 (1959), 142-163. |
| Reference:
|
[127] C. E. Shannon: The zero-error capacity of a noisy channel.IRE Trans. 3 (1056), 8 - 32. MR 0089131 |
| Reference:
|
[128] P. C. Shields: The Theory of Bernoulli Shifts.Univ. of Chicago Press, Chicago 1973. Zbl 0308.28011, MR 0442198 |
| Reference:
|
[129] P. C. Shields: Stationary coding of processes.IEEE Trans. Inform. Theory IT-25 (1979), 283-291. Zbl 0401.94018, MR 0528006 |
| Reference:
|
[130] P. C. Shields: Almost block independence.Z. Wahrsch. verw. Gebiete 49 (1979), 119-123. Zbl 0393.60031, MR 0539668 |
| Reference:
|
[131] P. C. Shields, D. L. Neuhoff: Block and sliding-block source coding.IEEE Trans. Inform. Theory 1T-23 (1977), 211-215. Zbl 0383.94018, MR 0446738 |
| Reference:
|
[132] K. Sigmund: On the prevalence of zero entropy.Israel J. Math. 10 (1971), 281-288. Zbl 0225.28012, MR 0297970 |
| Reference:
|
[133] Ya. G. Sinai: On the notion of entropy of a dynamical system.(in Russian). Doklady AN SSSR 124 (1959), 768-771. MR 0103256 |
| Reference:
|
[134] Ya. G. Sinai: On weak isomorphism of transformations with an invariant measure.(in Russian). Mat. Sbornik 63 (1964), 23-42. MR 0161961 |
| Reference:
|
[135] S. Smale: Differentiable dynamical systems.Bull. Amer. Math. Soc. 73 (1967), 747-817. Zbl 0202.55202, MR 0228014 |
| Reference:
|
[136] M. Smorodinsky: Ergodic Theory, Entropy.(Lecture Notes in Mathematics 214.) Springer-Verlag, Berlin- Heidelberg- New York 1971. Zbl 0213.07502, MR 0422582 |
| Reference:
|
[137] M. Smorodinsky: A partition on a Bernoulli shift which is not weak Bernoulli.Math. Systems Theory 5 (1971), 201-203. MR 0297971 |
| Reference:
|
[138] Š. Šujan: Generators of an abelian group of invertible measure-preserving transformations.Monatsh. Math. 90 (1980), 68-79. MR 0593832 |
| Reference:
|
[139] Š. Šujan: Epsilon-rates, epsilon-quantiles, and group coding theorems for firiitely additîve information sources.Kybernetika 16 (1980), 105-119. MR 0575419 |
| Reference:
|
[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. |
| Reference:
|
[141] Š. Šujan: Channels with additive asymptotically mean stationary noise.Kybernetika 17 (1981), 1-15. MR 0629345 |
| Reference:
|
[142] Š. Šujan: On the capacity of asymptotically mean stationary channels.Kybernetika 17 (1981), 122-233. MR 0628210 |
| Reference:
|
[143] Š. Šujan: Continuity and quantization of channels with infinite alphabets.Kybernetika 17 (1981), 465-478. MR 0674062 |
| Reference:
|
[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 0668232 |
| Reference:
|
[145] Š. Šujan: A local structure of stationary perfectly noiseless codes between stationary nonergodic sources. I: General considerations.Kybernetika 18 (1982), 361-376. MR 0686518 |
| Reference:
|
[146] Š. Šujan: A local structure of stationary perfectly noiseless codes between stationary nonergodic sources. II: Applications.Kybernetika 18 (1982), 465-484. MR 0707396 |
| Reference:
|
[147] Š. Šujan: Codes in ergodic theory and information: Some examples.Proc. Conf. Ergodic Theory and Related Topics, Akademie-Verlag, Berlin 1982 (to appear). |
| Reference:
|
[148] Š. Šujan: Finite generators for amenable group actions.(submitted). |
| Reference:
|
[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. Zbl 0329.28008, MR 0399419 |
| Reference:
|
[150] S. Tuncel: Conditional pressure and coding.Israel J. Math. 39 (1981), 101 - 112. Zbl 0472.28016, MR 0617293 |
| Reference:
|
[151] P. Walters: Ergodic Theory. Introductory Lectures.(Lectures Notes in Mathematics 458.) Springer-Verlag, Berlin -Heidelberg-New York 1975. Zbl 0299.28012, MR 0480949 |
| Reference:
|
[152] B. Weiss: The isomorphism problem in ergodic theory.Bull. Amer. Math. Soc. 78 (1972), 668-684. Zbl 0255.28014, MR 0304616 |
| Reference:
|
[153] K. Winkelbauer: On discrete information sources.Trans. 3rd Prague Conf. Inform. Theory etc., NČSAV, Prague 1964, 765-830. Zbl 0126.35702, MR 0166000 |
| Reference:
|
[154] K. Winkelbauer: On the asymptotic rate of nonergodic information sources.Kybernetika 6 (1970), 128-148. MR 0275979 |
| Reference:
|
[155] K. Winkelbauer: On the existence of finite generators for invertible measure-preserving transformations.Comment. Math. Univ. Carolinae 18 (1977), 789 - 812. Zbl 0368.28020, MR 0463403 |
| Reference:
|
[156] J. Wolfowitz: Coding Theorems of Information Theory.2nd ed. Springer-Verlag, New York 1964. Zbl 0132.39704, MR 0176851 |
| Reference:
|
[157] G. M. Zaslavskij: On the isomorphism problem for stationary processes.(in Russian). Teoria veroyatnostej i primen. 9 (1964), 241 - 298. Zbl 0154.18901, MR 0164377 |
| Reference:
|
[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 0379017 |
| Reference:
|
[159] J. Ziv: Coding theorems for individual sequences.IEEE Trans. Inform. Theory IT-24 (1978), 405-413. Zbl 0416.94006, MR 0504371 |
| Reference:
|
[160] J. Ziv, A. Lempel: Compression of individual sequences via variable-rate coding.IEEE Trans. Inform. Theory IT-24 (1978), 530-536. Zbl 0392.94004, MR 0507465 |
| . |
