| Title:
|
A generalized coding problem for discrete information sources (English) |
| Author:
|
Šujan, Štefan |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
13 |
| Issue:
|
7 |
| Year:
|
1977 |
| Pages:
|
(1),3-93 |
| . |
| Category:
|
math |
| . |
| MSC:
|
94A15 |
| idMR:
|
MR0465531 |
| . |
| Date available:
|
2009-09-24T16:59:42Z |
| Last updated:
|
2012-06-05 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/125531 |
| . |
| Reference:
|
[1] R. Ahlswede P. Gacs J. Korner: Bounds on conditional probabilities with applications in multi-user communication.Z. Wahrscheinlichkeitstheorie verw. Gebiete 34 (1976), 157-177. MR 0472221 |
| Reference:
|
[2] R. Ash: Information theory.Interscience Publishers, New York-London-Sydney 1965. Zbl 0141.34904, MR 0229475 |
| Reference:
|
[3] R. R. Bahadur: Some limit theorems in statistics.Regional Conference Series in Applied Mathematics 4, SIAM, Philadelphia 1971. Zbl 0257.62015, MR 0315820 |
| Reference:
|
[4] R. R. Bahadur, M. Raghavachari: Some asymptotic properties of likelihood ratios on general sample spaces.Proc. Sixth Berkeley Symp. Math. Stat. Prob., Vol. 1 (1970), 129-152. MR 0400500 |
| Reference:
|
[5] J. R. Blum D. L. Hanson: On invariant probability measures I.Pacific J. of Math. 10 (1960), 4, 1125-1130. |
| Reference:
|
[6] D. L. Brown: Non-local optimality of appropriate LRT's.Ann. Math. Statistics 42, (1971), 1206-1240. MR 0314167 |
| Reference:
|
[7] K. L. Chung: Markov chains with stationary transition probabilities.Second ed. Springer-Veflag, Berlin-Gottingen-Heidelberg 1967. Zbl 0146.38401, MR 0217872 |
| Reference:
|
[8] N. Dunford J. T. Schwartz: Linear operators Part I: General theory.Interscience Publishers, New York 1958. MR 1009162 |
| Reference:
|
[9] R. R. Farrell: Representation of invariant measures.Illionois J. of Math. 6(1962), 447-467. Zbl 0108.14203, MR 0150264 |
| Reference:
|
[10] A. Feinstein: Foundations of information theory.McGraw-Hill Book Co., New York 1958. Zbl 0082.34602, MR 0095087 |
| Reference:
|
[11] R. Gray L. Davisson: The ergodic decomposition of stationary discrete random processes.IEEE IT-20 (1974), 5, 625-636. MR 0373763 |
| Reference:
|
[12] R. Gray L. Davisson: Source coding theorem without the ergodic assumption.IEEE IT-20 (1974), 4, 502-516. MR 0476163 |
| Reference:
|
[13] P. R. Halmos: Measure theory.D. van Nostrand, New York 1950. Zbl 0040.16802, MR 0033869 |
| Reference:
|
[14] E. Hewitt K. Yosida: Finitely additive measures.Transactions of the American Math. Society 72 (1952), 46-66. MR 0045194 |
| Reference:
|
[15] S. Horowitz: Transition probabilities and contractions of L_{\infty}.Z. Wahrscheinlichkeitstheorie verw. Gebiete 24 (1972), 263-274. MR 0331516 |
| Reference:
|
[16] K. Jacobs: Lectures in ergodic theory, Vol. I, II.Aarhus Universitet, Mathematisk Institut 1962/1963. MR 0159922 |
| Reference:
|
[17] J. L. Kelley: General Topology.9th ed. D. van Nostrand, Princeton N. J. 1968. Zbl 0157.53002, MR 0239550 |
| Reference:
|
[18] D. F. Kerridge: Inaccuracy and inference.Journal of the Royal Stat. Society, Ser. B 23 (1961), 184-194. Zbl 0112.10302, MR 0123375 |
| Reference:
|
[19] A. N. Kolmogorov: New metric invariant of transitive dynamical systems and automorphisms of Lebesgue spaces.(In Russian), DAN SSSR 119 (1958), 5, 861-864. MR 0103254 |
| Reference:
|
[20] N. Kryloff N. Bogoliouboff: La théorie générale de la mesure dans son application à l'étude des systèmes dynamiques de la mécanique non linéaire.Ann. of Math. 38 (1937), 65-113. MR 1503326 |
| Reference:
|
[21] S. Kullback: Information theory and statistics.Wiley, New York 3958. Zbl 0897.62003, MR 0103557 |
| Reference:
|
[22] K. Marton: Error exponent for source coding with a fidelity criterion.IEEE IT-20 (1974), 2, 197-199. Zbl 0305.94027, MR 0363655 |
| Reference:
|
[23] B. McMillan: The basic theorems of information theory.Ann. Math. Stat. 24 (1953), 196-219. Zbl 0050.35501, MR 0055621 |
| Reference:
|
[24] J. F. Mertens: Integration des mesures non denombrablement additives: une generalisation du lemme de Fatou et du theoreme de convergence de Lebesgue.Annales de la Société Scientifique de Bruxelles 84, II (1970), 231-239. Zbl 0205.35703, MR 0279270 |
| Reference:
|
[25] R. R. Olshen: Representing finitely additive invariant probabilities.Ann. Math. Stat. 39 (1968), 2131-2135. Zbl 0185.44203, MR 0239633 |
| Reference:
|
[26] J. C. Oxtoby: Ergodic sets.Bull. Amer. Math. Society 58 (1952), 116-136. Zbl 0046.11504, MR 0047262 |
| Reference:
|
[27] K. R. Parthasarathy: On the integral representation of the rate of transmission of a stationary channel.Illinois J. of Math. 5 (1961), 2, 299-305. Zbl 0100.33903, MR 0121259 |
| Reference:
|
[28] K. R. Parthasarathy: A note on McMillan's theorem for countable alphabets.Transactions of the 3rd Prague Conf. on Inform. Theory etc., Prague 1964, 541 - 543. Zbl 0199.21401, MR 0166006 |
| Reference:
|
[29] D. Potschke: A statistical interpretation of the B-rate of information theory.Presented at the 1974 European Meeting of Statisticians and Seventh Prague conf. on Inform. Theory etc., Prague 1974. |
| Reference:
|
[30] R. Phelps: Lectures on Chocquet's theorem.D. van Nostrand, Princeton, N. J., 1966. MR 0193470 |
| Reference:
|
[31] H. Rasiowa, R. Sikorski: Mathematics of metamathematics.PWN, Warszawa 1963. Zbl 0122.24311, MR 0163850 |
| Reference:
|
[32] V. A. Rochlin: New progress in the theory of transformations with invariant measure.(In Rusian). Usp. Mat. Nauk 15 (1960), 3-26. MR 0132155 |
| Reference:
|
[33] C. P. Schnorr: Zufälligkeit und Wahrscheinlichkeit.Lect. Notes in Math. 218. Springer-Verlag, Berlin-Heidelberg-New York 1971. Zbl 0232.60001, MR 0414225 |
| Reference:
|
[34] C. E. Shannon: A mathematical theory of communication.Bell Sys. Techn. J. 27 (1948), 379-432, 623-656. Zbl 1154.94303, MR 0026286 |
| Reference:
|
[35] Ja. G. Sinaj: On the notion of entropy of a dynamical system.(In Russian). DAN SSSR 124 (1959), 4, 768-771. |
| Reference:
|
[36] Ja. G. Sinaj: On flows with finite entropy.(In Russian). DAN SSSR 125 (1959), 6, 1200-1202. MR 0103257 |
| Reference:
|
[37] Š. Šujan: On the integral representation of the entropy rate.To appear in Studia Sci. Math. Hungar. MR 0545093 |
| Reference:
|
[38] Š. Šujan: On the asymptotic B-rate.Submitted to Studia Sci. Math. Hungar. |
| Reference:
|
[39] G. Tusnády: On asymptotically optimal tests.To appear in Annals of Statistics. MR 0431512 |
| Reference:
|
[40] K. Winkelbauer: On discrete information sources.Transactions of the 3rd Prague Conf. on Inform. Theory etc., Prague 1964, 765-830. Zbl 0126.35702, MR 0166000 |
| Reference:
|
[41] K. Winkelbauer: On the asymptotic rate of non-ergodic information sources.Kybernetika 6 (1970), 2, 127-148. Zbl 0245.94013, MR 0275979 |
| Reference:
|
[42] J. Wolfowitz: Coding theorems of information theory.Second ed. Springer-Verlag, New York 1964. Zbl 0132.39704, MR 0176851 |
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