A generalized coding problem for discrete information sources

Šujan, Štefan

Kybernetika, Tome 13 (1977), pp. 1-93

Détail

Classification : 94A15

Bibliographie

[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

[2] R. Ash: Information theory. Interscience Publishers, New York-London-Sydney 1965. | MR | Zbl

[3] R. R. Bahadur: Some limit theorems in statistics. Regional Conference Series in Applied Mathematics 4, SIAM, Philadelphia 1971. | MR | Zbl

[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

[5] J. R. Blum D. L. Hanson: On invariant probability measures I. Pacific J. of Math. 10 (1960), 4, 1125-1130.

[6] D. L. Brown: Non-local optimality of appropriate LRT's. Ann. Math. Statistics 42, (1971), 1206-1240. | MR

[7] K. L. Chung: Markov chains with stationary transition probabilities. Second ed. Springer-Veflag, Berlin-Gottingen-Heidelberg 1967. | MR | Zbl

[8] N. Dunford J. T. Schwartz: Linear operators Part I: General theory. Interscience Publishers, New York 1958. | MR

[9] R. R. Farrell: Representation of invariant measures. Illionois J. of Math. 6(1962), 447-467. | MR | Zbl

[10] A. Feinstein: Foundations of information theory. McGraw-Hill Book Co., New York 1958. | MR | Zbl

[11] R. Gray L. Davisson: The ergodic decomposition of stationary discrete random processes. IEEE IT-20 (1974), 5, 625-636. | MR

[12] R. Gray L. Davisson: Source coding theorem without the ergodic assumption. IEEE IT-20 (1974), 4, 502-516. | MR

[13] P. R. Halmos: Measure theory. D. van Nostrand, New York 1950. | MR | Zbl

[14] E. Hewitt K. Yosida: Finitely additive measures. Transactions of the American Math. Society 72 (1952), 46-66. | MR

[15] S. Horowitz: Transition probabilities and contractions of L_{\infty}. Z. Wahrscheinlichkeitstheorie verw. Gebiete 24 (1972), 263-274. | MR

[16] K. Jacobs: Lectures in ergodic theory, Vol. I, II. Aarhus Universitet, Mathematisk Institut 1962/1963. | MR

[17] J. L. Kelley: General Topology. 9th ed. D. van Nostrand, Princeton N. J. 1968. | MR | Zbl

[18] D. F. Kerridge: Inaccuracy and inference. Journal of the Royal Stat. Society, Ser. B 23 (1961), 184-194. | MR | Zbl

[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

[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

[21] S. Kullback: Information theory and statistics. Wiley, New York 3958. | MR | Zbl

[22] K. Marton: Error exponent for source coding with a fidelity criterion. IEEE IT-20 (1974), 2, 197-199. | MR | Zbl

[23] B. McMillan: The basic theorems of information theory. Ann. Math. Stat. 24 (1953), 196-219. | MR | Zbl

[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. | MR | Zbl

[25] R. R. Olshen: Representing finitely additive invariant probabilities. Ann. Math. Stat. 39 (1968), 2131-2135. | MR | Zbl

[26] J. C. Oxtoby: Ergodic sets. Bull. Amer. Math. Society 58 (1952), 116-136. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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.

[30] R. Phelps: Lectures on Chocquet's theorem. D. van Nostrand, Princeton, N. J., 1966. | MR

[31] H. Rasiowa, R. Sikorski: Mathematics of metamathematics. PWN, Warszawa 1963. | MR | Zbl

[32] V. A. Rochlin: New progress in the theory of transformations with invariant measure. (In Rusian). Usp. Mat. Nauk 15 (1960), 3-26. | MR

[33] C. P. Schnorr: Zufälligkeit und Wahrscheinlichkeit. Lect. Notes in Math. 218. Springer-Verlag, Berlin-Heidelberg-New York 1971. | MR | Zbl

[34] C. E. Shannon: A mathematical theory of communication. Bell Sys. Techn. J. 27 (1948), 379-432, 623-656. | MR | Zbl

[35] Ja. G. Sinaj: On the notion of entropy of a dynamical system. (In Russian). DAN SSSR 124 (1959), 4, 768-771.

[36] Ja. G. Sinaj: On flows with finite entropy. (In Russian). DAN SSSR 125 (1959), 6, 1200-1202. | MR

[37] Š. Šujan: On the integral representation of the entropy rate. To appear in Studia Sci. Math. Hungar. | MR

[38] Š. Šujan: On the asymptotic B-rate. Submitted to Studia Sci. Math. Hungar.

[39] G. Tusnády: On asymptotically optimal tests. To appear in Annals of Statistics. | MR

[40] K. Winkelbauer: On discrete information sources. Transactions of the 3rd Prague Conf. on Inform. Theory etc., Prague 1964, 765-830. | MR | Zbl

[41] K. Winkelbauer: On the asymptotic rate of non-ergodic information sources. Kybernetika 6 (1970), 2, 127-148. | MR | Zbl

[42] J. Wolfowitz: Coding theorems of information theory. Second ed. Springer-Verlag, New York 1964. | MR | Zbl