A generalized coding problem for discrete information sources

Štefan Šujan

Kybernetika (1977)

  • Volume: 13, Issue: Suppl, page (1)-93
  • ISSN: 0023-5954

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Šujan, Štefan. "A generalized coding problem for discrete information sources." Kybernetika 13.Suppl (1977): (1)-93. <http://eudml.org/doc/28686>.

@article{Šujan1977,
author = {Šujan, Štefan},
journal = {Kybernetika},
language = {eng},
number = {Suppl},
pages = {(1)-93},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A generalized coding problem for discrete information sources},
url = {http://eudml.org/doc/28686},
volume = {13},
year = {1977},
}

TY - JOUR
AU - Šujan, Štefan
TI - A generalized coding problem for discrete information sources
JO - Kybernetika
PY - 1977
PB - Institute of Information Theory and Automation AS CR
VL - 13
IS - Suppl
SP - (1)
EP - 93
LA - eng
UR - http://eudml.org/doc/28686
ER -

References

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  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. (1976) MR0472221
  2. R. Ash, Information theory, Interscience Publishers, New York-London-Sydney 1965. (1965) Zbl0141.34904MR0229475
  3. R. R. Bahadur, Some limit theorems in statistics, Regional Conference Series in Applied Mathematics 4, SIAM, Philadelphia 1971. (1971) Zbl0257.62015MR0315820
  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. (1970) MR0400500
  5. J. R. Blum D. L. Hanson, On invariant probability measures I, Pacific J. of Math. 10 (1960), 4, 1125-1130. (1960) 
  6. D. L. Brown, Non-local optimality of appropriate LRT's, Ann. Math. Statistics 42, (1971), 1206-1240. (1971) MR0314167
  7. K. L. Chung, Markov chains with stationary transition probabilities, Second ed. Springer-Veflag, Berlin-Gottingen-Heidelberg 1967. (1967) Zbl0146.38401MR0217872
  8. N. Dunford J. T. Schwartz, Linear operators Part I: General theory, Interscience Publishers, New York 1958. (1958) MR1009162
  9. R. R. Farrell, Representation of invariant measures, Illionois J. of Math. 6(1962), 447-467. (1962) Zbl0108.14203MR0150264
  10. A. Feinstein, Foundations of information theory, McGraw-Hill Book Co., New York 1958. (1958) Zbl0082.34602MR0095087
  11. R. Gray L. Davisson, The ergodic decomposition of stationary discrete random processes, IEEE IT-20 (1974), 5, 625-636. (1974) MR0373763
  12. R. Gray L. Davisson, Source coding theorem without the ergodic assumption, IEEE IT-20 (1974), 4, 502-516. (1974) MR0476163
  13. P. R. Halmos, Measure theory, D. van Nostrand, New York 1950. (1950) Zbl0040.16802MR0033869
  14. E. Hewitt K. Yosida, Finitely additive measures, Transactions of the American Math. Society 72 (1952), 46-66. (1952) MR0045194
  15. S. Horowitz, Transition probabilities and contractions of L, Z. Wahrscheinlichkeitstheorie verw. Gebiete 24 (1972), 263-274. (1972) MR0331516
  16. K. Jacobs, Lectures in ergodic theory, Vol. I, II, Aarhus Universitet, Mathematisk Institut 1962/1963. (1962) MR0159922
  17. J. L. Kelley, General Topology, 9th ed. D. van Nostrand, Princeton N. J. 1968. (1968) Zbl0157.53002MR0239550
  18. D. F. Kerridge, Inaccuracy and inference, Journal of the Royal Stat. Society, Ser. B 23 (1961), 184-194. (1961) Zbl0112.10302MR0123375
  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. (1958) MR0103254
  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. (1937) MR1503326
  21. S. Kullback, Information theory and statistics, Wiley, New York 3958. Zbl0897.62003MR0103557
  22. K. Marton, Error exponent for source coding with a fidelity criterion, IEEE IT-20 (1974), 2, 197-199. (1974) Zbl0305.94027MR0363655
  23. B. McMillan, The basic theorems of information theory, Ann. Math. Stat. 24 (1953), 196-219. (1953) Zbl0050.35501MR0055621
  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. (1970) Zbl0205.35703MR0279270
  25. R. R. Olshen, Representing finitely additive invariant probabilities, Ann. Math. Stat. 39 (1968), 2131-2135. (1968) Zbl0185.44203MR0239633
  26. J. C. Oxtoby, Ergodic sets, Bull. Amer. Math. Society 58 (1952), 116-136. (1952) Zbl0046.11504MR0047262
  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. (1961) Zbl0100.33903MR0121259
  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. (1964) Zbl0199.21401MR0166006
  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. (1974) 
  30. R. Phelps, Lectures on Chocquet's theorem, D. van Nostrand, Princeton, N. J., 1966. (1966) MR0193470
  31. H. Rasiowa, R. Sikorski, Mathematics of metamathematics, PWN, Warszawa 1963. (1963) Zbl0122.24311MR0163850
  32. V. A. Rochlin, New progress in the theory of transformations with invariant measure, (In Rusian). Usp. Mat. Nauk 15 (1960), 3-26. (1960) MR0132155
  33. C. P. Schnorr, Zufälligkeit und Wahrscheinlichkeit, Lect. Notes in Math. 218. Springer-Verlag, Berlin-Heidelberg-New York 1971. (1971) Zbl0232.60001MR0414225
  34. C. E. Shannon, A mathematical theory of communication, Bell Sys. Techn. J. 27 (1948), 379-432, 623-656. (1948) Zbl1154.94303MR0026286
  35. Ja. G. Sinaj, On the notion of entropy of a dynamical system, (In Russian). DAN SSSR 124 (1959), 4, 768-771. (1959) 
  36. Ja. G. Sinaj, On flows with finite entropy, (In Russian). DAN SSSR 125 (1959), 6, 1200-1202. (1959) MR0103257
  37. Š. Šujan, On the integral representation of the entropy rate, To appear in Studia Sci. Math. Hungar. MR0545093
  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. MR0431512
  40. K. Winkelbauer, On discrete information sources, Transactions of the 3rd Prague Conf. on Inform. Theory etc., Prague 1964, 765-830. (1964) Zbl0126.35702MR0166000
  41. K. Winkelbauer, On the asymptotic rate of non-ergodic information sources, Kybernetika 6 (1970), 2, 127-148. (1970) Zbl0245.94013MR0275979
  42. J. Wolfowitz, Coding theorems of information theory, Second ed. Springer-Verlag, New York 1964. (1964) Zbl0132.39704MR0176851

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