×

On the asymptotic rate of non-ergodic information sources. (English) Zbl 0245.94013


MSC:

94A15 Information theory (general)

References:

[1] P. R. Halmos: Measure theory. New York 1950. · Zbl 0040.16802
[2] A. I. Khinchin: Mathematical foundations of information theory. Dover Publications, New York 1957. · Zbl 0088.10404
[3] N. Kryloff N. Bogoliouboff: La théorie générale de la mesure dans son application à l’étude des systèmes dynamique de la mécanique non linéaire. Ann. of Math. 38 (1937), 65-113. · JFM 63.1002.01
[4] B. McMillan: The basic theorems of information theory. Ann. Math. Stat. 24 (1953), 196-219. · Zbl 0050.35501 · doi:10.1214/aoms/1177729028
[5] J. C. Oxtoby: Ergodic sets. Bull. Amer. Math. Soc. 58 (1952), 116-136. · Zbl 0046.11504 · doi:10.1090/S0002-9904-1952-09580-X
[6] K. R. Parthasarathy: On the integral representation of the rate of transmission of a stationary channel. Illinois Journ. of Math. 5 (1961), 2, 299-305. · Zbl 0100.33903
[7] K. R. Parthasarathy: A note on McMillan’s theorem for countable alphabets. Transact. Third Prague Conf. on Inform. Theory etc., Prague 1964, 541-543. · Zbl 0199.21401
[8] K. R. Parthasarathy: Effective entropy rate and transmission of information through channels with additive random noise. Manuscript, 1962. · Zbl 0119.34003
[9] A. Perez: Notions généralizées d’incertitude, d’entropie et d’information. Transact. First Prague Conf. on Inform. Theory etc., Prague 1957, 183-208.
[10] A. Perez: Sur la théorie de l’information dans le cas d’un alphabet abstrait. Transact. First Prague Conf. on Inform. Theory etc., Prague 1957, 209-243. · Zbl 0106.33102
[11] A. Perez: Extensions of Shannon-McMillan’s limit theorem to more general stochastic processes. Transact. Third Prague Conf. on Inform. Theory etc., Prague 1964, 545-574. · Zbl 0126.35703
[12] V. A. Rohlin: New progress in the theory of transformation with invariant measure. (In Russian). Usp. matem. nauk 15 (1960), 3-26.
[13] C. E. Shannon: A mathematical theory of communication. Bell System Tech. Journ. 27 (1948), Part I, 379-423. · Zbl 1154.94303
[14] I. G. Sinal: On the flows with finite entropy. (In Russian). Dokl. Akad. Nauk 125 (1959), 6, 1200-1202. · Zbl 0117.35202
[15] K. Winkelbauer: On discrete information sources. Transact. Third Prague Conf. on Inform. Theory etc., Prague 1964, 765-830. · Zbl 0126.35702
[16] K. Winkelbauer: Axiomatic definition of channel capacity and entropy rate. Transact. Fourth Prague Conf. on Inform. Theory etc., Prague 1967, 661-705.
[17] K. Winkelbauer: Channels with finite past history. Transact. Second Prague Conf. on Inform. Theory etc., Prague 1960, 685-831. · Zbl 0161.16904
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.