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Continuity and quantization of channels with infinite alphabets. (English) Zbl 0479.94012

MSC:
94A24 Coding theorems (Shannon theory)
94A34 Rate-distortion theory in information and communication theory
94A17 Measures of information, entropy
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References:
[1] K. Winkelbauer: On the coding theorem for decomposable channels I, II. Kybernetika 7 (1971), 109-123, 230-255. · Zbl 0244.94006
[2] J. C. Kieffer: A general formula for the capacity of a stationary nonanticipatory channel. Inform. and Control 26 (1974), 381-391. · Zbl 0292.94017
[3] R. M. Gray D. S. Ornstein: Block coding for discrete stationary d-continuous noisy channels. IEEE Trans. Inform. Theory 25 (1979), 292-306. · Zbl 0398.94013
[4] J. Wolfowitz: Coding Theorems of Information Theory. 2nd Springer-Verlag, Berlin - Gottingen -New York 1964. · Zbl 0132.39704
[5] J. C. Kieffer: Block coding for a stationary channel satisfying a weak continuity condition.
[6] R. M. Gray J. C. Kieffer: Mutual information rate, distortion and quantization in metric spaces. IEEE Trans. Inform. Theory 26 (1980), 412-422. · Zbl 0452.94010
[7] Š. Šujan: Channels with additive asymptotically mean stationary noise. Kybernetika 17 (1981), 1, 1-15. · Zbl 0455.94008
[8] P. Billingsley: Convergence of Probability Measures. J. Wiley, New York-London-Sydney-Toronto 1968. · Zbl 0172.21201
[9] J. C. Kieffer: On the transmission of Bernoulli sources over stationary channels. Ann. Prob. 8 (1980), 942-961. · Zbl 0452.94012
[10] Š. Šujan: A generalized coding problem for discrete information sources. Supplement. Kybernetika 13 (1977), 95 pp.
[11] P. Billingsley: Ergodic Theory and Information. J. Wiley, New York 1965. · Zbl 0141.16702
[12] R. L. Dobrushin: A general formulation of the basic Shannon theorem of information theory. (in Russian). Uspehi mat. nauk 14 (1959), 3-104.
[13] K. Winkelbauer: On the asymptotic rate of non-ergodic information sources. Kybernetika 6 (1970), 2, 127-148. · Zbl 0245.94013
[14] R. M. Gray L. D. Davisson: Source coding without the ergodic assumption. IEEE Trans. Inform. Theory 20 (1974), 502-516. · Zbl 0301.94026
[15] Š. Šujan: Block transmissibility and quantization. · Zbl 0526.94008
[16] F. Topsøe: Preservation of weak convergence under mappings. Ann. Math. Statist. 38 (1967), 1661-1665. · Zbl 0178.21201
[17] Š. Šujan: On the capacity of asymptotically mean stationary channels. Kybernetika 17 (1981), 3, 222-233. · Zbl 0483.94009
[18] K. Jacobs: Über die Struktur der mittleren Entropie. Math. Z. 78 (1962), 33-43. · Zbl 0105.32801
[19] J. C. Kieffer: Some universal noiseless multiterminal source coding theorems. Inform. and Control 46 (1980), 93-107. · Zbl 0452.94013
[20] K. Winkelbauer: On discrete information sources. Trans. 3rd Prague Conf. Inform. Theory, NČSAV Prague 1964, 765-830. · Zbl 0126.35702
[21] K. Winkelbauer: On the capactiy of decomposable channels. Trans. 6th Prague Conf. Inform. Theory, Academia, Prague 1973, 903-914.
[22] R. M. Gray D. L. Neuhoff P. C. Shields: A generalization of Ornstein’s d-distance with applications to information theory. Ann. Prob. 3 (1975), 315-328. · Zbl 0304.94025
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