Alphabet-oriented and user-oriented source coding theories. (English) Zbl 0637.94006

Alphabet-oriented source coding theory as mentioned in the title is classical rate-distortion theory as covered e.g. in the book by Berger. Within this framework a joint source-channel coding theory is proved which generalizes existing results. Several examples are provided. A new user-oriented source coding theory is proposed and motivated, which makes use of distortion measures which are not of the average type. A forthcoming paper is announced (co-authored by O. Šefl and called “Spectrum-oriented source coding theory”) which will present results in the new theory.
Reviewer: A.Sgarro


94A29 Source coding
94A34 Rate-distortion theory in information and communication theory
94A24 Coding theorems (Shannon theory)
60G10 Stationary stochastic processes
94A05 Communication theory
Full Text: EuDML


[1] J. Anděl: Statistical Analysis of Time Series (in Czech). SNTL, Prague 1976. German edition: Akademie Verlag, Berlin 1984.
[2] T. Berger: Rate Distortion Theory. Prentice-Hall, Englewood Cliffs 1971.
[3] P. Billingsley: Information and Ergodic Theory. J. Wiley, New York 1965. · Zbl 0141.16702
[4] A. Buzo A. H. Gray, Jr. R. M. Gray, J. D. Markel: Speech coding based upon vector quantization. IEEE Trans, on Acoustics Speech and Signal Proc. 28 (1980), 562-574. · Zbl 0524.94012 · doi:10.1109/TASSP.1980.1163445
[5] I. Csiszár, J. Körner: Information Theory. Academic Press, New York 1981. · Zbl 0568.94012
[6] J. L. Doob: Stochastic Processes. J. Wiley, New York 1953. · Zbl 0053.26802
[7] R. G. Gallager: Information Theory and Reliable Communication. J. Wiley, New York 1968. · Zbl 0198.52201
[8] R. M. Gray, L. D. Davisson: Source coding without the ergodic assumption. IEEE Trans. Inform. Theory 20 (1974), 502- 516. · Zbl 0301.94026 · doi:10.1109/TIT.1974.1055248
[9] F. Liese, I. Vajda: Convex Statistical Distances. Teubner, Leipzig 1987. · Zbl 0656.62004
[10] J. D. Markel, A. H. Gray, Jr.: Linear Prediction of Speech. Springer-Verlag, Berlin 1976. · Zbl 0443.94002
[11] J. Nedoma: The capacity of a discrete channel. Trans. 1st Prague Conf. on Inform. Theory, Statist. Dec. Functions, Random Processes, Publ. House Czechosl. Acad. Sci., Prague 1957. · Zbl 0088.10701
[12] D. S. Ornstein: Bernoulli shifts with the same entropy are isomorphic. Adv. in Math. 4 (1970), 338-352. · Zbl 0197.33502 · doi:10.1016/0001-8708(70)90029-0
[13] C. E. Shannon: A mathematical theory of communication. Bell. System Tech. J. 27 (1948), 623-656. · Zbl 1154.94303
[14] C. E. Shannon: Coding theorems for a discrete source with a fidelity criterion. IRE Nat. Convention Record, Part 4, 142-163.
[15] J. Šedivý: A DPCM vector quantizer for speech transmission. Circuit Theory and Design 85 (V. Zima, J. Kvasil, Academia, Prague/North Holland, Amsterdam 1985, pp. 588-591.
[16] O. Šefl, I. Vajda: Spectrum-oriented source coding theory. Kybernetika 23 (1987), 6 · Zbl 0658.94007
[17] Š. Šujan: Ergodic theory, entropy and coding problems of information theory. Kybernetika 19 (1983), supplement, pp. 1-67. · Zbl 0542.94006
[18] I. Vajda: Basic Theory of Information. · Zbl 0171.40203
[19] J. Wolfowitz: Coding Theorems of Information Theory. Second edition. Springer-Verlag, Berlin 1964. · Zbl 0132.39704
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.