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December, 1969 On the Optimum Rate of Transmitting Information
J. H. B. Kemperman
Ann. Math. Statist. 40(6): 2156-2177 (December, 1969). DOI: 10.1214/aoms/1177697293


The present paper is partly expository and does not assume any previous knowledge of information theory or coding theory. It is meant to be the first in a series of papers on coding theory for noisy channels, this series replacing the report [12] which was widely circulated. A few of the results were reported in [11], [27] and [28]. In Sections 2 and 3 we present certain refinements and generalizations of known methods of Shannon, Fano, Feinstein and Gallager. A discussion of some other methods may be found in the surveys by Kotz [15] and Wolfowitz [28] such as those of Khintchine [14], McMillan [18] and Wolfowitz [25], [26]. Section 4 contains a number of applications. Most of this section is devoted to a certain memoryless channel with additive noise. Some of the proofs have been collected in Section 5. Finally, Section 6 describes some new results on the relative entropy $H(\mu_1\mid\mu_2),$ of one measure $\mu_1$ relative to another measure $\mu_2$, and its relation with the total variation $\|\mu_1 - \mu_2\|$.


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J. H. B. Kemperman. "On the Optimum Rate of Transmitting Information." Ann. Math. Statist. 40 (6) 2156 - 2177, December, 1969.


Published: December, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0287.94021
MathSciNet: MR252112
Digital Object Identifier: 10.1214/aoms/1177697293

Rights: Copyright © 1969 Institute of Mathematical Statistics

Vol.40 • No. 6 • December, 1969
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