The Annals of Mathematical Statistics
- Ann. Math. Statist.
- Volume 40, Number 6 (1969), 2156-2177.
On the Optimum Rate of Transmitting Information
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  which was widely circulated. A few of the results were reported in ,  and . 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  and Wolfowitz  such as those of Khintchine , McMillan  and Wolfowitz , . 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 $\|\mu_1 - \mu_2\|$.
Ann. Math. Statist., Volume 40, Number 6 (1969), 2156-2177.
First available in Project Euclid: 27 April 2007
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Kemperman, J. H. B. On the Optimum Rate of Transmitting Information. Ann. Math. Statist. 40 (1969), no. 6, 2156--2177. doi:10.1214/aoms/1177697293. https://projecteuclid.org/euclid.aoms/1177697293