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On the Optimum Rate of Transmitting Information

J. H. B. Kemperman
The Annals of Mathematical Statistics
Vol. 40, No. 6 (Dec., 1969), pp. 2156-2177
Stable URL: http://www.jstor.org/stable/2239528
Page Count: 22
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On the Optimum Rate of Transmitting Information
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Abstract

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(μ1∣μ2), of one measure μ1 relative to another measure μ2, and its relation with the total variation |μ1 - μ2|.

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