The Annals of Mathematical Statistics

Proof of Shannon's Transmission Theorem for Finite-State Indecomposable Channels

David Blackwell, Leo Breiman, and A. J. Thomasian

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Abstract

For finite-state indecomposable channels, Shannon's basic theorem, that transmission is possible at any rate less than channel capacity but not at any greater rate, is proved. A necessary and sufficient condition for indecomposability, from which it follows that every channel with finite memory is indecomposable, is given. An important tool is a modification, for some processes which are not quite stationary, of theorems of McMillan and Breiman on probabilities of long sequences in ergodic processes.

Article information

Source
Ann. Math. Statist. Volume 29, Number 4 (1958), 1209-1220.

Dates
First available in Project Euclid: 27 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177706452

Digital Object Identifier
doi:10.1214/aoms/1177706452

Mathematical Reviews number (MathSciNet)
MR118570

Zentralblatt MATH identifier
0096.10901

JSTOR
links.jstor.org

Citation

Blackwell, David; Breiman, Leo; Thomasian, A. J. Proof of Shannon's Transmission Theorem for Finite-State Indecomposable Channels. Ann. Math. Statist. 29 (1958), no. 4, 1209--1220. doi:10.1214/aoms/1177706452. https://projecteuclid.org/euclid.aoms/1177706452


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