Open Access
December, 1958 Proof of Shannon's Transmission Theorem for Finite-State Indecomposable Channels
David Blackwell, Leo Breiman, A. J. Thomasian
Ann. Math. Statist. 29(4): 1209-1220 (December, 1958). DOI: 10.1214/aoms/1177706452


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.


Download Citation

David Blackwell. Leo Breiman. A. J. Thomasian. "Proof of Shannon's Transmission Theorem for Finite-State Indecomposable Channels." Ann. Math. Statist. 29 (4) 1209 - 1220, December, 1958.


Published: December, 1958
First available in Project Euclid: 27 April 2007

zbMATH: 0096.10901
MathSciNet: MR118570
Digital Object Identifier: 10.1214/aoms/1177706452

Rights: Copyright © 1958 Institute of Mathematical Statistics

Vol.29 • No. 4 • December, 1958
Back to Top