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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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.

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

First available in Project Euclid: 27 April 2007

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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.

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