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.
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. https://doi.org/10.1214/aoms/1177706452
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