Proof of Shannon's Transmission Theorem for Finite-State Indecomposable Channels
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.
Permanent link to this document: http://projecteuclid.org/euclid.aoms/1177706452
Digital Object Identifier: doi:10.1214/aoms/1177706452
Mathematical Reviews number (MathSciNet): MR118570
Zentralblatt MATH identifier: 0096.10901