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# On the Transmission of Bernoulli Sources Over Stationary Channels

John C. Kieffer
The Annals of Probability
Vol. 8, No. 5 (Oct., 1980), pp. 942-961
Stable URL: http://www.jstor.org/stable/2242938
Page Count: 20
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## Abstract

For a discrete-time finite-alphabet stationary channel $\nu$ satisfying a weak continuity requirement, it is shown that there are capacities $C_s(\nu)$ and $C_b(\nu)$ which have the following operational significance. A Bernoulli source $\mu$ is transmissible over $\nu$ via sliding-block coding if and only if the entropy $H(\mu)$ of $\mu$ is no greater than $C_s(\nu); \mu$ is transmissible via block coding if and only if $H(\mu)$ is no greater than $C_b(\nu)$. The weak continuity requirement is satisfied for the $\bar{d}$-continuous channels of Gray-Ornstein as well as other channels. An example of a channel is given to show that the case $C_s(\nu) \neq C_b(\nu)$ can occur.

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