Open Access
October, 1980 On the Transmission of Bernoulli Sources Over Stationary Channels
John C. Kieffer
Ann. Probab. 8(5): 942-961 (October, 1980). DOI: 10.1214/aop/1176994623


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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John C. Kieffer. "On the Transmission of Bernoulli Sources Over Stationary Channels." Ann. Probab. 8 (5) 942 - 961, October, 1980.


Published: October, 1980
First available in Project Euclid: 19 April 2007

zbMATH: 0452.94012
MathSciNet: MR586778
Digital Object Identifier: 10.1214/aop/1176994623

Primary: 94A15

Keywords: Bernoulli sources , block codes , sliding-block codes , Stationary channels

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • October, 1980
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