On the Transmission of Bernoulli Sources Over Stationary Channels

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.