Abstract
For stationary channels, channel entropy is defined as the supremum of the conditional output entropy over all stationary input sources. If the channel is $\bar{d}$-continuous and conditionally almost block independent, channel entropy gives an upper bound to the output rate of the channel. Furthermore, the channel can be approximated arbitrarily well in the $\bar{d}$-metric by any primitive channel whose noise source entropy exceeds channel entropy and cannot be so approximated if the noise source entropy is less than channel entropy.
Citation
David L. Neuhoff. Paul C. Shields. "Channel Entropy and Primitive Approximation." Ann. Probab. 10 (1) 188 - 198, February, 1982. https://doi.org/10.1214/aop/1176993922
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