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Channel Entropy and Primitive Approximation

David L. Neuhoff and Paul C. Shields
The Annals of Probability
Vol. 10, No. 1 (Feb., 1982), pp. 188-198
Stable URL: http://www.jstor.org/stable/2243780
Page Count: 11
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Channel Entropy and Primitive Approximation
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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 d̄-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 d̄-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.

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