Every channel can be expressed as a convex combination of deterministic
channels with each deterministic channel corresponding to one particular
intrinsic state. Such convex combinations are in general not unique, each
giving rise to a specific intrinsic-state distribution. In this paper we study
the maximum and the minimum capacities of a channel when the realization of its
intrinsic state is causally available at the encoder and/or the decoder.
Several conclusive results are obtained for binary-input channels and
binary-output channels. Byproducts of our investigation include a
generalization of the Birkhoff-von Neumann theorem and a condition on the
uselessness of causal state information at the encoder.