Definition (Operational channel capacity)

The operational capacity $C_{op}$, of a discrete channel is the supremum of all achievable rates: $$C_{op}=\sup\{R:R \mbox{ is achievable}\}$$

Definition (Operational channel capacity (continuous))

The operational capacity, $C_{op}(P)$ of the Gaussian channel with power constraint $P$ is the supremum of all achievable rates: $$C_{op}(P)=\sup\{R: R\mbox{ achievable}\}$$