Compound channel

A compound channel is an information theoretic model for a channel whose law is governed by an unknown parameter. A discrete memoryless compound channel $\mathcal{W}$ is a collection of channels $\{W_{\theta}(y|x) : \theta \in \Theta\}$, where $\theta$ is the parameter of the channel and $\Theta$ is the set of possible values for the parameter. Codes for this channel must achieve reliable communication regardless of the parameter $\theta$.