I've got a channel matrix $P$ of the form $\begin{bmatrix} Q \\ R \end{bmatrix}$ where $Q,R$ are channel matrices of symmetric channels, so they now have different input alphabets but the same output alphabet.
How do you work out the capacity of this channel?
Intuitively I feel like it would be the maximum of the capacities of the individual channel matrices but I really have no idea how to start on proving it.
Thanks!