Past exam of the communication Theory course of the University of Oxford / 2008 / 2 / c / ii / Solution

Let $X$ be the original input, $U$ the output of the first channel, and $Y$ the final output. The independent erasure flag is observable from $Y$. The mutual information chain rule, conditioning on that flag, givesThe same uniform input maximizes $I(X;U)$ as in the binary symmetric channel. ThusThis scaling works because the erasure event is independent of both the input and the first channel noise.