Expanding information capacity of Gaussian Channel

Question

I'm currently try to understand a Gaussian Capacity Channel. I found litterature on internet, and some expand the information capacity of a Gaussian Channel as follow: $$I(X,Y)= h(Y) -h(Y\mid X) = h(Y) - h(X+Z\mid X).$$

Can anyone explain me this expansion? Does it mean that $h(Y\mid X)=h(X+Z\mid X)$?

Answer 1

It simply means that the channel output $Y$ is the sum of the channel input $X$ and the noise $Z$, i.e. $Y=X+Z$.