# Channel capacity of a coin flip

I'm having some issue in understanding the channel capacity.

$C=max_{p(x)}I(X, Y)$

In particular the practical side. For example (an exercise), if I toss a fair coin and I transmit the result in a binary channel. What's the channel capacity?

I'm trying to imagine the channel graph. I believe is something like this.

H --1--> H

T --1--> T

A noiseless channel like this has $C=log|X|$ so $C=log2=1bit$. Why? I could represent it like this:

x --0.5--> H

x --0.5--> T

And the channel capacity becomes $C=log1=0$ because $|X|=1$.

Please someone help I'm quite confused.

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