I'm reading about Channel capacity from Elements of Information theory - Wiley (2006). The definition of channel capacity, which is characterized by $p(y|x)$, is
$\hspace{3.0cm} C = \max_{p(x)} I(X; Y)$
According to the definition, the only way to increase channel capacity is to modify its characteristic $p(y|x)$. To do this, we can do nothing rather than modify the channel itself, not the source or the method of transmitting information (e.g. use feedback).
Am I right ? If I were wrong, please correct me.
Yes, of course. A channel, in this context, corresponds exactly to the transition probabilities $p(y|x)$. The capacity depends only on $p(y|X)$, hence it's a property of a channel. It would make no sense to think of "increase the capacity of a channel" without modifying the channel itself.