We have no satisfactory capacity formula for most channels with finite states.

Here, we consider some interesting examples of finite state channels,

such as Gilbert-Elliot channel, trapdoor channel, etc., to reveal special

characters of problems and difficulties to determine the capacities.

Meanwhile, we give a simple expression of the capacity formula for

Gilbert-Elliot channel by using a hidden Markov source for the optimal

input process. This idea should be extended to other finite state channels.