Response to the following problem:
Consider a BSC in which the channel can be in three states. In state S = 0 the output of the channel is always 0, regardless of the channel input. In state S = 1, the output is always 1, again regardless of the channel input. In state S = 2 the channel in noiseless, i.e., the output is always equal to the input. We assume that P(S = 0) = P(S = 1) = p2.
1. Determine the capacity of this channel, assuming no state information is available to the transmitter or the receiver.
2. Determine the capacity of the channel, assuming that channel state information S is available at both sides.