The channel C is (known as the Z channel) shown in Figure P-12.43.
1. Find the input probability distribution that achieves capacity.
2. What is the input distribution and capacity for the special cases ? = 0, ? = 1, and ? = 0.5?
3. Show that if n such channels are cascaded, the resulting channel will be equivalent to a Z channel with ?1 = ?n.
4. What is the capacity of the equivalent Z channel when n→∞?
