Choice of channels. Find the capacity C of the union of two channels (X1, p1(y1|x1), Y1) and (X2, p2(y2|x2), Y2), where at each
time, one can send a symbol over channel 1 or channel 2 but
not both. Assume that the output alphabets are distinct and do not
intersect.
Show that 2C = 2C1 + 2C2 . Thus, 2C is the effective alphabet
size of a channel with capacity C.