Suppose the symbols fall into several groups such that the noise never causes a symbol in one group to be mistaken for a symbol in another group. Let the capacity for the nth group be n (in bits per second) when we use only the symbols in this group. Show that for best use of the entire set, the total probability Pn of all symbols in the nth group should be 2Cn Pn= 26 'n Suppose the symbols fall into several groups such that the noise never causes a symbol in one group to be mistaken for a symbol in another group. Let the capacity for the nth group be n (in bits per second) when we use only the symbols in this group. Show that the channel capacity is C = log(2Cn). n