(a) Show that in a code of M code words satisfying the Kraft inequality with equality, the maximum length is at most M - 1. Explain why this ensures that the number of distinct such codes is finite.
(b) Consider the number SM of distinct full code trees with M terminal nodes. Count two trees as being different if the corresponding set of code words is different. That is, ignore the set of source symbols and the mapping between source symbols and code words. Show that (S2) = 1 and show that, for M > 2,
