 McMillan inequality

The lengths of a finite uniquely decodable code satisfy ${\sum }_a{2}^{-l(a)}\le 1$, even when the code is not a prefix code. Distinct concatenations of $r$ codewords remain distinct; counting the possible binary strings of each total length bounds $({\sum }_a{2}^{-l(a)}{)}^r$ by $r{\max }_{a}l(a)$. Taking $r$th roots proves the claim.