McMillan inequality
= McMillan inequality
{c}
The lengths of a finite <uniquely decodable code> satisfy $\sum_a2^{-l(a)}\leq1$, 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 $(\sum_a2^{-l(a)})^r$ by $r\max_a l(a)$. Taking $r$th roots proves the claim.