Cumulative Shannon code

Order source probabilities as $p_1\ge \cdots \ge p_N$, putand take the first $l_i$ binary digits of $b_i$ as the codeword for symbol $i$. Since $b_j-b_i\ge p_i\ge 2^{-l_i}$ for $j>i$, two cumulative probabilities cannot lie in the same dyadic interval selected by the earlier codeword. The resulting code is prefix-free.