Kraft inequality

The Kraft inequality in information theory states (roughly?) that, for any probability distribution $p(x)$, there is a prefix code C under which each $x$ is encoded with a codeword of length $\lceil\log_2 p(x)\rceil$ bits, and that this code minimizes the expected code length.

Conversely, any code can be seen as representing a data distribution, where each element $x$ with codeword $C(x)$ has probability $2^{-|C(x)|}$.

Reference: https://arxiv.org/abs/math/0406077