Dyadic distribution

A dyadic (or 2-adic) distribution is a specific type of discrete probability distribution that is of some theoretical importance in data compression.

Definition

A dyadic distribution is a probability distribution whose probability mass function is

${\displaystyle f(i)=2^{-x_{i}}}$

where ${\displaystyle x_{i}}$ is some whole number.

It is possible to find a binary code defined on this distribution, which has an average code length that is equal to the entropy.^[1]