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


 * $$f(i) = 2^{-x_i}$$

where $$x_i$$ 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.