Dyadic distribution

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

Definition

A dyadic distribution on the nonnegative integers 0, 1, 2, ... is a probability distribution whose probability mass function is

$f(u)=2^{-n_{u}},\quad u\in U$

where n_u is some (positive) integer. More generally it is a categorical distribution in which the probability assigned to any label is of the above form

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

References

• Cover, T.M., Joy A. Thomas, J.A. (2006) Elements of information theory, Wiley. ISBN 0-471-24195-4