Dyadic distribution

Dyadic distribution

A dyadic 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 nu 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.[citation needed]

References

  • Cover, T.M., Joy A. Thomas, J.A. (2006) Elements of information theory, Wiley. ISBN 0471241954

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