Unary coding: Difference between revisions

Revision as of 05:00, 20 July 2006

Revision as of 12:22, 21 February 2007

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'''Unary coding''' is an [[entropy encoding]] that represents a [[Naturalnatural number]], ''n'', with ''n-1'' − 1 ones followed by a zero. For example 5 is represented as 11110. Some representations use ''n'' ones followed by a zero. Also the use ofThe ones &and zeros are interchangeable without loss of generality.

Unary coding is easily shown to be an optimally efficient encoding for the following discrete [[probability distribution]]

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:<math>P(n) = (k-1)k^{-n}\,</math>

for which <math>''k'' \&ge; \varphi&phi; \approx= 1.618 033 989</math>61803398879&hellip;, the [[golden ratio]], or, more generally, for any distribution for which

:<math>P(n) \ge P(n+1) + P(n+2)\, </math>