Unary coding: Difference between revisions

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'''Unary coding''',<ref group="nb" name="NB1"/> sometimes called '''thermometer code''', is an [[entropy encoding]] that represents a [[natural number]], ''n'', with ''n'' ones followed by a zero (if ''natural number'' is understood as ''non-negative integer'') or with ''n''&nbsp;&minus;&nbsp;1 ones followed by a zero (if ''natural number'' is understood as ''strictly positive integer''). For example 5 is represented as 111110 or 11110. Some representations use ''n'' or ''n''&nbsp;&minus;&nbsp;1 zeros followed by a one. The ones and zeros are interchangeable [[without loss of generality]]. Unary coding is both a [[prefix-free code]] and a [[self-synchronizing code]].

{| class="wikitable"

! n (non-negative) !! n (strictly positive) !! Unary code !! Alternative

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==Unary coding in biological networks==

New research has shown that unary coding is used in the neural circuits responsible for [[birdsong]] production.<ref>Fiete, I.R. and H.S. Seung, Neural network models of birdsong production, learning, and coding. New Encyclopediaof Neuroscience. Eds. L. Squire, T. Albright, F. Bloom, F. Gage, and N. Spitzer. Elsevier, 2007.<name="Fiete_2007"/ref><ref>{{cite journal | last1 name= Moore | first1 = J.M. | display-authors = 1 | last2 = et al | year = 2011 | title = Motor pathway convergence predicts syllable repertoire size in oscine birds | journal = Proc. Natl. Acad. Sci. USA | volume = 108 | issue = | pages = 16440–16445 | doi=10.1073"Moore_2011"/pnas.1102077108 | pmid=21918109 | pmc=3182746}}</ref> The nucleus in the brain of the songbirds that plays a part in both the learning and the production of bird song is the HVC (high vocal center). This coding works as space coding which is an efficient strategy for biological circuits due to its inherent simplicity and robustness.

==Generalized unary coding==

A generalized version of unary coding is able to represent numbers much more efficiently than standard unary coding.<ref>{{cite journal | last1 name= Kak | first1 = S | year = 2015 | title = Generalized unary coding | url = http://link.springer.com/article/10.1007/s00034-015-0120-7#page-1 | journal = Circuits, Systems and Signal Processing | volume = 35| issue = | pages = 1419–1426| doi=10.1007/s00034-015-0120-7}}<"Kak_2015"/ref> Here's an example of generalized unary coding for integers from 1 through 15 that requires only 7 bits (where three bits are arbitrarily chosen in place of a single one in standard unary to show the number). Note that the representation is cyclic where one uses markers to represent higher integers in higher cycles.

{| class="wikitable"

! n !! Unary code !! Generalized unary

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==See also==

*[[Unary numeral system]]

==Notes==

{{Reflist|group="nb"|refs=

<ref group="nb" name="NB1">The aquivalent to the term "unary coding" in German scientific literature is "{{lang|de|BCD-Zählcode}}", which would translate into "[[Binary coded decimal]] counting code". This must not be confused with the similar German term "{{lang|de|BCD-Code}}" translating to [[BCD code]] in English.</ref>

}}

==References==

{{Reflist}}|refs=

<ref name="Fiete_2007">{{cite book |author-last1=Fiete |author-first1=I. R. |author-first2=H. S. |author-last2=Seung |chapter=Neural network models of birdsong production, learning, and coding |title=New Encyclopedia of Neuroscience |editor-first1=L. |editor-last1=Squire |editor-first2=T. |editor-last2=Albright |editor-first3=F. |editor-last3=Bloom |editor-first4=F. |editor-last4=Gage |editor-first5=N. |editor-last5=Spitzer |publisher=[[Elsevier]] |date=2007}}</ref>

<ref name="Moore_2011">{{cite journal |author-last1=Moore |author-first1=J. M. |display-authors=etal |date=2011 |title=Motor pathway convergence predicts syllable repertoire size in oscine birds |journal=Proc. Natl. Acad. Sci. USA |volume=108 |pages=16440–16445 |doi=10.1073/pnas.1102077108 |pmid=21918109 |pmc=3182746}}</ref>

<ref name="Kak_2015">{{cite journal |author-last1=Kak |author-first1=S. |date=2015 |title=Generalized unary coding |url=http://link.springer.com/article/10.1007/s00034-015-0120-7#page-1 |journal=Circuits, Systems and Signal Processing |volume=35 |pages=1419–1426 |doi=10.1007/s00034-015-0120-7}}</ref>

}}

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