Prefix code: Difference between revisions

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A '''prefix code''' is a type of [[code]] system (typically a [[variable-length code]]) distinguished by its possession of the "prefix property"; which states that there is no valid [[code word]] in the system that is a [[prefix (computer science)|prefix]] (start) of any other valid code word in the set. For example, a code with code words {9, 59, 55} has the prefix property; a code consisting of {9, 5, 59, 55} does not, because "5" is a prefix of both "59" and "55". With a prefix code, a receiver can identify each word without requiring a special marker between words.

Prefix codes are also known as '''prefix-free codes''', '''prefix condition codes''' and '''instantaneous codes'''. Although [[Huffman coding]] is just one of many algorithms for deriving prefix codes, prefix codes are also widely referred to as "Huffman codes", even when the code was not produced by a Huffman algorithm. The term '''comma-free code''' is sometimes also applied as a synonym for prefix-free codes<ref>US [[Federal Standard 1037C]]</ref><ref>{{citation|title=ATIS Telecom Glossary 2007|url=http://www.atis.org/glossary/definition.aspx?id=6416|accessdate=December 4, 2010}}</ref> but in most mathematical books and articles (e. g. <ref>{{citation|last1=Berstel|first1=Jean|last2=Perrin|first2=Dominique|title=Theory of Codes|publisher=Academic Press|year=1985}}</ref><ref>{{citation|doi=10.4153/CJM-1958-023-9|last1=Golomb|first1=S. W.|author1-link=Solomon W. Golomb|last2=Gordon|first2=Basil|author1-link=Basil Gordon|last3=Welch|first3=L. R.|title=Comma-Free Codes|journal=Canadian Journal of Mathematics|volume=10|issue=2|pages=202–209|year=1958|url=http://books.google.com/books?id=oRgtS14oa-sC&pg=PA202}}</ref>) it is used to mean [[self-synchronizing code]]s, a subclass of prefix codes.

Using prefix codes, a message can be transmitted as a sequence of concatenated code words, without any [[out-of-band]] markers to [[framing (telecommunication)|frame]]{{Disambiguation needed|date=February 2012}} the words in the message. The recipient can decode the message unambiguously, by repeatedly finding and removing prefixes that form valid code words. This is not possible with codes that lack the prefix property, for example {0,&nbsp;1,&nbsp;10,&nbsp;11}: a receiver reading a "1" at the start of a code word would not know whether that was the complete code word "1", or merely the prefix of the code word "10" or "11".