Punctured code: Difference between revisions

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{{Short description|Signal coding technique}}

In [[coding theory]], '''puncturing''' is the process of removing some of the parity bits after encoding with an [[error correction and detection|error-correction code]]. This has the same effect as encoding with an error-correction code with a higher rate, or less redundancy. However, with puncturing the same decoder can be used regardless of how many bits have been punctured, thus puncturing considerably increases the flexibility of the system without significantly increasing its complexity.

{{confuse|Puncturing (topology)}}

In [[coding theory]], '''puncturing''' is the process of removing some of the [[Parity bit|parity bits]] after encoding with an [[error correction and detection|error-correction code]]. This has the same effect as encoding with an error-correction code with a higher rate, or less redundancy. However, with puncturing the same decoder can be used regardless of how many bits have been punctured, thus puncturing considerably increases the flexibility of the system without significantly increasing its complexity.

[[File:Punct.png|thumb|600px| Short illustration of the puncturing procedure.]]

In some cases, aA pre-defined pattern of puncturing is used in an encoder, in some cases. Then, the inverse operation, known as depuncturing, is implemented by the decoder.

Puncturing is used in [[UMTS]] during the rate matching process. It is also used in [[Wi-Fi]], Wi-SUN, [[GPRS]], [[EDGE (telecommunication)|EDGE]], [[DVB-T]] and [[EDGEDigital Audio Broadcasting|DAB]], as well as in the [[DVB-T]] and [[Digital Radio Mondiale|DRM]] Standards.

Puncturing is often used with the [[Viterbi algorithm]] in coding systems.

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Puncturing was introduced by [[Gustave Solomon]] and [[J. J. Stiffler]] in 1964.{{refn|{{cite news|last1=Solomom |first= G.|first2=J. J.|last2= Stiffler |title= Punctured Systematic Cyclic Codes<!--<<corrected "coder" to "codes"--> |work=IEEE Convention Record |volume=12 |year= 1964}} }}{{refn|{{cite journal|last1=Solomon |first1=G. |last2= Stiffler |first2=J.J. |date= April 1965 |title= Algebraically punctured cyclic codes |journal= Information and Control| volume=8 |number=2 |pages=170&ndash;79 |doi= 10.1016/S0019-9958(65)90080-X |doi-access=free }} }}

==See also==

* [[Singleton bound]], an upper bound in coding theory

==References==

{{reflist}}

* {{cite book | title=Introduction to the Theory of Error-Correcting Codes |title-link= Introduction to the Theory of Error-Correcting Codes | volume=48 | series=Wiley Series in Discrete Mathematics and Optimization | first=Vera | last=Pless |authorlink=Vera Pless| edition=Third | publisher=John Wiley & Sons | year=2011 | isbn=1118030990978-1118030998 }}

[[Category:Coding theory]]