Turbo code: Difference between revisions

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In [[information theory]], '''turbo codes''' (originally in French ''Turbocodes'') are a class of high-performance [[forward error correction]] (FEC) codes developed around 1990–91, but first published in 1993. They were the first practical codes to closely approach the maximum channel capacity or [[Shannon–Hartley theorem|Shannon limit]], a theoretical maximum for the [[code rate]] at which reliable communication is still possible given a specific noise level. Turbo codes are used in [[3G]]/[[4G]] mobile communications (e.g., in [[UMTS]] and [[LTE (telecommunication)|LTE]]) and in ([[Deep Space Network|deep space]]) [[satellite]] [[telecommunication|communications]] as well as other applications where designers seek to achieve reliable information transfer over bandwidth- or latency-constrained communication links in the presence of data-corrupting noise. Turbo codes compete with [[Low-density parity-check code|low-density parity-check]] (LDPC) codes, which provide similar performance. Until the patent for turbo codes expired,<ref>{{cite patent |url=https://www.google.com/patents/US5446747 |country=US |number=5446747}}</ref> the patent-free status of LDPC codes was an important factor in LDPC's continued relevance.<ref name="Closing">{{cite journal |author=Erico Guizzo |title=CLOSING IN ON THE PERFECT CODE |journal=IEEE Spectrum |date=Mar 1, 2004 |url=https://spectrum.ieee.org/closing-in-on-the-perfect-code|archive-url=https://archive.today/20230423205925/https://spectrum.ieee.org/closing-in-on-the-perfect-code|url-status=dead|archive-date=23 April 2023}} "Another advantage, perhaps the biggest of all, is that the LDPC patents have expired, so companies can use them without having to pay for intellectual-property rights."</ref>

The name "turbo code" arose from the feedback loop used during normal turbo code decoding, which was analogized to the exhaust feedback used for engine [[turbocharging]]. [[Joachim Hagenauer|Hagenauer]] has argued the term turbo code is a misnomer since there is no feedback involved in the encoding process.<ref>{{cite journal |url=http://www.ima.umn.edu/csg/bib/bib16.0429hage.pdf |first1=Joachim |last1=Hagenauer |title=Iterative Decoding of Binary Block and Convolutional Codes |accessdate=20 March 2014 |url-status=dead |archiveurl=https://web.archive.org/web/20130611235418/http://www.ima.umn.edu/csg/bib/bib16.0429hage.pdf |archivedate=11 June 2013 |first2=Elke |last2=Offer |first3=Luiz |last3=Papke |volume=42 |issue=2 |date=March 1996 |journal=IEEE Transactions on Information Theory|pages=429–445 |doi=10.1109/18.485714 }}</ref>

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*{{cite conference |last1=Garzón-Bohórquez |first1=Ronald |first2=Charbel Abdel |last2=Nour |first3=Catherine |last3=Douillard |title=Improving Turbo codes for 5G with parity puncture-constrained interleavers |conference=9th International Symposium on Turbo Codes and Iterative Information Processing (ISTC)|date=2016 |pages=151–5 |url=https://hal.science/hal-01421989/file/Final%20Manuscript.pdf |doi=10.1109/ISTC.2016.7593095}}

==External links==

* {{cite journal |first=Erico |last=Guizzo |url=https://spectrum.ieee.org/computing/software/closing-in-on-the-perfect-code |archive-url=https://web.archive.org/web/20091011113149/http://www.spectrum.ieee.org/computing/software/closing-in-on-the-perfect-code |url-status=dead |archive-date=11 October 2009 |title=Closing In On The Perfect Code |journal=IEEE Spectrum |date=March 2004 |volume=41 |issue=3 |pages=36–42 |doi=10.1109/MSPEC.2004.1270546 |s2cid=21237188 |url-access=subscription }}

* [http://www.csee.wvu.edu/~mvalenti/documents/valenti01.pdf "The UMTS Turbo Code and an Efficient Decoder Implementation Suitable for Software-Defined Radios"] {{Webarchive|url=https://web.archive.org/web/20161020193559/http://www.csee.wvu.edu/~mvalenti/documents/valenti01.pdf |date=20 October 2016 }} (''International Journal of Wireless Information Networks'')

* {{cite journal |first=Dana |last=Mackenzie | title=Take it to the limit | journal=New Scientist | volume=187 | issue=2507 | year=2005 | pages=38–41 |url=https://www.newscientist.com/article.ns?id=mg18725071.400}}

* [httphttps://www.sciencenews.org/articlesarticle/20051105/bob8.asppushing-limit "Pushing the Limit"], a ''[[Science News]]'' feature about the development and genesis of turbo codes

* [http://www-turbo.enst-bretagne.fr/ International Symposium On Turbo Codes]

* [http://www.iterativesolutions.com/Matlab.htm Coded Modulation Library], an open source library for simulating turbo codes in matlab