Turbo code: Difference between revisions

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{{Short description|High-performance forward error correction codes}}

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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 [[LDPC code]]s ("low-density parity-check"), which provide similar performance.

{{Short description|High-performance forward error correction codes}}

{{Use mdy dates|date = March 2019}}

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 [[LDPC code]]s ("low-density parity-check"), which provide similar performance.

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 web |url=http://www.ima.umn.edu/csg/bib/bib16.0429hage.pdf |first1=Joachim |last1=Joachim Hagenauer |display-authors=etal |title=Iterative Decoding of Binary Block and Convolutional Codes |accessdate=2014-03-20 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 |df=dmy }}</ref>

==History==

The fundamental patent application for turbo codes was filed on 23 April 23, 1991. The patent application lists [[Claude Berrou]] as the sole inventor of turbo codes. The patent filing resulted in several patents including [https://www.google.com/patents/US5446747 US Patent 5,446,747], which expired 29 August 29, 2013.

The first public paper on turbo codes was "''Near Shannon Limit Error-correcting Coding and Decoding: Turbo-codes''".<ref>{{Citation|url=https://www.researchgate.net/publication/3604275|first=Claude|first2=Alain|first3=Punya|last=Berrou|last2=Glavieux|last3=Thitimajshima|title=Near Shannon Limit Error – Correcting|accessdate=11 February 2010}}</ref> This paper was published 1993 in the Proceedings of IEEE International Communications Conference. The 1993 paper was formed from three separate submissions that were combined due to space constraints. The merger caused the paper to list three authors: Berrou, [[Alain Glavieux|Glavieux]], and [[Punya Thitimajshima|Thitimajshima]] (from Télécom Bretagne, former [[École Nationale Supérieure des Télécommunications de Bretagne|ENST Bretagne]], France). However, it is clear from the original patent filing that Berrou is the sole inventor of turbo codes and that the other authors of the paper contributed material other than the core concepts.

Turbo codes were so revolutionary at the time of their introduction that many experts in the field of coding did not believe the reported results. When the performance was confirmed a small revolution in the world of coding took place that led to the investigation of many other types of iterative signal processing.

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* [[MediaFLO]], terrestrial mobile television system from [[Qualcomm]].

* The [[return link|interaction channel]] of [[satellite communication]] systems, such as [[DVB-RCS]]<ref>[http://www.etsi.org/deliver/etsi_en/301700_301799/301790/01.05.01_60/en_301790v010501p.pdf Digital Video Broadcasting (DVB); Interaction channel for Satellite Distribution Systems], ETSI EN 301 790, V1.5.1, May 2009.</ref> and [http://www.dvb.org/standards/dvb-rcs2 DVB-RCS2].

* Recent [[NASA]] missions such as [[Mars Reconnaissance Orbiter]] use turbo codes as an alternative to [[Reed–Solomon_error_correctionReed–Solomon error correction|RS]]-[[Viterbi decoder|Viterbi]] codes.

* [[IEEE 802.16]] ([[WiMAX]]), a wireless metropolitan network standard, uses block turbo coding and convolutional turbo coding.

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* [http://itpp.sourceforge.net IT++ Home Page] The [[IT++]] is a powerful C++ library which in particular supports turbo codes

* [http://www.inference.phy.cam.ac.uk/mackay/CodesTurbo.html Turbo codes publications by David MacKay]

* [https://aff3ct.github.io AFF3CT Home Page] ([[AFF3CT|A Fast Forward Error Correction Toolbox]]) for high speed turbo codes simulations in software

* [http://www.scholarpedia.org/article/Turbo_codes Turbo code] by Dr. Sylvie Kerouédan and [[Claude Berrou|Dr. Claude Berrou]] (scholarpedia.org).

* [https://www.intel.com/content/dam/www/programmable/us/en/pdfs/literature/an/an505.pdf 3GPP LTE Turbo Reference Design].

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* [https://www.mathworks.com/help/comm/examples/parallel-concatenated-convolutional-coding-turbo-codes.html Parallel Concatenated Convolutional Coding: Turbo Codes (MatLab Simulink)]

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==Further reading==

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===Publications===

* Battail, Gérard. "A conceptual framework for understanding turbo codes." IEEE Journal on Selected Areas in Communications 16.2 (1998): 245-254245–254.

* Brejza, Matthew F., et al. "20 years of turbo coding and energy-aware design guidelines for energy-constrained wireless applications." IEEE Communications Surveys & Tutorials 18.1 (2016): 8-288–28.

* Garzón-Bohórquez, Ronald, Charbel Abdel Nour, and Catherine Douillard. "Improving Turbo codes for 5G with parity puncture-constrained interleavers." Turbo Codes and Iterative Information Processing (ISTC), 2016 9th International Symposium on. IEEE, 2016.