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Convolutional codes were introduced in 1955 by [[Peter Elias]]. It was thought that convolutional codes could be decoded with arbitrary quality at the expense of computation and delay. In 1967 [[Andrew Viterbi]] determined that convolutional codes could be maximum-likelihood decoded with reasonable complexity using time invariant trellis based decoders — the [[Viterbi algorithm]]. Other trellis-based decoder algorithms were later developed, including the [[BCJR]] decoding algorithm.
Recursive systematic convolutional codes were invented by [[Claude Berrou]] around 1991. These codes proved especially useful for iterative processing including the processing of concatenated codes such as [[turbo codes]].<ref>Benedetto, Sergio, and Guido Montorsi. "[https://ieeexplore.ieee.org/abstract/document/390945/ Role of recursive convolutional codes in turbo codes]." Electronics Letters 31.11 (1995): 858-859.</ref>
Using the "convolutional" terminology, a classic convolutional code might be considered a [[Finite impulse response]] (FIR) filter, while a recursive convolutional code might be considered an [[Infinite impulse response]] (IIR) filter.
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==Where convolutional codes are used==
[[File:GSM convol code.png|thumb|right|400px|Stages of channel coding in GSM.<ref>Eberspächer J. et al. GSM-architecture, protocols and services. – John Wiley & Sons, 2008. - p.97</ref>
Convolutional codes are used extensively to achieve reliable data transfer in numerous applications, such as [[digital video]], radio, [[mobile communications]] (e.g., in GSM, GPRS, EDGE and 3G networks (until 3GPP Release 7)<ref>3rd Generation Partnership Project (September 2012). "3GGP TS45.001: Technical Specification Group GSM/EDGE Radio Access Network; Physical layer on the radio path; General description". Retrieved 2013-07-20.</ref><ref>Halonen, Timo, Javier Romero, and Juan Melero, eds. GSM, GPRS and EDGE performance: evolution towards 3G/UMTS. John Wiley & Sons, 2004. - p. 430</ref>) and [[satellite communications]].<ref>Butman, S. A., L. J. Deutsch, and R. L. Miller. [http://tda.jpl.nasa.gov/progress_report/42-63/63H.PDF "Performance of concatenated codes for deep space missions."] The Telecommunications and Data Acquisition Progress Report 42-63, March–April 1981 (1981): 33-39.</ref> These codes are often implemented in [[concatenated code|concatenation]] with a hard-decision code, particularly [[Reed–Solomon error correction|Reed–Solomon]]. Prior to [[turbo codes]] such constructions were the most efficient, coming closest to the [[Shannon-Hartley theorem|Shannon limit]].
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{{main article|Turbo code}}
[[File:Turbo codes scheme.png|thumb|350 px| A turbo code with component codes 13, 15.<ref>[http://www.scholarpedia.org/article/Turbo_codes Turbo code]</ref> Turbo codes get their name because the decoder uses feedback, like a turbo engine. Permutation means the same as the interleaving. C1 and C2 are recursive convolutional codes. Recursive and non-recursive convolutional codes are not so much different in BER performance, however, recursive type of is implemented in Turbo convolutional codes due to better interleaving properties.<ref>Benedetto, Sergio, and Guido Montorsi. "[https://ieeexplore.ieee.org/abstract/document/390945/ Role of recursive convolutional codes in turbo codes]." Electronics Letters 31.11 (1995): 858-859.</ref>
Simple Viterbi-decoded convolutional codes are now giving way to [[turbo code]]s, a new class of iterated short convolutional codes that closely approach the theoretical limits imposed by [[Shannon's theorem]] with much less decoding complexity than the Viterbi algorithm on the long convolutional codes that would be required for the same performance. [[Concatenated code|Concatenation]] with an outer algebraic code (e.g., [[Reed–Solomon error correction|Reed–Solomon]]) addresses the issue of [[error floor]]s inherent to turbo code designs.
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