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==Popular convolutional codes==
[[File:Conv code 177 133.png||400px|left|thumb|Shift-register for the (7, [171, 133]) convolutional code polynomial.]]
[[File:Lenss.png|thumb|right|300px|Theoretical bit-error rate curves of encoded QPSK (soft decision), additive white Gaussian noise channel. Longer constraint lengths produce more powerful codes, but the [[complexity]] of the Viterbi algorithm [[exponential growth|increases exponentially]] with constraint lengths, limiting these more powerful codes to deep space missions where the extra performance is easily worth the increased decoder complexity.]]
An especially popular Viterbi-decoded convolutional code, used at least since the [[Voyager program]] has a constraint length ''k'' of 7 and a rate ''r'' of 1/2.<ref> Butman, S. A., L. J. Deutsch, and R. L. Miller. [https://ipnpr.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>
▲* [[Mars Pathfinder]], [[Mars Exploration Rover]] and the [[Cassini probe]] to Saturn use a ''k'' of 15 and a rate of 1/6; this code performs about 2 dB better than the simpler ''k''=7 code at a cost of 256× in decoding complexity (compared to Voyager mission codes).
The convolutional code with a constraint length of 2 and a rate of 1/2 is used in [[GSM]] as an error correction technique.<ref>[http://www.scholarpedia.org/article/Global_system_for_mobile_communications_(GSM) Global system for mobile communications (GSM)]</ref>
==Punctured convolutional codes==
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