Editing Convolutional code (section)

== Popular convolutional codes ==
[[File:Conv code 177 133.png|400px|left|thumb|Shift-register for the (7, [171, 133]) convolutional code polynomial. Branches: <math>h^1 = 171_o = [1111001]_b</math>, <math>h^2 = 133_o = [1011011]_b</math>. All of the math operations should be done by modulo 2.]]
[[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.]]

In fact, predefined convolutional codes structures obtained during scientific researches are used in the industry. This relates to the possibility to select catastrophic convolutional codes (causes larger number of errors).

An especially popular Viterbi-decoded convolutional code, used at least since the [[Voyager program]], has a constraint length {{mvar|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–Huygens|Cassini probe]] to Saturn use a {{mvar|K}} of 15 and a rate of 1/6; this code performs about 2&nbsp;dB better than the simpler <math>K=7</math> 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>