Convolutional code: Difference between revisions

Revision as of 19:01, 10 February 2019

Revision as of 06:09, 13 February 2019

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==Popular convolutional codes==

[[File:Lenss.png|thumb|right|300px|Theoretical bit-error rate curves of encoded QPSK (soft decision), additive white Gaussian noise channel.]]

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.

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* 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.

* [[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).

[[File:Conv code 177 133.png||500px|center|thumb|Shift-register for the (7,[177,133]) convolutional code polynomial.]]

==Punctured convolutional codes==