Standards/convolutional

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[https://en.wikipedia.org/wiki/Convolutional_code Convolutional codes] are used in communication systems for [https://en.wikipedia.org/wiki/Error_detection_and_correction#Error-correcting_codes error correction].
 
[https://en.wikipedia.org/wiki/Convolutional_code Convolutional codes] are used in communication systems for [https://en.wikipedia.org/wiki/Error_detection_and_correction#Error-correcting_codes error correction].
 
They allow to have a very low [https://en.wikipedia.org/wiki/Bit_error_rate Bit Error Rate] (BER) and are preferably used in the case of noisy channels.
 
They allow to have a very low [https://en.wikipedia.org/wiki/Bit_error_rate Bit Error Rate] (BER) and are preferably used in the case of noisy channels.
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These codes are often implemented in concatenation with a hard-decision code, such as [[Standards/Reed Solomon|Reed Solomon]].
  
 
= Definitions =
 
= Definitions =
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A convolutional code is specified by:
 
A convolutional code is specified by:
 
* <code>n</code> : number of output bits
 
* <code>n</code> : number of output bits
* <code>k</code> : number of input bits, usually 1
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* <code>k</code> : number of input bits
 
* <code>m</code> : number of registers
 
* <code>m</code> : number of registers
 
* <code>G<sub>i</sub></code> : the <code>n</code> generator polynomials
 
* <code>G<sub>i</sub></code> : the <code>n</code> generator polynomials
  
 
= Coder =
 
= Coder =
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The following picture shows a (2, 1, 3) convolutional encoder
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with generator polynomials G<sub>1</sub>&nbsp;=&nbsp;111 and G<sub>2</sub>&nbsp;=&nbsp;101 :
  
 
= Decoders =
 
= Decoders =

Revision as of 14:09, 8 July 2016

Contents

Convolutional codes are used in communication systems for error correction. They allow to have a very low Bit Error Rate (BER) and are preferably used in the case of noisy channels.

These codes are often implemented in concatenation with a hard-decision code, such as Reed Solomon.

Definitions

A convolutional code is specified by:

  • n : number of output bits
  • k : number of input bits
  • m : number of registers
  • Gi : the n generator polynomials

Coder

The following picture shows a (2, 1, 3) convolutional encoder with generator polynomials G1 = 111 and G2 = 101 :

Decoders

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