Standards/convolutional

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(Coder)
(Coder)
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The following picture shows a (2, 1, 3) convolutional encoder
 
The following picture shows a (2, 1, 3) convolutional encoder
with generator polynomials G<sub>1</sub>&nbsp;=&nbsp;111 and G<sub>2</sub>&nbsp;=&nbsp;101 :
+
with generator polynomials G<sub>1</sub>&nbsp;=&nbsp;111 and G<sub>2</sub>&nbsp;=&nbsp;101&nbsp;:
  
 
[[File:Convolutional encoder 2-1-3.svg|center|Convolutional encoder (2,1,3)]]
 
[[File:Convolutional encoder 2-1-3.svg|center|Convolutional encoder (2,1,3)]]
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 +
The graph of the convolutional encoder is presented in the following picture&nbsp;:
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[[File:Convolutional encoder 2-1-3 graph.svg |center|Convolutional encoder (2,1,3) graph]]
  
 
= Decoders =
 
= Decoders =

Revision as of 10:27, 11 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 :

Convolutional encoder (2,1,3)

The graph of the convolutional encoder is presented in the following picture :

Convolutional encoder (2,1,3) graph

Decoders

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