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. | ||
+ | |||
+ | 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 | + | * <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 = | ||
+ | |||
+ | The following picture shows a (2, 1, 3) convolutional encoder | ||
+ | with generator polynomials G<sub>1</sub> = 111 and G<sub>2</sub> = 101 : | ||
= Decoders = | = Decoders = |
Revision as of 15:09, 8 July 2016
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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
: then
generator polynomials
Coder
The following picture shows a (2, 1, 3) convolutional encoder with generator polynomials G1 = 111 and G2 = 101 :