Convolutional Code - Punctured Convolutional Codes

Punctured Convolutional Codes

Puncturing is a technique used to make a m/n rate code from a "basic" rate 1/2 code. It is reached by deletion of some bits in the encoder output. Bits are deleted according to puncturing matrix. The following puncturing matrices are the most frequently used:

Code rate Puncturing matrix Free distance (for NASA standard K=7 convolutional code)
1/2
(No perf.)
1
1
10
2/3
1 0
1 1
6
3/4
1 0 1
1 1 0
5
5/6
1 0 1 0 1
1 1 0 1 0
4
7/8
1 0 0 0 1 0 1
1 1 1 1 0 1 0
3

For example, if we want to make a code with rate 2/3 using the appropriate matrix from the above table, we should take a basic encoder output and transmit every second bit from the first branch and every bit from the second one. The specific order of transmission is defined by the respective communication standard.

Punctured convolutional codes are widely used in the satellite communications, for example, in INTELSAT systems and Digital Video Broadcasting.

Punctured convolutional codes are also called "perforated".

Read more about this topic:  Convolutional Code

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