Editing Convolutional code (section)

== Punctured convolutional codes ==
{{See also|Punctured code}}

[[File:Soft34.png|thumb|right|300px|Convolutional codes with 1/2 and 3/4 code rates (and constraint length 7, Soft decision, 4-QAM / QPSK / OQPSK).<ref>[https://ch.mathworks.com/help/comm/ug/punctured-convolutional-coding-1.html Punctured Convolutional Coding (MathWorks)]</ref>]]

Convolutional code with any code rate can be designed based on polynomial selection;<ref>{{Cite web|url=https://www.mathworks.com/help/comm/ref/poly2trellis.html|title=Convert convolutional code polynomials to trellis description – MATLAB poly2trellis}}</ref> however, in practice, a puncturing procedure is often used to achieve the required code rate. [[Punctured code|Puncturing]] is a technique used to make a ''m''/''n'' rate code from a "basic" low-rate (e.g., 1/''n'') code. It is achieved by deleting of some bits in the encoder output. Bits are deleted according to a ''puncturing matrix''. The following puncturing matrices are the most frequently used:

{| class="wikitable" |cellpadding="2"
! Code rate
! Puncturing matrix
! width="128px" | Free distance (for NASA standard K=7 convolutional code)
|-
| 1/2<br />(No perf.)
|
{| border="0"
|-
| 1
|-
| 1
|}
| 10
|-
| 2/3
|
{| border="0"
|-
| 1
| 0
|-
| 1
| 1
|}
| 6
|-
| 3/4
|
{| border="0"
|-
| 1
| 0
| 1
|-
| 1
| 1
| 0
|}
| 5
|-
| 5/6
|
{| border="0"
|-
| 1
| 0
| 1
| 0
| 1
|-
| 1
| 1
| 0
| 1
| 0
|}
| 4
|-
| 7/8
|
{| border="0"
|-
| 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 first 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 [[Communications satellite|satellite communications]], for example, in [[Intelsat]] systems and [[DVB|Digital Video Broadcasting]].

Punctured convolutional codes are also called "perforated".