Convolutional code: Difference between revisions

Revision as of 17:23, 3 October 2020

Revision as of 15:58, 9 October 2020

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All possible transitions can be shown as below:

[[Image:Convolutional code trellis diagram.svg|left|thumb|340px|none|Img.6. A trellis diagram for the encoder on Img.1. A path through the trellis is shown as a red line. The solid lines indicate transitions where a "0" is input and the dashed lines where a "1" is input.]]

An actual encoded sequence can be represented as a path on this graph. One valid path is shown in red as an example.

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[[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>https://www.mathworks.com/help/comm/ref/poly2trellis.html</ref>; however, in practice, a puncturing procedure is often used to achieve the required code rate. [[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:

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