Editing Convolutional code (section)

== Recursive and non-recursive codes ==
The encoder on the picture above is a ''non-recursive'' encoder. Here's an example of a recursive one and as such it admits a feedback structure:

[[Image:Convolutional encoder recursive.svg|thumb|340px|none|Img.2. Rate 1/2 8-state recursive systematic convolutional encoder. Used as constituent code in 3GPP 25.212 Turbo Code.]]

The example encoder is ''[[systematic code|systematic]]'' because the input data is also used in the output symbols (Output 2). Codes with output symbols that do not include the input data are called  ''non-systematic.''

Recursive codes are typically systematic and, conversely, non-recursive codes are typically non-systematic. It isn't a strict requirement, but a common practice.

The example encoder in Img. 2. is an 8-state encoder because the 3 registers will create 8 possible encoder states (2<sup>3</sup>). A corresponding decoder trellis will typically use 8 states as well.

Recursive systematic convolutional (RSC) codes have become more popular due to their use in Turbo Codes. Recursive systematic codes are also referred to as pseudo-systematic codes.

Other RSC codes and example applications include:

[[File:Two-state_RSC_code.png|thumb|340px|none|Img. 3. Two-state recursive systematic convolutional (RSC) code. Also called an 'accumulator.']]

Useful for [[Low-density parity-check code|LDPC]] code implementation and as inner constituent code for [[serial concatenated convolutional codes]] (SCCC's).

[[File:Four-state_RSC_code.png|thumb|340px|none|Img. 4. Four-state recursive systematic convolutional (RSC) code.]]

Useful for SCCC's and multidimensional turbo codes.

[[File:Sixteen-state_RSC_code.png|thumb|340px|none|Img. 5. Sixteen-state recursive systematic convolutional (RSC) code.]]

Useful as constituent code in low error rate turbo codes for applications such as satellite links. Also suitable as SCCC outer code.