Systematic convolutional encoder

Example: A systematic encoder for a (2,1,2) convolutional code.

 

Fig. 1 Example of convolutional encoders - a systematic encoder for a (2,1,2) convolutional code.

 

 Forney [For70] demonstrated for any noncatastrophic convolutional code that there is an equivalent systematic code with feedback which generates the same set of codewords.

Considering the generator matrix

G(D) = [1+D+D2 1+D ]

for encoder in Fig. 2 less 1, an equivalent systematic generator matrix is

Both codes to be equivalent must contain the same set of all code sequences.

 

  Make your own experiment Play with this encoder.