Communications Blockset

Implementing a Systematic Encoder with Feedback

This section explains how to use the Convolutional Encoder block to implement a systematic encoder with feedback. A code is systematic if the actual message words appear as part of the code words. The following diagram shows an example of a systematic encoder.

To implement this encoder, set the Trellis structure parameter in the Convolutional Encoder block to poly2trellis(5, [37 33], 37). This setting corresponds to

• Constraint length, 5
• Generator polynomial pair, [37 33]
• Feedback polynomial, 37

The feedback polynomial is represented by the binary vector [1 1 1 1 1], corresponding to the upper row of binary digits. These digits indicate connections from the outputs of the registers to the adder. Note that the initial 1 corresponds to the input bit. The octal representation of the binary number 11111 is 37.

To implement a systematic code, set the first generator polynomial to be the same as the feedback polynomial in the Trellis structure parameter of the Convolutional Encoder block. In this example, both polynomials have the octal representation 37.

The second generator polynomial is represented by the binary vector [1 1 0 1 1], corresponding to the lower row of binary digits. The octal number corresponding to the binary number 11011 is 33.

For more information on setting the mask parameters for the Convolutional Encoder block, see Polynomial Description of a Convolutional Encoder in the Communications Toolbox documentation.

Example: A Rate 2/3 Feedforward Encoder

Example: Soft-Decision Decoding