APP Decoder

Input Signals and Output Signals

The input L(u) represents the sequence of log-likelihoods of encoder input bits, while the input L(c) represents the sequence of log-likelihoods of code bits. The outputs L(u) and L(c) are updated versions of these sequences, based on information about the encoder.

If the convolutional code uses an alphabet of 2ⁿ possible symbols, this block's L(c) vectors have length Q*n for some positive integer Q. Similarly, if the decoded data uses an alphabet of 2^k possible output symbols, then this block's L(u) vectors have length Q*k.

This block accepts a column vector input signal with any positive integer for Q.

If you only need the input L(c) and output L(u), you can attach a Simulink Ground (Simulink) block to the input L(u) and a Simulink^® Terminator (Simulink) block to the output L(c).

This block accepts single and double data types. Both inputs, however, must be of the same type. The output data type is the same as the input data type.

Specifying the Encoder

To define the convolutional encoder that produced the coded input, use the Trellis structure parameter. This parameter is a MATLAB^® structure whose format is described in Trellis Description of a Convolutional Code. You can use this parameter field in two ways:

To indicate how the encoder treats the trellis at the beginning and end of each frame, set the Termination method parameter to either Truncated or Terminated. The Truncated option indicates that the encoder resets to the all-zeros state at the beginning of each frame. The Terminated option indicates that the encoder forces the trellis to end each frame in the all-zeros state. If you use the Convolutional Encoder block with the Operation mode parameter set to Truncated (reset every frame), use the Truncated option in this block. If you use the Convolutional Encoder block with the Operation mode parameter set to Terminate trellis by appending bits, use the Terminated option in this block.

Specifying Details of the Algorithm

You can control part of the decoding algorithm using the Algorithm parameter. The True APP option implements a posteriori probability decoding as per equations 20–23 in section V of [1]. To gain speed, both the Max* and Max options approximate expressions like

by other quantities. The Max option uses max(a_i) as the approximation, while the Max* option uses max(a_i) plus a correction term given by $$\ln (1+\exp (-\left|a_{i-1}-a_i\right|))$$ [3].

The Max* option enables the Scaling bits parameter in the dialog box. This parameter is the number of bits by which the block scales the data it processes internally (multiplies the input by (2^numScalingBits) and divides the pre-output by the same factor). Use this parameter to avoid losing precision during the computations.