Decode convolutional code using a posteriori probability (APP) method
Convolutional sublibrary of Error Detection and Correction
The APP Decoder block performs a posteriori probability (APP) decoding of a convolutional code.
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 2k 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
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:
If you have a variable in the MATLAB workspace that contains the trellis structure, enter its name as the Trellis structure parameter. This way is preferable because it causes Simulink to spend less time updating the diagram at the beginning of each simulation, compared to the usage described next.
If you want to specify the encoder using its constraint length, generator polynomials, and possibly feedback connection polynomials, use a
poly2trelliscommand within the Trellis structure field. For example, to use an encoder with a constraint length of 7, code generator polynomials of 171 and 133 (in octal numbers), and a feedback connection of 171 (in octal), set the Trellis structure parameter to
To indicate how the encoder treats the trellis at the beginning and end of each
frame, set the Termination method parameter to either
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
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
APP option implements a posteriori probability decoding as per
equations 20–23 in section V of . To gain speed, both the
Max options approximate expressions like
by other quantities. The
Max option uses
max(ai) as the approximation, while
Max* option uses
max(ai) plus a correction term given
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
- Trellis structure
MATLAB structure that contains the trellis description of the convolutional encoder.
- Termination method
Terminated. This parameter indicates how the convolutional encoder treats the trellis at the beginning and end of frames.
- Number of scaling bits
An integer between 0 and 8 that indicates by how many bits the decoder scales data in order to avoid losing precision. This field is active only when Algorithm is set to
- Disable L(c) output port
Select this check box to disable the secondary block output, L(c).
 Benedetto, S., G. Montorsi, D. Divsalar, and F. Pollara, “A Soft-Input Soft-Output Maximum A Posterior (MAP) Module to Decode Parallel and Serial Concatenated Codes,” JPL TDA Progress Report, Vol. 42-127, November 1996.
 Benedetto, Sergio and Guido Montorsi, “Performance of Continuous and Blockwise Decoded Turbo Codes.” IEEE Communications Letters, Vol. 1, May 1997, 77–79.
 Viterbi, Andrew J., “An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes,” IEEE Journal on Selected Areas in Communications, Vol. 16, February 1998, 260–264.
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Introduced before R2006a