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.
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.
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.
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 in the Communications System Toolbox™ documentation. 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,
poly2trellis command 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 indicate how the encoder treats the trellis at the beginning
and end of each frame, set the Termination method parameter
Truncated option indicates that the
encoder resets to the all-zeros state at the beginning of each frame.
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
(reset every frame), use the
in this block. If you use the Convolutional
Encoder block with the Operation mode parameter
Terminate trellis by appending bits,
Terminated option in this block.
You can control part of the decoding algorithm using the Algorithm parameter.
True APP option implements a posteriori
probability decoding as per equations 20–23 in section V of .
To gain speed, both the
approximate expressions like
by other quantities. The
uses max(ai) as the approximation,
Max* option uses max(ai)
plus a correction term given by .
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^
divides the pre-output by the same factor). Use this parameter to
avoid losing precision during the computations.
MATLAB structure that contains the trellis description of the convolutional encoder.
This parameter indicates how the convolutional encoder treats the
trellis at the beginning and end of frames.
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
Select this check box to disable the secondary block output, L(c).
For an example using this block, see the Iterative Decoding of a Serially Concatenated Convolutional Code example.
 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.