Turbo Decoder
Decode input signal using parallel concatenated decoding scheme
Libraries:
Communications Toolbox /
Error Detection and Correction /
Convolutional
Description
The Turbo Decoder block decodes the input signal using a parallel concatenated decoding scheme. The iterative decoding scheme uses the a posteriori probability (APP) decoder as the constituent decoder, an interleaver, and a deinterleaver. The two constituent decoders use the same trellis structure and decoding algorithm. For more information, see Parallel Concatenated Convolutional Decoding Scheme and APP Decoder.
This icon shows the block with all ports enabled.
Examples
Parallel Concatenated Convolutional Coding: Turbo Codes
Characterize the performance of turbo codes over a noisy channel.
Ports
Input
In — Parallel concatenated codeword
column vector
Parallel concatenated codeword, specified as a column vector of length M, where M is the length of the parallel concatenated codeword.
Data Types: double
 single
IntrInd — Interleaver indices
column vector of integers
Interleaver indices, specified as a column vector of integers. The
vector must be of length L. Each element of the
vector must be an integer in the range [1, L] and
must be unique. L is the length of the decoded binary
output message, Out
. The interleaver indices define
the mapping used to permute the input bits at the decoder.
Dependencies
To enable this port, set the Source of interleaver
indices parameter to Input
port
.
Data Types: double
InInd — Input indices
column vector of integers
Input indices for the bit ordering and puncturing used on the fully encoded data, specified as a column vector of integers. The length of the InInd vector must equal the length of the input data vector In. Element values in the vector must be relative to the fully encoded data for the coding scheme, including the tail bits for all streams.
Dependencies
To enable this port, set the Source of input
indices parameter to Input
port
.
Data Types: double
Output
Out — Decoded message
binary column vector
Decoded message, returned as a binary column vector of length
L, where L is the length of
the decoded binary output message. This output inherits its data type
from the In
input.
Parameters
To edit block parameters interactively, use the Property Inspector. From the Simulink^{®} Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.
Trellis structure — Trellis description of constituent convolutional code
poly2trellis(4,[13 15],13)
(default)  structure
Specify the trellis as a MATLAB^{®} structure that contains the trellis description for a rate K ∕ N constituent convolutional code. K is the number of input bit streams, and N is the number of output bit streams.
Note
K must be 1 for the turbo coder. For more information, see Coding Rate.
You can either use the poly2trellis
function to
create the trellis structure or create it manually. For more about this
structure, see Trellis Description of a Convolutional Code and the
istrellis
function.
The trellis structure contains these fields.
numInputSymbols — Number of symbols input to encoder
2^{K}
Number of symbols input to the encoder, specified as an integer equal to 2^{K}, where K is the number of input bit streams.
numOutputSymbols — Number of symbols output from encoder
2^{N}
Number of symbols output from the encoder, specified as an integer equal to 2^{N}, where N is the number of output bit streams.
numStates — Number of states in encoder
power of 2
Number of states in the encoder, specified as a power of 2.
nextStates — Next states
matrix of integers
Next states for all combinations of current states and current inputs, specified
as a matrix of integers. The matrix size must be numStates
by
2^{K}.
outputs — Outputs
matrix of octal numbers
Outputs for all combinations of current states and current inputs, specified as a matrix of
octal numbers. The matrix size must be numStates
by
2^{K}.
Source of interleaver indices — Source of interleaver indices
Property
(default)  Input port
Specify the source of the interleaver indices as
Property
or Input
port
.
When you set this parameter to
Property
, the block uses the Interleaver indices parameter to specify the interleaver indices.When you set this parameter to
Input port
, the block uses theIntrInd
input port to specify the interleaver indices.
Interleaver indices — Interleaver indices
(64:1:1).'
(default)  column vector of integers
Specify the interleaver indices that define the mapping used to permute codeword bits input to the decoder as a column vector of integers. The vector must be of length L. Each element of the vector must be an integer in the range [1, L] and must be unique. L is the length of the decoded binary output message.
Dependencies
To enable this parameter, set the Source of interleaver
indices parameter to
Property
.
Source of input indices — Source of input indices
Auto
 Property
 Input port
Specify the source of the input indices as Auto
, Property
, or
Input port
.
When you set this parameter to
Auto
, the block computes input indices that assume the second systematic stream is punctured and all tail bits are included in the input.When you set this parameter to
Property
, the block uses the input indices that you specify for the Input indices parameter.When you set this parameter to
Input port
, the block uses the InInd input port to specify the input indices. The vector length and values for the input indices and coded input signal can change with each execution of the block.
Input indices — Input indices
getTurboIOIndices(64,2,3)
(default)  column vector of integers
Specify the input indices for the bit ordering and puncturing used on the fully encoded data as a column vector of integers. The vector length of this parameter must equal the length of the input data vector In.
Dependencies
To enable this parameter, set the Source of input
indices parameter to
Property
.
Decoding algorithm — Decoding algorithm
True APP
(default)  Max*
 Max
Specify the decoding algorithm that the constituent APP decoders use to
decode the input signal as True APP
,
Max*
, Max
. When
you set this parameter to True APP
the block
implements true a posteriori probability decoding. When
you set this parameter to Max*
or
Max
the block uses approximations to increase
the speed of the computations. For more information, see APP Decoder.
Number of scaling bits — Number of scaling bits
3
(default)  integer in the range [0, 8]
Specify the number of bits which the constituent APP decoders must use to scale the input data to avoid losing precision during computations as an integer in the range [0, 8]. The constituent decoders multiply the input by 2^{k} and divide the preoutput by the same factor. k is the value of the Number of scaling bits parameter. For more information, see APP Decoder.
Dependencies
This enable this parameter, set the Decoding
algorithm parameter to
Max*
.
Number of decoding iterations — Number of decoding iterations
6
(default)  positive integer
Specify the number of decoding iterations the block uses as a positive integer. The block iterates and provides updates to the loglikelihood ratios (LLR) of the uncoded output bits. The output of the block is the harddecision output of the final LLR update.
Simulate using — Type of simulation to run
Interpreted execution
(default)  Code generation
Type of simulation to run, specified as Interpreted
execution
or Code generation
.
Interpreted execution
— Simulate the model by using the MATLAB interpreter. This option requires less startup time, but the speed of subsequent simulations is slower than with theCode generation
option. In this mode, you can debug the source code of the block.Code generation
— Simulate the model by using generated C code. The first time you run a simulation, Simulink generates C code for the block. The model reuses the C code for subsequent simulations unless the model changes. This option requires additional startup time, but the speed of the subsequent simulations is faster than with theInterpreted execution
option.
For more information, see Interpreted Execution vs. Code Generation (Simulink).
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

More About
Parallel Concatenated Convolutional Decoding Scheme
The turbo decoder uses a parallel concatenated convolutional decoding scheme to decode a coded input signal. The parallel concatenated decoding scheme uses an iterative APP Decoder with two constituent decoders, an interleaver, and a deinterleaver. This figure shows the decoding scheme. Typically, the decoder input data comes from the demodulator output.
The two constituent decoders use the same trellis structure and decoding algorithm. The softinput softoutput APP decoders (SISO 1 and SISO 2) output an updated sequence of loglikelihoods of the encoder input bits, π(u;O).The sequence is based on the received sequence of loglikelihoods of the channel (coded) bits, π(c;I), and code parameters.
The decoder iteratively updates these likelihoods for a fixed number of decoding iterations and then outputs the decision bits. The interleaver used in the decoder is identical to the interleaver used in the encoder. The deinterleaver performs the inverse permutation with respect to the interleaver. The decoder does not assume knowledge of the tail bits and excludes these bits from the iterations.
For more information, see Coding Rate.
APP Decoder
The Turbo Decoder block implements the softinputsoftoutput APP decoding algorithm according to [1] and [2].
The True APP
option of the Decoding
algorithm parameter implements APP decoding as per equations 20–23 in
section V of [1]. To gain speed,
the Max*
and Max
values of the
Decoding algorithm parameter approximate expressions like $$\mathrm{log}{\displaystyle \sum _{i}\mathrm{exp}({a}_{i})}$$ by other quantities. The Max
option
uses max(a_{i}) as the approximation. The
Max*
option uses
max(a_{i}) plus a correction term
given by the expression $$\mathrm{ln}(1+\mathrm{exp}(\left{a}_{i1}{a}_{i}\right))$$.
Setting the Decoding algorithm parameter to
Max*
enables the Number of scaling
bits parameter of this block. This parameter denotes the number of
bits by which this block scales the data it processes (multiplies the input by
2^{k} and divides the preoutput
by the same factor, where k is the value of Number of
scaling bits). Use this parameter to avoid losing precision during
computations.
Coding Rate
In general, the coding rate of a constituent convolutional code is represented as a rate K ∕ N code. K is the number of input bit streams. N is the number of output bit streams.
Note
K must be 1 to use the Turbo Encoder and Turbo Decoder blocks.
Alternatively, the High Rate Convolutional Codes for Turbo Coding example performs turbo
coding for K greater than 1 by using the comm.ConvolutionalEncoder
and
comm.APPDecoder
System objects in
MATLAB.
The decoder accepts an Melement column vector input signal and returns an Lelement column vector containing the decoded binary output message. L is the interleaver block length. M is the length of the parallel concatenated codeword.
For a given input trellis, when you set the Source of input
indices parameter to Auto
,
M and L are related by
L = (M – 2 × numTails)
∕ (2 × N – 1) , where:
numTails = log_{2}(
trellis.numStates
) × NN = log_{2}(
trellis.numOutputSymbols
). For a rate 1 ∕ 2 trellis, N = 2.
For more information about trellis structures, see the poly2trellis
function. For more information about the constituent
decoders, see Parallel Concatenated Convolutional Decoding Scheme.
References
[1] Benedetto, S., G. Montorsi, D. Divsalar, and F. Pollara. "A SoftInput SoftOutput Maximum A Posterior (MAP) Module to Decode Parallel and Serial Concatenated Codes." Jet Propulsion Lab TDA Progress Report (November 1996): 42–127.
[2] Viterbi, A.J. “An Intuitive Justification and a Simplified Implementation of the MAP Decoder for Convolutional Codes.” IEEE^{®} Journal on Selected Areas in Communications 16, no. 2 (February 1998): 260–64. https://doi.org/10.1109/49.661114.
[3] Berrou, C., A. Glavieux, and P. Thitimajshima. “Near Shannon Limit ErrorCorrecting Coding and Decoding: TurboCodes.” Proceedings of ICC 93  IEEE International Conference on Communications, 2: 1064–70. Geneva, Switzerland: IEEE, 1993. https://doi.org/10.1109/icc.1993.397441.
[4] Schlegel, Christian, and Lance Perez. Trellis and Turbo Coding. IEEE Press Series on Digital & Mobile Communication. Piscataway, NJ; Hoboken, NJ: IEEE Press; WileyInterscience, 2004.
[5] 3GPP TS 36.212. "Multiplexing and channel coding." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (EUTRA).
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2011b
See Also
Blocks
Functions
Objects
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