Turbo Encoder
Encode binary data using parallel concatenated encoding scheme
Libraries:
Communications Toolbox /
Error Detection and Correction /
Convolutional
Description
The Turbo Encoder block encodes a binary input signal using a parallel concatenated coding scheme. This coding scheme employs two identical convolutional encoders and one internal interleaver. Each constituent encoder is independently terminated by tail bits. For more information about the constituent encoders, see Parallel Concatenated Convolutional Encoding Scheme.
This icon shows the block with all ports enabled.
Examples
Ports
Input
In — Input message
binary column vector
Input message, specified as a binary column vector of length L, where L is the length of the uncoded input message.
Data Types: double
 int8
 fi(data,0,1)
IntrInd — Interleaver indices
column vector of integers
Interleaver indices, specified as a column vector of integers. The vector must be of length L, where L is the length of the binary input message. Each element of the vector must be an integer in the range [1, L] and must be unique. The interleaver indices define the mapping used to permute the input bits at the encoder.
Dependencies
To enable this port, set the Source of interleaver
indices property to Input
port
.
Data Types: double
OutInd — Output indices
column vector of integers
Output indices for the bit ordering and puncturing used on the fully encoded data, specified as a column vector of integers. Element values in the vector must be relative to the fully encoded data for the coding scheme, including the tail bits for all streams.
Tunable: Yes
Dependencies
To enable this port, set the Source of output indices property to
Input port
.
Data Types: double
Output
Out — Parallel concatenated codeword
binary column vector
Parallel concatenated codeword, returned as a binary column vector of
length M, where M is the number of
bits in the parallel concatenated codeword. This output inherits its
data type from the In
input.
Data Types: double
 int8
 fi(data,0,1)
Parameters
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 the Trellis Description of a Convolutional Code topic 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 as a column vector of integers. The vector must be of length L, where L is the length of the binary input message. Each element of the vector must be an integer in the range [1, L] and must be unique. The interleaver indices define the mapping used to permute the input bits at the encoder.
Dependencies
To enable this parameter, set the Source of interleaver
indices parameter to
Property
.
Source of output indices — Source of output indices
Auto
 Property
 Input port
Specify the source of the output indices as Auto
, Property
, or
Input port
.
When you set this parameter to
Auto
, the block computes output indices that puncture the second systematic stream and include all tail bits.When you set this parameter to
Property
, the block uses the output indices that you specify for the Output indices parameter.When you set this parameter to
Input port
, the block uses the OutInd input port to specify the output indices. The vector length and values for the output indices and coded output signal can change with each execution of the block.
Output indices — Output indices
getTurboIOIndices(64,2,3)
(default)  column vector of integers
Specify the output indices for the bit ordering and puncturing used on the fully encoded data as a column vector of integers. The number of bits output from the encoder is equal to the length of this parameter. The maximum length must not exceed the fully encoded length of (L+mLen) × N × 2), where L is the input vector length, mLen is the memory length, and N is the number of constituent coder encoded streams.
Dependencies
To enable this parameter, set the Source of output
indices parameter to
Property
.
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 Simulation Modes (Simulink).
Block Characteristics
Data Types 

Multidimensional Signals 

VariableSize Signals 

^{a} ufix(1) only. 
More About
Parallel Concatenated Convolutional Encoding Scheme
The turbo encoder uses a parallel concatenated convolutional encoding scheme to encode a binary input signal. The coding scheme uses two constituent encoders and one internal interleaver as shown in this figure. Each constituent encoder is terminated independently by tail bits.
The Source of output indices parameter specifies the source for the output indices used for symbol puncturing and repetition.
When you set the Source of output indices parameter to
Auto
, the block computes the output indices. In this case, the constituent encoders have a rate 1 ∕ N code, and the number of bits output from the turbo encoder is L × (2 × N – 1) + (2 × numTails). L is the input vector length, and numTails is given by log2(TrellisStructure.numStates
) × N. The tail bits due to the termination are appended at the end after the encoded input bits.The coding scheme uses two identical constituent encoders and one internal interleaver. Each constituent encoder is terminated independently by tail bits. The output of the turbo encoder consists of the systematic (X) and parity (Z) bit streams of the first encoder and only the parity (Z^{’}) bit streams of the second encoder. Tail bits are appended at the end for all streams.
When you set the Source of output indices parameter to
Input port
orProperty
, you specify the output indices with the OutInd input port or the Output indices parameter, respectively. In this case, the object runs using the output indices you specify. The output indices are specified relative to the fully encoded output for all streams.The output of the turbo encoder consists of the systematic (X and X^{’}) and parity (Z and Z^{’}) bit streams of first and second constituent encoders. The number of bits output equals the vector length of the output indices you provide.
For more information, see Coding Rate and Tail bits.
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.
The encoder accepts an Lelement column vector input signal and returns an Melement column vector output signal. The effective code rate of the turbo encoder is L ∕ M. L is the length of the binary input message, and M is the number of bits output in the parallel concatenated codeword.
When you set the Source of output indices parameter to
Auto
, systematic bits from the second encoder (X^{’}, shown in the figure found in Parallel Concatenated Convolutional Encoding Scheme) are not output to the parallel concatenated codeword. For a given trellis, M and L are related by M = L × (2 × N – 1) + 2 × numTails, where numTails is the number of tail bits. For more information, see Tail bits.When you set the Source of output indices parameter is to
Input port
orProperty
, M equals the length of the output indices vector specified by the OutInd input port or the Output indices parameter, respectively.
Tail bits
The turbo encoder treats each input independently. For each input message, extra bits are used to set the encoder states to an allzeros state. Each constituent encoder is terminated independently by tail bits. The turbo encoder output consists of the interlaced systematic and parity streams, with the tail bits multiplexed to the end of the encoded data streams.
The number of tail bits, numTails, output by each constituent encoder depends on values in the trellis structure used by each coder.
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
encoders, see Parallel Concatenated Convolutional Encoding Scheme.
Encoder Schematic for Rate 1/3 Turbo Code Example
This figure shows the encoder configuration for a trellis specified by the default value of
the Trellis structure parameter, poly2trellis(4,[13
15],13)
.
For an input vector length of 64 bits, the output of the encoder block is 204 bits. The first 192 bits correspond to the three 64 bit streams (systematic (X) and parity (Z) bit streams from the first encoder and the parity (Z^{’}) bit stream of the second encoder), interlaced as per X, Z, and Z^{’}. The last 12 bits correspond to the tail bits from the two encoders when the switches are in the lower position corresponding to the dashed lines. The first group of six bits (three systematic bits and three parity bits) are the output tail bits from the first constituent encoder. The second group of six bits (three systematic bits and three parity bits) are the output tail bits from the second constituent encoder.
Due to the tail bits, the encoder output code rate is slightly less than 1/3.
References
[1] Berrou, C., A. Glavieux, and P. Thitimajshima. “Near Shannon Limit ErrorCorrecting Coding and Decoding: TurboCodes.” Proceedings of ICC 93  IEEE International Conference on Communications, Geneva, Switzerland, May 1993, 1064–70. https://doi.org/10.1109/icc.1993.397441.
[2] 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, 42–127, (November 1996).
[3] Schlegel, Christian, and Lance Perez. Trellis and Turbo Coding. IEEE Press Series on Digital & Mobile Communication. Piscataway, NJ ; Hoboken, NJ: IEEE Press ; WileyInterscience, 2004.
[4] 3GPP TS 36.212. "Multiplexing and channel coding." 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (EUTRA). https://www.3gpp.org.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Version History
Introduced in R2011b
See Also
Blocks
Functions
Objects
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
 América Latina (Español)
 Canada (English)
 United States (English)
Europe
 Belgium (English)
 Denmark (English)
 Deutschland (Deutsch)
 España (Español)
 Finland (English)
 France (Français)
 Ireland (English)
 Italia (Italiano)
 Luxembourg (English)
 Netherlands (English)
 Norway (English)
 Österreich (Deutsch)
 Portugal (English)
 Sweden (English)
 Switzerland
 United Kingdom (English)