Turbo Decoder

Decode input signal using parallel concatenated decoding scheme

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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.

• Open Model

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 the IntrInd 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 pre-output 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 log-likelihood ratios (LLR) of the uncoded output bits. The output of the block is the hard-decision 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 the Code 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 the Interpreted execution option.

For more information, see Interpreted Execution vs. Code Generation (Simulink).

Block Characteristics

Data Types	double | single
Multidimensional Signals	no
Variable-Size Signals	yes

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 soft-input soft-output APP decoders (SISO 1 and SISO 2) output an updated sequence of log-likelihoods of the encoder input bits, π(u;O).The sequence is based on the received sequence of log-likelihoods 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 soft-input-soft-output 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 $$\log {\displaystyle \sum _i\exp (a_i)}$$ 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 $$\ln (1+\exp (-\left|a_{i-1}-a_i\right|))$$.

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 pre-output 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 M-element column vector input signal and returns an L-element 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 = log₂(trellis.numStates) × N

• N = log₂(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 Soft-Input Soft-Output 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 Error-Correcting Coding and Decoding: Turbo-Codes.” 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; Wiley-Interscience, 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 (E-UTRA).

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2011b