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# Turbo Decoder

Decode input signal using parallel concatenated decoding scheme

## Library

Convolutional sublibrary of Error Detection and Correction

## 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.

### Block Diagram of Iterative Turbo Decoding

The previous block diagram illustrates that the APP decoders (labeled as SISO modules in the previous image) output an updated sequence of log-likelihoods of the encoder input bits, π(u;O). This sequence is based on the received sequence of log-likelihoods of the channel (coded) bits, π(c;I), and code parameters.

The decoder block iteratively updates these likelihoods for a fixed number of decoding iterations and then outputs the decision bits. The interleaver (π) that the decoder uses is identical to the one the encoder uses. The deinterleaver (π-1) 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.

### Dimensions

This block accepts an M-by-1 column vector input signal and outputs an L-by-1 column vector signal. For a given trellis, L and M are related by:

$L=\text{\hspace{0.17em}}\frac{\left(M-2\cdot numTails\right)}{\left(2\cdot n-1\right)}$

and

$M=\text{\hspace{0.17em}}L\cdot \left(2\cdot n-1\right)+\text{\hspace{0.17em}}\text{​}2\cdot numTails$

where

M = decoder input length

L = decoder output length

n = log2(trellis.NumOutputSymbols), for a rate 1/2 trellis, n = 2

numTails = log2(trellis.numStates) * n

### Bit Stream Ordering

The bit ordering subsystem reorganizes the incoming data into the two log likelihood ratio (LLR) streams input to the constituent decoders. This subsystem reconstructs the second systematic stream and reorders the bits so that they match the two constituent encoder outputs at the transmitter. This ordering subsystem is the inverse of the reordering subsystem at the turbo encoder.

## Dialog Box

Trellis structure

Trellis structure of constituent convolutional code.

Specify the trellis as a MATLAB® structure that contains the trellis description of the constituent convolutional code. Alternatively, use the poly2trellis function to create a custom trellis using the constraint length, code generator (octal), and feedback connection (octal).

The default structure is the result of poly2trellis(4, [13 15], 13).

Source of interleaver indices

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 secondary input port, IntrInd, to specify the interleaver indices.

Interleaver indices

Specify the mapping that the Turbo encoder block uses to permute the input bits as a column vector of integers. The default is (64:-1:1).'. This mapping is a vector with the number of elements equal to L, the length of the output signal. Each element must be an integer between 1 and L, with no repeated values.

Decoding algorithm

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

• Max* or Max – the block uses approximations to increase the speed of the computations.

Number of scaling bits

Specify the number of bits which the constituent APP decoders must use to scale the input data to avoid losing precision during computations. The decoder multiplies the input by 2^Number of scaling bits and divides the pre-output by the same factor. The value for this parameter must be a scalar integer between 0 and 8. This parameter only applies when you set Decoding algorithm to Max*. The default is 3.

Number of decoding iterations

Specify the number of decoding iterations the block uses. The default is 6. 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

Specify if the block simulates using Code generation or Interpreted execution. The default is Interpreted execution.

## Supported Data Type

PortSupported Data Types
In
• Double

• Single

Out
• Double

## Examples

For an example that uses the Turbo Encoder and Turbo Decoder blocks, see the Parallel Concatenated Convolutional Coding: Turbo CodesParallel Concatenated Convolutional Coding: Turbo Codes example.

Turbo Encoder

## References

[1] Berrou, C., A. Glavieux, and P. Thitimajshima. "Near Shannon limit error correcting coding and decoding: turbo codes," Proceedings of the IEEE International Conference on Communications, Geneva, Switzerland, May 1993, pp. 1064–1070.

[2] Benedetto, S., G. Montorsi, D. Divsalar, and F. Pollara. " Soft-Input Soft-Output Maximum A Posterior (MAP) Module to Decode Parallel and Serial Concatenated Codes,"Jet Propulsion Lab TDA Progress Report, Vol. 42–27, Nov. 1996.

[3] Schlegel, Christian B. and Lance C. Perez. Trellis and Turbo Coding, IEEE Press, 2004.

[4] 3GPP TS 36.212 v9.0.0, 3rd Generation partnership project; Technical specification group radio access network; Evolved Universal Terrestrial Radio Acess (E-UTRA); Multiplexing and channel coding (release 9), 2009-12.