comm.TurboDecoder

Decode input signal using parallel concatenated decoding scheme

Description

The comm.TurboDecoder System object™ uses a parallel concatenated decoding scheme to decode a coded input signal. The input signal is typically the soft-decision output from the baseband demodulation operation. For more information, see Parallel Concatenated Convolutional Decoding Scheme.

To decode an input signal using a parallel concatenated decoding scheme:

1. Create the comm.TurboDecoder object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

turbodec = comm.TurboDecoder

turbodec = comm.TurboDecoder(trellis,interlvrindices,numiter)

turbodec = comm.TurboDecoder(___,Name,Value)

Description

turbodec = comm.TurboDecoder creates a turbo decoder System object. This object uses the a-posteriori probability (APP) constituent decoder to iteratively decode the parallel-concatenated convolutionally encoded input data.

turbodec = comm.TurboDecoder(trellis,interlvrindices,numiter) creates a turbo decoder System object with the TrellisStructure, InterleaverIndices, and numiter, respectively. The trellis input must be specified as described by the TrellisStructure property. The interlvrindices input must be specified as described by the InterleaverIndices property. The numiter input must be specified as described by the NumIterations property.

turbodec = comm.TurboDecoder(___,Name,Value) sets properties using one or more name-value pairs in addition to any input argument combination from previous syntaxes. Enclose each property name in quotes. For example, comm.TurboDecoder('InterleaverIndicesSource','Input port') configures a turbo decoder System object with the interleaver indices to be supplied as an input argument to the System object when it is called.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

TrellisStructure — Trellis description of constituent convolutional code

poly2trellis(4,[13 15],13) (default) | structure

Trellis description of the constituent convolutional code, specified as a structure that contains the trellis description for a rate K ∕ N 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.

Data Types: double

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.

Data Types: double

numStates — Number of states in encoder

power of 2

Number of states in the encoder, specified as a power of 2.

Data Types: double

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.

Data Types: double

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.

Data Types: double

Data Types: struct

InterleaverIndicesSource — Source of interleaver indices

'Property' (default) | 'Input port'

Source of interleaver indices, specified as 'Property' or 'Input port'.

• When you set this property to 'Input port', the object executes using the input argument interlvrindices when you call the object. The vector length and values for the interleaver indices and coded input signal can change with each call to the object.

• When you set this property to 'Property', the object executes using the interleaver indices that you specified with the InterleaverIndices property when configuring the object.

Data Types: char | string

InterleaverIndices — Interleaver indices

(64:-1:1).' (default) | column vector of integers

Interleaver indices that define the mapping used to permute the codeword bits input to the decoder, 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 decoded output message, decmsg. Each element of the vector must be an integer in the range [1, L] and must be unique.

Dependencies

To enable this property, set the InterleaverIndicesSource property to 'Property'.

Data Types: double

InputIndicesSource — Source of input indices

'Auto' (default) | 'Property' | 'Input port'

Source of input indices, specified as 'Auto', 'Property', or 'Input port'.

• When you set this property to 'Auto', the object computes input indices that assume the second systematic stream is punctured and all tail bits are included in the input.

• When you set this property to 'Property', the object uses the input indices that you specify for the InputIndices property.

• When this property is set to 'Input port', the object executes using the input indices specified by the input argument inindices. The vector length and values for the input indices and the coded input signal can change with each call to the object.

Data Types: char | string

InputIndices — Input indices

getTurboIOIndices(64,2,3) (default) | 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 this property must equal the length of the input data vector codeword.

Dependencies

To enable this property, set the InputIndicesSource property to 'Property'.

Data Types: double

Algorithm — Decoding algorithm

'True APP' (default) | 'Max*' | 'Max'

Decoding algorithm, specified as 'True APP', 'Max*', or 'Max'. When you set this property to 'True APP', the object implements true APP decoding. When you set this property to 'Max*' or 'Max', the object uses approximations to increase the speed of the computations. For more information, see APP Decoder.

Data Types: char | string

NumScalingBits — Number of scaling bits

3 (default) | integer in the range [0, 8]

Number of scaling bits, specified as an integer in the range [0, 8]. This property sets the number of bits the constituent decoders use to scale the input data to avoid losing precision during computations. The constituent decoders multiply the input by 2 ^{NumScalingBits} and divide the pre-output by the same factor. For more information, see APP Decoder.

Dependencies

This enable this property, set the Algorithm property to 'Max*'.

Data Types: double

NumIterations — Number of decoding iterations

6 (default) | positive integer

Number of decoding iterations, specified as a positive integer. This property sets the number of decoding iterations used for each call to the object. The object iterates and provides updates to the log-likelihood ratios (LLR) of the uncoded output bits. The output of the object is the hard-decision output of the final LLR update.

Data Types: double

Usage

Syntax

decmsg = turbodec(codeword)

decmsg = turbodec(codeword,interlvrindices)

decmsg = turbodec(codeword,interlvrindices,inindices)

Description

decmsg = turbodec(codeword) decodes the input codeword using the parallel concatenated convolutional decoding scheme that is specified by the trellis structure and interleaver indices. turbodec returns the binary decoded data. For more information, see Parallel Concatenated Convolutional Decoding Scheme.

decmsg = turbodec(codeword,interlvrindices) additionally specifies the interleaver indices. To enable this syntax, set the InterleaverIndicesSource property to 'Input port'. The interleaver indices define the mapping used to permute the input at the decoder.

decmsg = turbodec(codeword,interlvrindices,inindices) additionally specifies the bit ordering and puncturing used on the fully encoded data. To enable this syntax, set the InputIndicesSource property to 'Input port'. The input indices vector values must be relative to the fully encoded data, including the tail bits for the coding scheme for all streams.

Input Arguments

codeword — 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

interlvrindices — 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 decoded output message, decmsg. 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 decoder.

Tunable: Yes

Dependencies

To enable this property, set the InterleaverIndicesSource property to 'Input port'.

Data Types: double

inindices — 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 inindices vector must equal the length of the input data vector codeword. Element values in the inindices vector must be relative to the fully encoded data, including the tail bits for the coding scheme for all streams.

Dependencies

To enable this argument, set the InputIndicesSource property to 'Input port'.

Data Types: double

Output Arguments

decmsg — Decoded message

binary column vector

Decoded message, returned as a binary column vector of length L, where L is the length of the decoded output message. This output signal is the same as data type of the codeword input.

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Define Output and Input Indices for Full-Length and Punctured Turbo Coding

Define output indices by using the OutputIndices property for turbo encoding and define the input indices by using the InputIndices property for turbo decoding. Show full-length punctured encoding and decoding for a rate 1/2 code and 10-bit block length.

Initialize Parameters

Define parameters to initialize the encoder.

blkLen = 10;
trellis = poly2trellis(4,[13 15],13);
n = log2(trellis.numOutputSymbols);
mLen = log2(trellis.numStates);

Full-Length Encoding and Decoding

Initialize variables and turbo encoding and decoding System objects for full-length coding. Turbo encode and decode the message. Display the turbo coding rate. Check the length of the coded output versus the length of the output indices vector.

fullOut = (1:(mLen+blkLen)*2*n)';
outLen = length(fullOut);
netRate = blkLen/outLen;
data = randi([0 1],blkLen,1);
intIndices  = randperm(blkLen);

turboEnc = comm.TurboEncoder('TrellisStructure',trellis);
turboEnc.InterleaverIndices = intIndices;
turboEnc.OutputIndicesSource = 'Property';
turboEnc.OutputIndices = fullOut;

turboDec = comm.TurboDecoder('TrellisStructure',trellis);
turboDec.InterleaverIndices = intIndices;
turboDec.InputIndicesSource = 'Property';
turboDec.InputIndices = fullOut;

encMsg = turboEnc(data);      % Encode

disp(['Turbo coding rate: ' num2str(netRate)])

Turbo coding rate: 0.19231

encOutLen = length(encMsg)    % Display encoded length

encOutLen = 52

isequal(encOutLen,outLen)     % Check lengths

ans = logical
   1

rxMsg = turboDec(2*encMsg-1); % Decode

isequal(data, rxMsg)          % Compare bits with decoded bits

ans = logical
   1

Punctured Encoding and Decoding

Specify the output indices for puncturing of the second systematic stream by using the getTurboIOIndices function. Initialize variables and turbo encoding and decoding System objects for punctured coding. Turbo encode and decode the message. Display the turbo coding rate. Check the length of the coded output versus the length of the output indices vector.

puncOut = getTurboIOIndices(blkLen,n,mLen);
outLen = length(puncOut);
netRate = blkLen/outLen;
data = randi([0 1],blkLen,1);
intIndices  = randperm(blkLen);

turboEnc = comm.TurboEncoder('TrellisStructure',trellis);
turboEnc.InterleaverIndices = intIndices;
turboEnc.OutputIndicesSource = 'Property';
turboEnc.OutputIndices = puncOut;

turboDec = comm.TurboDecoder('TrellisStructure',trellis);
turboDec.InterleaverIndices = intIndices;
turboDec.InputIndicesSource = 'Property';
turboDec.InputIndices = puncOut;

encMsg = turboEnc(data);   % Encode

disp(['Turbo coding rate: ' num2str(netRate)])

Turbo coding rate: 0.25641

encOutLen = length(encMsg) % Display encoded length

encOutLen = 39

isequal(encOutLen, outLen) % Check lengths

ans = logical
   1

rxMsg = turboDec(2*encMsg-1); % Decode

isequal(data, rxMsg)          % Compare bits with decoded bits

ans = logical
   1

Compare Full and Punctured Outputs

The output of the encoder interlaces the individual bit streams. The third bit of every 4-bit tuple is removed from the full-length code to produce the punctured code. This third output bit stream corresponds to the second systematic bit stream. Display the indices of the full-length code and the indices of the punctured code to show that the third bit of every 4-bit tuple is punctured.

fullOut'

ans = 1×52

     1     2     3     4     5     6     7     8     9    10    11    12    13    14    15    16    17    18    19    20    21    22    23    24    25    26    27    28    29    30    31    32    33    34    35    36    37    38    39    40    41    42    43    44    45    46    47    48    49    50

puncOut'

ans = 1×39

     1     2     4     5     6     8     9    10    12    13    14    16    17    18    20    21    22    24    25    26    28    29    30    32    33    34    36    37    38    40    41    42    44    45    46    48    49    50    52

Transmit and Receive Turbo-Encoded Data over BPSK-Modulated AWGN Channel

Simulate the transmission and reception of BPSK data over an AWGN channel by using turbo encoding and decoding.

Specify simulation parameters, and then compute the effective coding rate and noise variance. For BPSK modulation, ${\mathit{E}}_{\mathrm{S}}/{\mathit{N}}_0$ equals ${\mathit{E}}_{\mathrm{b}}/{\mathit{N}}_0$ because the number of bits per symbol (bps) is 1. To ease reuse of this code for other modulation schemes, calculations in this example include the bps terms. Define the packet length, trellis structure, and number of iterations. Calculate the noise variance using ${\mathit{E}}_{\mathrm{S}}/{\mathit{N}}_0$ and the code rate. Set the random number generator to its default state to ensure that the results are repeatable.

modOrd = 2; % Modulation order
bps = log2(modOrd); % Bits per symbol
EbNo = 1; % Energy per bit to noise power spectral density ratio in dB
EsNo = EbNo + 10*log10(bps); % Energy per symbol to noise power spectral density ratio in dB

L = 256; % Input packet length in bits
trellis = poly2trellis(4,[13 15 17],13);
numiter = 4;
n = log2(trellis.numOutputSymbols);
numTails = log2(trellis.numStates)*n;
M = L*(2*n - 1) + 2*numTails; % Output codeword packet length
rate = L/M; % Coding rate

snrdB = EsNo + 10*log10(rate); % Signal to noise ratio in dB
noiseVar = 1./(10.^(snrdB/10)); % Noise variance

rng default

Generate random interleaver indices.

intrlvrIndices = randperm(L);

Create a turbo encoder and decoder pair. Use the defined trellis structure and random interleaver indices. Configure the decoder to run a maximum of four iterations.

turboenc = comm.TurboEncoder(trellis,intrlvrIndices);
turbodec = comm.TurboDecoder(trellis,intrlvrIndices,numiter);

Create a BPSK modulator and demodulator pair, where the demodulator outputs soft bits determined using an LLR method.

bpskmod = comm.BPSKModulator;
bpskdemod = comm.BPSKDemodulator('DecisionMethod','Log-likelihood ratio', ...
    'Variance',noiseVar);

Create an AWGN channel object and an error rate object.

awgnchan = comm.AWGNChannel('NoiseMethod','Variance','Variance',noiseVar);
errrate = comm.ErrorRate;

The main processing loop performs these steps.

1. Generate binary data.

2. Turbo encode the data.

3. Modulate the encoded data.

4. Pass the modulated signal through an AWGN channel.

5. Demodulate the noisy signal by using LLR to output soft bits.

6. Turbo decode the demodulated data. Because the bit mapping from the demodulator is opposite of the mapping expected by the turbo decoder, the decoder input must use the inverse of the demodulated signal.

7. Calculate the error statistics.

for frmIdx = 1:100
    data = randi([0 1],L,1);
    encodedData = turboenc(data);
    modSignal = bpskmod(encodedData);
    receivedSignal = awgnchan(modSignal);
    demodSignal = bpskdemod(receivedSignal);
    receivedBits = turbodec(-demodSignal);
    errorStats = errrate(data,receivedBits);
end

Display the error data.

fprintf('Bit error rate = %5.2e\nNumber of errors = %d\nTotal bits = %d\n', errorStats)

Bit error rate = 2.34e-04
Number of errors = 6
Total bits = 25600

Perform Turbo Coding on 16-QAM Signal in AWGN Channel

Simulate an end-to-end communication link by using a 16-QAM signal and turbo codes in an AWGN channel. Inside a frame processing loop, packet sizes are randomly selected to be 500, 1000, or 1500 bits. Because the packet size varies, the interleaver indices are provided to the turbo encoder and decoder as an input argument of their associated System object. Compare turbo coded bit error rate results to uncoded bit error rate results.

Initialize Simulation

Set the modulation order and range of ${\mathit{E}}_{\mathrm{b}}/{\mathit{N}}_0$ values. Compute the number of bits per symbol and the energy per symbol to noise ratio (${\mathit{E}}_{\mathrm{S}}/{\mathit{N}}_0$) based on the modulation order and ${\mathit{E}}_{\mathrm{b}}/{\mathit{N}}_0$. To get repeatable results, seed the random number.

modOrder = 16;               % Modulation order
bps = log2(modOrder);        % Bits per symbol
EbNo = (2:0.5:4);            % Energy per bit to noise power spectral density ratio in dB
EsNo = EbNo + 10*log10(bps); % Energy per symbol to noise power spectral density ratio in dB
rng(1963);

Create a turbo encoder and decoder pair. Because the packet length varies for each frame, specify that the interleaver indices be supplied by an input argument of the System object when executed. Specify that the decoder perform four iterations.

turboEnc = comm.TurboEncoder('InterleaverIndicesSource','Input port');
turboDec = comm.TurboDecoder('InterleaverIndicesSource','Input port','NumIterations',4);
trellis = poly2trellis(4,[13 15 17],13);
n = log2(turboEnc.TrellisStructure.numOutputSymbols);
numTails = log2(turboEnc.TrellisStructure.numStates)*n;

Create an error rate object.

errRate = comm.ErrorRate;

Main Processing Loop

The frame processing loop performs these steps.

1. Select a random packet length, and generate random binary data.

2. Compute the output codeword length and coding rate.

3. Compute the signal to noise ratio (SNR) and noise variance.

4. Generate interleaver indices.

5. Turbo encode the data.

6. Apply 16-QAM modulation, and normalize the average signal power.

7. Pass the modulated signal through an AWGN channel.

8. Demodulate the noisy signal by using an LLR method, output soft bits, and normalize the average signal power.

9. Turbo decode the data. Because the bit mapping order from the demodulator is opposite the mapping order expected by the turbo decoder, the decoder input must use the inverse of the demodulated signal.

10. Calculate the error statistics.

ber = zeros(1,length(EbNo));
for k = 1:length(EbNo)
    % numFrames = 100;
    errorStats = zeros(1,3);
    %for pktIdx = 1:numFrames
    L = 500*randi([1 3],1,1);         % Packet length in bits
    M = L*(2*n - 1) + 2*numTails;     % Output codeword packet length
    rate = L/M;                       % Coding rate for current packet
    snrdB = EsNo(k) + 10*log10(rate); % Signal to noise ratio in dB
    noiseVar = 1./(10.^(snrdB/10));   % Noise variance
    
    while errorStats(2) < 100 && errorStats(3) < 1e7
        data = randi([0 1],L,1);
        intrlvrIndices = randperm(L);
        encodedData = turboEnc(data,intrlvrIndices);
        modSignal = qammod(encodedData,modOrder, ...
            'InputType','bit','UnitAveragePower',true);
        rxSignal = awgn(modSignal,snrdB);
        demodSignal = qamdemod(rxSignal,modOrder,'OutputType','llr', ...
            'UnitAveragePower',true,'NoiseVariance',noiseVar);
        rxBits = turboDec(-demodSignal,intrlvrIndices); % Demodulated signal is negated
        errorStats = errRate(data,rxBits);
    end
    % Save the BER data and reset the bit error rate object
    ber(k) = errorStats(1);
    reset(errRate)
end

Plot Results

Plot the bit error rate and compare it to the uncoded bit error rate.

semilogy(EbNo,ber,'-o')
grid
xlabel('Eb/No (dB)')
ylabel('Bit Error Rate')
uncodedBER = berawgn(EbNo,'qam',modOrder); % Estimate of uncoded BER
hold on
semilogy(EbNo,uncodedBER)
legend('Turbo','Uncoded','location','sw')

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 comm.TurboDecoder System object implements the soft-input soft-output APP decoding algorithm according to [1] and [2].

The 'True APP' option of the Algorithm property implements APP decoding as per equations 20–23 in section V of [1]. To gain speed, the 'Max*' and 'Max' values of the Algorithm property 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 Algorithm property to 'Max*' enables the NumScalingBits property of this System object. This property denotes the number of bits by which this System object scales the data it processes (multiplies the input by 2^{NumScalingBits} and divides the pre-output by the same factor). Use this property 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 comm.TurboEncoder and comm.TurboDecoder System objects. 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 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 InputIndicesSource property 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, 42–127, (November 1996).

[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, Geneva, Switzerland, May 1993, 1064–70. 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). https://www.3gpp.org.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2012a