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(Not recommended) Encode binary low-density parity-check (LDPC) code

comm.LDPCEncoder is not recommended. Instead, use the ldpcEncode function. For more information, see Compatibility Considerations.


The comm.LDPCEncoder System object™ applies LDPC coding to a binary input message. LDPC codes are linear error control codes with sparse parity-check matrices and long block lengths that can attain performance near the Shannon limit.

To encode a binary LDPC code:

  1. Create the comm.LDPCEncoder 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?




ldpcencoder = comm.LDPCEncoder creates a binary LDPC encoder System object. This object performs LDPC encoding based on the default parity-check matrix.

ldpcencoder = comm.LDPCEncoder(parity) sets the ParityCheckMatrix property to parity and creates an LDPC encoder System object. The parity input must be specified as described by the ParityCheckMatrix property.

ldpcencoder = comm.LDPCEncoder(___,Name,Value) sets properties using one or more name-value pairs, in addition to inputs from any of the prior syntaxes. For example, comm.LDPCEncoder('ParityCheckMatrix',sparse(I(:,1),I(:,2),1)) configures an LDPC encoder System object to encode data using the parity matrix sparse(I(:,1),I(:,2),1). Enclose each property name in quotes.


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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.

Parity-check matrix, specified as a sparse (NK)-by-N binary-valued matrix. N is the length of the output codeword vector, and must be in the range (0, 231). K is the length of the uncoded message and must be less than N. The last (NK) columns in the parity-check matrix must be an invertible matrix in the Galois field of order 2, gf(2).

You can also specify the parity-check matrix as a two-column nonsparse index matrix, I, that defines the row and column indices of the 1s in the parity-check matrix such that sparse(I(:,1),I(:,2),1).

This property accepts numeric data types. When you set this property to a sparse binary matrix, this property also accepts the logical data type.

The default value uses the dvbs2ldpc function to configure a sparse parity-check matrix for half-rate LDPC coding, as specified in the DVB-S.2 standard.


  • When the last (NK) columns of the parity-check matrix form a triangular matrix, forward or backward substitution is performed to solve the parity-check equation.

  • When the last (NK) columns of the parity-check matrix do not form a triangular matrix, a matrix inversion is performed to solve the parity-check equation. If a large matrix needs to be inverted, initializations or updates take more time.

Example: dvbs2ldpc(R,'indices') configures the index matrix for the DVB-S.2 standard, where R is the code rate, and 'indices' specifies the output format of dvbs2ldpc as a two-column double-precision matrix that defines the row and column indices of the 1s in the parity-check matrix.

Data Types: double | logical




codeword = ldpcencoder(message) codes the input message using an LDPC code based on a parity-check matrix. The LDPC codeword output is a solution to the parity-check equation.

Input Arguments

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Input message, specified as a K-by-1 column vector containing binary-valued elements. K is the length of the uncoded message.

Data Types: double | logical

Output Arguments

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LDPC codeword, returned as an N-by-1 column vector. N is the number of bits in the LDPC codeword. The output signal inherits its data type from the input signal. The LDPC codeword output is a solution to the parity-check equation. The input message comprises the first K bits of the LDPC codeword output, and the parity check comprises the remaining (NK) bits.

Data Types: double | logical

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:


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stepRun System object algorithm
releaseRelease resources and allow changes to System object property values and input characteristics
resetReset internal states of System object


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Transmit an LDPC-encoded, QPSK-modulated bit stream through an AWGN channel. Demodulate and decode the received signal. Compute the error statistics for the reception of uncoded and LDPC-coded signals.

Define simulation variables. Create System objects for the LDPC encoder, LDPC decoder, QPSK modulator, and QPSK demodulators.

M = 4; % Modulation order (QPSK)
snr = [0.25,0.5,0.75,1.0,1.25];
numFrames = 10;
ldpcEncoder = comm.LDPCEncoder;
ldpcDecoder = comm.LDPCDecoder;
pskMod = comm.PSKModulator(M,'BitInput',true);
pskDemod = comm.PSKDemodulator(M,'BitOutput',true,...
    'DecisionMethod','Approximate log-likelihood ratio');
pskuDemod = comm.PSKDemodulator(M,'BitOutput',true,...
    'DecisionMethod','Hard decision');
errRate = zeros(1,length(snr));
uncErrRate = zeros(1,length(snr));

For each SNR setting and all frames, compute the error statistics for uncoded and LDPC-coded signals.The outer for loop processes each SNR value. The inner for loop processes frames of input data.

for ii = 1:length(snr)
    ttlErr = 0;
    ttlErrUnc = 0;
    pskDemod.Variance = 1/10^(snr(ii)/10);
    for counter = 1:numFrames
        data = logical(randi([0 1],32400,1));
        % Transmit and receiver uncoded signal data
        mod_uncSig = pskMod(data);
        rx_uncSig = awgn(mod_uncSig,snr(ii),'measured');
        demod_uncSig = pskuDemod(rx_uncSig);
        numErrUnc = biterr(data,demod_uncSig);
        ttlErrUnc = ttlErrUnc + numErrUnc;
        % Transmit and receive LDPC coded signal data
        encData = ldpcEncoder(data);
        modSig = pskMod(encData);
        rxSig = awgn(modSig,snr(ii),'measured');
        demodSig = pskDemod(rxSig);
        rxBits = ldpcDecoder(demodSig);
        numErr = biterr(data,rxBits);
        ttlErr = ttlErr + numErr;
    ttlBits = numFrames*length(rxBits);
    uncErrRate(ii) = ttlErrUnc/ttlBits;
    errRate(ii) = ttlErr/ttlBits;

Run this code to plot the error statistics for uncoded and LDPC-coded data.

legend('Uncoded','LDPC coded')
xlabel('SNR (dB)')

Compatibility Considerations

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Not recommended starting in R2021b

Extended Capabilities

Introduced in R2012a