guide to simulating convolutional codes and LDPC codes in MATLAB,

Here’s a step-by-step guide to simulating convolutional codes and LDPC codes in MATLAB, including encoding, modulation, AWGN channel, decoding, and BER calculation.

Part 1: Convolutional Codes

Convolutional codes use shift registers and polynomial generators to encode data. We’ll use the Viterbi algorithm for decoding.

MATLAB Code for Convolutional Codes

% Simulation Parameters
numBits = 1e6;              % Number of information bits
EbN0_dB = 0:2:10;           % SNR range (dB)
codeRate = 1/2;             % Code rate (k/n)
trellis = poly2trellis(7, [171 133]); % Polynomial: (171,133) in octal

% Initialize BER results
ber_conv = zeros(size(EbN0_dB));

% Generate random bits
dataBits = randi([0 1], numBits, 1);

% Convolutional Encoder
encoder = comm.ConvolutionalEncoder('TrellisStructure', trellis);
encodedBits = encoder(dataBits);

% BPSK Modulation
modulated = 2*encodedBits - 1; % Map 0→-1, 1→+1

% Simulate for each SNR
for idx = 1:length(EbN0_dB)
    % Add AWGN
    snr = EbN0_dB(idx) + 10*log10(codeRate); % Adjust SNR for code rate
    received = awgn(modulated, snr, 'measured');
    
    % BPSK Demodulation (soft decision: LLR)
    demodulated = -real(received); % Log-likelihood ratio (LLR)
    
    % Viterbi Decoder
    decoder = comm.ViterbiDecoder('TrellisStructure', trellis, ...
        'InputFormat', 'unquantized', 'TracebackDepth', 34);
    decodedBits = decoder(demodulated);
    
    % Calculate BER
    [~, ber_conv(idx)] = biterr(dataBits, decodedBits);
end

% Plot BER
figure;
semilogy(EbN0_dB, ber_conv, 'bo-', 'LineWidth', 2);
grid on;
xlabel('Eb/N0 (dB)');
ylabel('BER');
title('Convolutional Code (Rate 1/2) Performance');

Part 2: LDPC Codes

LDPC (Low-Density Parity-Check) codes use sparse parity-check matrices and iterative belief propagation for decoding.

MATLAB Code for LDPC Codes

% Simulation Parameters
numBits = 1e6;              % Number of information bits
EbN0_dB = 0:2:10;           % SNR range (dB)
codeRate = 1/2;             % Code rate (k/n)

% Generate LDPC matrix (DVB-S2 standard)
H = dvbs2ldpc(codeRate);
ldpcEncoder = ldpcEncoder(H);
ldpcDecoder = ldpcDecoder(H, 'Algorithm', 'Belief Propagation');

% Initialize BER results
ber_ldpc = zeros(size(EbN0_dB));

% Generate random bits
dataBits = randi([0 1], numBits, 1);

% LDPC Encoding
encodedBits = ldpcEncoder(dataBits);

% BPSK Modulation
modulated = 2*encodedBits - 1; % Map 0→-1, 1→+1

% Simulate for each SNR
for idx = 1:length(EbN0_dB)
    % Add AWGN
    snr = EbN0_dB(idx) + 10*log10(codeRate); % Adjust SNR for code rate
    received = awgn(modulated, snr, 'measured');
    
    % BPSK Demodulation (soft decision: LLR)
    demodulated = -2 * real(received) / (0.5^2); % LLR calculation
    
    % LDPC Decoding
    decodedBits = ldpcDecoder(demodulated);
    
    % Calculate BER
    [~, ber_ldpc(idx)] = biterr(dataBits, decodedBits);
end

% Plot BER
figure;
semilogy(EbN0_dB, ber_ldpc, 'ro-', 'LineWidth', 2);
grid on;
xlabel('Eb/N0 (dB)');
ylabel('BER');
title('LDPC Code (Rate 1/2) Performance');

Key Notes

Convolutional Codes:
- Uses a rate-1/2 encoder with polynomials [171, 133] (octal).
- Viterbi decoding with soft decisions (LLR).
- Adjust TracebackDepth for better performance.
LDPC Codes:
- Uses the DVB-S2 standard parity-check matrix.
- Belief propagation (iterative message-passing) for decoding.
- LLR calculation assumes BPSK modulation over AWGN.
Modulation & Channel:
- BPSK modulation for simplicity.
- Adjust SNR to account for code rate:
  SNR = EbN0 + 10*log10(codeRate).
Performance:
- LDPC codes outperform convolutional codes at higher SNRs.
- Convolutional codes are simpler but less efficient.

How to Run

Ensure you have the Communications Toolbox in MATLAB.
Run the code for both convolutional and LDPC codes.
Compare BER curves to analyze performance.

Extensions

Try different code rates (e.g., 3/4 for LDPC).
Use higher-order modulation (QPSK, 16-QAM).
Compare with Turbo codes or Polar codes