BPSK_74Hamming_sim.m

EbNodB = 6;
R = 4 / 7; % (7, 4) Hamming (4/7 bits/symbol)
EbNo = 10 ^ (EbNodB / 10);
sigma = sqrt(1 / (2 * R * EbNo));

k = 4; % number of message bits
n = 7; % number of codeword bits

cwords = [ ...
     0     0     0     0     0     0     0;
     0     0     0     1     0     1     1;
     0     0     1     0     1     1     0;
     0     0     1     1     1     0     1;
     0     1     0     0     1     1     1;
     0     1     0     1     1     0     0;
     0     1     1     0     0     0     1;
     0     1     1     1     0     1     0;
     1     0     0     0     1     0     1;
     1     0     0     1     1     1     0;
     1     0     1     0     0     1     1;
     1     0     1     1     0     0     0;
     1     1     0     0     0     1     0;
     1     1     0     1     0     0     1;
     1     1     1     0     1     0     0;
     1     1     1     1     1     1     1];

Nblocks = 1000;
Nbiterrs = 0;
Nblkerrs = 0;
for i = 1 : Nblocks
    msg = randi([0 1], 1, k); % generate random k-bit message
    
    % Encoding
    cword = [msg ...
             mod(msg(1) + msg(2) + msg(3), 2) ...
             mod(msg(2) + msg(3) + msg(4), 2) ...
             mod(msg(1) + msg(2) + msg(4), 2)]; % (7, 4) Hamming
    
    s = 1 - 2 * cword; % BPSK bit to symbol conversion
    r = s + sigma * randn(1, n); % AWGN channel
    
    % Hard-Decision Decoding
    b = (r < 0); % threshold at zero
    dist = mod(repmat(b, 16, 1) + cwords, 2) * ones(7, 1);
    [mind1, pos] = min(dist);
    msg_cap1 = cwords(pos, 1:4);
    
    % Soft-Decision Decoding
    corr = (1 - 2 * cwords) * r';
    [mind2, pos] = max(corr);
    msg_cap2 = cwords(pos, 1:4);
    
    Nerrs = sum(msg ~= msg_cap1);
    if Nerrs > 0
        Nbiterrs = Nbiterrs + Nerrs;
        Nblkerrs = Nblkerrs + 1;
    end
    Nbiterrs = Nbiterrs + sum(msg ~= msg_cap2);
end

BER_sim = Nbiterrs / k / Nblocks;
FER_sim = Nblkerrs / Nblocks;

disp([EbNodB FER_sim BER_sim Nblkerrs Nbiterrs Nblocks])