some questions about hamming code

% Generate information array with 1000000 elements

N = 1000000

for i=1:N
    if rand <.5
       s(i)=0;
    else
       s(i)=1;
    end
end

% Generate 3bits check code
source = reshape(s,N/4,[]);
 for i = 1:N/4
   source(i,5) = xor(source(i,1),xor(source(1,2),source(1,3)));
   source(i,6) = xor(source(i,2),xor(source(1,3),source(1,4)));
   source(i,7) = xor(source(i,1),xor(source(1,2),source(1,4)));
 end 

%enery per bit to noise spectral density ratio      

EbNo = [-3:1:10];
% Generate white noise
b = randn(1,N*7/4);

%14 noise density

for j = 1:14

%join white noise

    sigma(j) = power(10,(-EbNo(j)/20))/ sqrt (2);
    for i = 1:N*7/4 
        n(i)=sigma(j)*b(i);
    end
    n = reshape(n,N/4,[]);
    y=source+n;

%Receive transmitted codeword  

    for i = 1 : N/4
        for k = 1 : 7
            if y(i,k) > 0
               y(i,k) = 1;
            else
               y(i,k) = 0;
            end
        end
    end
% decoding
H = [1 1 1 0 1 0 0
     0 1 1 1 0 1 0
     1 1 0 1 0 0 1
    ];

t_H = H';
syndrome = mod((y* t_H),2);
% calculate bit error probability
Nberreur(j)=0;
for i = 1 : N/4
    if (syndrome(i,1) == 1) & (syndrome(i,2) == 0) & (syndrome(i,3) == 1)
        Nberreur(j) = Nberreur(j) +1;
        y(i,1) = ~y(i,1);
    end
    if (syndrome(i,1) == 1) & (syndrome(i,2) == 1) & (syndrome(i,3) == 1)
        Nberreur(j) = Nberreur(j) +1;
        y(i,2) = ~y(i,2);
    end
    if (syndrome(i,1) == 1) & (syndrome(i,2) == 1) & (syndrome(i,3) == 0)
        Nberreur(j) = Nberreur(j) +1;
         y(i,3) = ~y(i,3);
    end
    if (syndrome(i,1) == 0) & (syndrome(i,2) == 1) & (syndrome(i,3) == 1)
        Nberreur(j) = Nberreur(j) +1;
        y(i,4) = ~y(i,4);
    end
end

%calculate bit error probability

    Tauxderreur2(j) = Nberreur(j) / N;
end

%show plot
 
semilogy(EbNo,Tauxderreur2);

My friends, I'm learning hamming code now. And I want to calculate bit error probability and this is an example. At first, I want to ask what "if rand <.5" means? I know what rand means but I have never met "<.5" before. Secondly, I wanna to ask why we use "syndrome = mod((y* t_H),2)" to decode? I try several arrays and it works, but I don't know why? Finally, should we join white noise for every time? Or it's just optional?

[Walter Roberson]

rand generates a new random number in the open range 0 to 1 .

< is comparison for less than

If you compare random over 0 to 1 as less than 0.5 then you are going to take the branch with aa 50% chance . If it were less than 0.374 then that would be aa 37.4% chance of taking the branch.