Main stats (Hamming correction for n=4)

%% Close all figures, clear workspace and console
close all;
clear;
clc;

%% NICE COMBINATIONS
% n = 3 and er = 0.1   (below 0.147)
% n = 4 and er = 0.05  (below 0.066)

%% Application - Hamming Code

n = 4;                   % rows of H
m = 2^n - n - 1;         % message bits || rows of G
H = ham_par(n);          % Creating a Hamming Code Parity Matrix
P = H(:, 1:(2^n-1-n));
G = [eye(2^n-1-n) P'];   % Creating Generator Matrix

% Creating messages words
u_list = dec2bin(0:2^m-1)-'0';

% Creating codewords
codewords = ones(2^m,2^n-1);
rows_codewords = size(codewords, 1);
cols_codewords = size(codewords, 2);

for i = 1:rows_codewords
    codewords(i,:) = mod(u_list(i,:)*G,2); % EINAI MOD 2?
end





%% Create the stats
counter_rounds = 0;
target = 1000;
num_of_corrections = 0;

while counter_rounds < target

    %% Simulating the Binary Symmetric Channel
    er = 0.05;  % Channel error
    in_data = codewords(randi([1 rows_codewords]), :); % Random codeword
    % in_data = codewords(2,:);
    x = zeros(1, cols_codewords); % x(0,1) to x(-1,0)

    for i = 1:cols_codewords
        if in_data(i) == 0
            x(i) = 1;
        else
            x(i) = -1;
        end
    end

    [out_data,err] = bsc(in_data,er);
    initial_errors = sum(err);




    if initial_errors == 1

        counter_rounds = counter_rounds + 1;
        disp("******** Counter " + num2str(counter_rounds) + " ********");
        %% Begin the process
        y = zeros(1, cols_codewords);     % out_data(0,1) to out_data(1,-1)
        for i = 1:length(out_data)
            if out_data(i) == 0
                y(i) = 1;
            else
                y(i) = -1;
            end
        end

        %% Print the state
        disp("x = " + num2str(x));
        disp("y = " + num2str(y));
        disp("Initial errors: "+num2str(initial_errors));

        %% Implementing the Graph

        pos = lk(x, y, er);   % old chan_node
        var_nodes = cell(1, 2^n-1);
        for i = 1:2^n-1

           var_nodes{i} = connections(H,i,pos);

        end
        check_nodes = cell(1,n);

        for i = 1:n
           check_nodes{i} = var2check(H,i,pos,0);
        end

        % Iterations
        limit = 100;
        counter = 0;
        SUM = -1;
        while (counter <= limit) && SUM ~= 0

            counter = counter + 1;

            for i = 1:n
                check_nodes =...
                var2check_updated(var_nodes,check_nodes,pos,i);
            end

            check_to_var = check2var(check_nodes, n);
            var_rec_sum = var_rec(check_to_var, pos);
            var_values = map_detection(var_rec_sum);
            % x^ = 1 - 2x => x = (1 - x^) / 2
            % x = x, x^ = var_values
            var_values_01 = (1 - var_values) / 2;
            temp = mod(H*var_values_01',2);
            SUM = sum(temp);
            var_nodes =...
            edges_values(var_nodes, check_to_var);

        end

        disp(' ')
        %disp("x^= " + num2str(var_values));
        %disp("x = " + num2str(x))
        disp("x = " + num2str(in_data));
        disp("x^= " + num2str(var_values_01));
        final_errors = sum(abs(x-var_values))/2;
        disp("Final errors: " + num2str(final_errors));
        display("**********************")
        display(' ')
        if final_errors == 0
            num_of_corrections = num_of_corrections + 1;
        end

    end

end


%% Display overall stats
disp("Iterations: " + num2str(target));
disp("Corrected codewords with 1 initial mistake: " + num2str(num_of_corrections))
percentage100 = 100 * num_of_corrections / target;
disp("Percentage of correction: " + num2str(percentage100) + "%");