Main stats and plots (Hamming probabilities plot for n=3)

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


%% NICE COMBINATIONS
% n = 3 and er = 0.00 - 0.20
% n = 4 and er = 0.00 - 0.06

% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%% Application - Hamming Code

n = 3;                   % 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

% Creating list of error probabilities
er_list = 0.01 : 0.005 : 0.2;
percentage100_list = zeros(1, length(er_list));
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% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~





% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%% MAIN FUNCTION - PLOT

for k = 1:length(er_list)

    er = er_list(k);
    display('**********************************');
    disp("Error probability = " + num2str(er));

    %% Create the stats
    counter_rounds = 0;
    target = 100;
    num_of_corrections = 0;

    while counter_rounds < target

        %% Simulating the Binary Symmetric Channel
        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
    percentage100 = 100 * num_of_corrections / target;
    percentage100_list(k) = percentage100;
    disp("Percentage of correction: " + num2str(percentage100) + "%");
    display(' ')

    %% 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) + "%");


end
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% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


er_list;
percentage100_list;
plot(er_list, percentage100_list);
xlabel('Error probability');
ylabel('Percentage (%) of correcting 1 mistake');