test_with_stats_and_plots.m

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


%% Application - LDPC CODE
%l_max = 3;
%r_max = 6;
l_optimum = [0.3, 0.5, 0.2];
r_optimum = [0.2, 0.2, 0.1, 0.1, 0.3, 0.1];


begin_n = 101;
end_n = 201;
step_n = 5;
n_list = begin_n : step_n : end_n;
all_n = floor((end_n - begin_n) / step_n) + 1;




for index = 1:length(n_list)
    n = n_list(index);
    [H, num_variables, num_checks, num_edges, rate_expected, counter_tries, initial_errors, final_errors]= LDPC_simulation_stats_plots(n, l_optimum, r_optimum, "find_appropriate_n");
    if isnan(H)
        n_list(index) = 0;
    end
end




%% Our data - stats variables
n_list = nonzeros(n_list);
LEN = length(n_list);
er = 0.1;
var_num_list = zeros(1, LEN);
check_num_list = zeros(1, LEN);
edges_num_list = zeros(1, LEN);
rates_list = zeros(1, LEN);
tries_list = zeros(1, LEN);
initial_list = zeros(1, LEN);
final_list = zeros(1, LEN);




% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
for INDEX = 1:LEN



    n = n_list(INDEX);
    [H, num_variables, num_checks, num_edges, rate_expected, counter_tries, initial_errors, final_errors]= LDPC_simulation_stats_plots(n, l_optimum, r_optimum, "anakyklwseis");




    %% Implementing the BEC and Graph
    x = zeros(1, n);
    [y, err] = bec(x, er);
    var_nodes = cell(1, num_variables);

    for i = 1:num_variables
       var_nodes{i} = connections(H,i,y);
    end

    check_nodes = cell(1,num_checks);

    for i = 1:num_checks
       check_nodes{i} = var2check(H,i,y,1);
    end

    % Iterations
    limit = 100;
    counter = 0;
    SUM_ALL = Inf;
    while (counter <= limit) && SUM_ALL == Inf

        counter = counter + 1;
        if counter > 1
            for i = 1:num_checks
                check_nodes =...
                var2check_updated(var_nodes,check_nodes,y,i);
            end
        end

        check_to_var = check2var(check_nodes, num_checks);
        var_nodes = edges_values(var_nodes, check_to_var);
        var_rec_sum = var_rec(var_nodes, y);
        SUM_ALL = sum(var_rec_sum);


    end




    var_values = var_rec_sum;
    initial_errors = sum(err);
    final_errors = length(nonzeros(abs(x-var_values)));

    % FOR STATISTICS PURPOSE
    var_num_list(INDEX) = num_variables;
    check_num_list(INDEX) = num_checks;
    edges_num_list(INDEX) = num_edges;
    rates_list(INDEX) = rate_expected;
    tries_list(INDEX) = counter_tries;
    initial_list(INDEX) = initial_errors;
    final_list(INDEX) = final_errors;



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






% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
% ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
%% STATS
display(' ');
display(' ');
pretty_display("      Appropriate n list:      ", n_list');
pretty_display("Num of variables nodes list:   ", var_num_list);
pretty_display("   Num of check nodes list:    ", check_num_list);
pretty_display("      Num of edges list:       ", edges_num_list);
pretty_display("     Expected rate list:       ", rates_list);
pretty_display("Tries to find NO RECYCLE list: ", tries_list);
pretty_display("       Initial errors list:    ", initial_list);
pretty_display("       Final errors list:      ", final_list);
display(' ');

appropriate_n = length(n_list);
perc100 = round(100 * appropriate_n / all_n, 2);
disp("In the interval [" + num2str(begin_n) + ", " + num2str(end_n) + "] with step = " + num2str(step_n) + ": ");
disp("There are " + num2str(appropriate_n) + "/" + num2str(all_n) + ...
    " values of 'n', that can be used for this LDPC code.");
disp("Percentage = " + num2str(perc100) + "%");


%% PLOTS
figure(1);
plot(n_list, var_num_list, 'black');
title("Graph characteristics");
xlabel("n = message length (variables)");
ylabel("Var, check, edges");
hold on
plot(n_list, check_num_list, 'blue');
hold on
plot(n_list, edges_num_list, 'red');
legend("Variables", "Checks", "Edges");

figure(2);
plot(n_list, rates_list, 'black');
title("Transmission rate 'r'");
xlabel("n = message length (variables)");
ylabel("Rate = r = r(n)");

figure(3);
plot(n_list, tries_list, 'black');
title("Tries until perfect graph");
xlabel("n = message length (variables)");
ylabel("Tries = Tries(n)");

figure(4);
plot(n_list, initial_list, 'black');
hold on
plot(n_list, final_list, 'blue');
title("Initial and final codeword errors");
xlabel("n = message length (variables)");
ylabel("Errors in codeword");
legend("Initial errors", "Final errors");
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