chapter_4_1_2_ch_encoding.m

% Define parameters
len = 100000; % Length of original binary data stream
N1 = 3; % First repetition factor; should be odd to avoid tie
N2 = 5; % Second repetition factor; should be odd to avoid tie
N3 = 7; % Third repetition factor; should be odd to avoid tie

% Generate binary data stream
bin_str = round(rand(1,len));

% Employ repetition code with repetition factors N1, N2, N3
chcode1_bin_str = zeros(1,N1*len);
chcode2_bin_str = zeros(1,N2*len);
chcode3_bin_str = zeros(1,N3*len);

for ind = 1:1:max([N1 N2 N3])
    if (ind<=N1)
        chcode1_bin_str(ind:N1:(N1*(len-1)+ind))=bin_str;
    end
    if (ind<=N2)
        chcode2_bin_str(ind:N2:(N2*(len-1)+ind))=bin_str;
    end
    if (ind<=N3)
        chcode3_bin_str(ind:N3:(N3*(len-1)+ind))=bin_str;
    end
end

% Corrupt both binary strings with zero-mean unit variance Gaussian
% noise followed by rounding (creates "bit flipping" errors)
noisy_bin_str = bin_str + randn(1,len);
rx_bin_str0 = zeros(1,len);
ind0 = find(noisy_bin_str >= 0.5);
rx_bin_str0(ind0) = 1;

noisy_chcode1_bin_str = chcode1_bin_str + randn(1,N1*len);
rx_chcode1_bin_str = zeros(1,N1*len);
ind1 = find(noisy_chcode1_bin_str >= 0.5);
rx_chcode1_bin_str(ind1) = 1;

noisy_chcode2_bin_str = chcode2_bin_str + randn(1,N2*len);
rx_chcode2_bin_str = zeros(1,N2*len);
ind2 = find(noisy_chcode2_bin_str >= 0.5);
rx_chcode2_bin_str(ind2) = 1;

noisy_chcode3_bin_str = chcode3_bin_str + randn(1,N3*len);
rx_chcode3_bin_str = zeros(1,N3*len);
ind3 = find(noisy_chcode3_bin_str >= 0.5);
rx_chcode3_bin_str(ind3) = 1;

% Decode three encoded binary sequences
dec1_bin = (vec2mat(rx_chcode1_bin_str,N1)).';
dec2_bin = (vec2mat(rx_chcode2_bin_str,N2)).';
dec3_bin = (vec2mat(rx_chcode3_bin_str,N3)).';

ind11 = find(((sum(dec1_bin,1))/N1) >= 0.5);
ind12 = find(((sum(dec2_bin,1))/N2) >= 0.5);
ind13 = find(((sum(dec3_bin,1))/N3) >= 0.5);

rx_bin_str1 = zeros(1,len);
rx_bin_str1(ind11) = 1;

rx_bin_str2 = zeros(1,len);
rx_bin_str2(ind12) = 1;

rx_bin_str3 = zeros(1,len);
rx_bin_str3(ind13) = 1;

% Calculate bit error rate
ber0 = sum(abs(bin_str - rx_bin_str0))/len;
ber1 = sum(abs(bin_str - rx_bin_str1))/len;
ber2 = sum(abs(bin_str - rx_bin_str2))/len;
ber3 = sum(abs(bin_str - rx_bin_str3))/len;

Y=[ber0, ber1, ber2, ber3];
f=figure;
b=bar(Y,'FaceColor','flat');
b.CData(2,:)=[0.6350 0.0780 0.1840];
b.CData(3,:)=[0.8500 0.3250 0.0980];
b.CData(4,:)=[0.4660 0.6740 0.1880];
xLabel = ["Orig","3*Bits","5*Bits","7*Bits"];
yLabel = ["Bit Error Rate (BER)"];
f.CurrentAxes.YLabel.String="Number of Bits";
f.CurrentAxes.XLabel.String="Channel Encoding by Different Factors";
set(gca,'xticklabel',xLabel);