BlockCodes.m

%Block codes
clc
clear all
close all
N=1e6; % number of message words used for simulation
n=7; k=4;
Nb=N*k;
P=[1 1 0; 0 1 1; 1 1 1; 1 0 1]; %parity matrix
G=[P eye(k)]; %Generator matrix
H=[eye(n-k) P']; %parity check matrix
E=[0 0 0 0 0 0 0; %error patterns
   1 0 0 0 0 0 0;
   0 1 0 0 0 0 0;
   0 0 1 0 0 0 0;
   0 0 0 1 0 0 0;
   0 0 0 0 1 0 0;
   0 0 0 0 0 1 0;
   0 0 0 0 0 0 1];
syn_array=E*H'; %syndrome for error pattern
ms=[0 0 0 0; 0 0 0 1; 0 0 1 0; 0 0 1 1; 0 1 0 0; 0 1 0 1; 0 1 1 0; 0 1 1 1;
    1 0 0 0; 1 0 0 1; 1 0 1 0; 1 0 1 1; 1 1 0 0; 1 1 0 1; 1 1 1 0; 1 1 1 1];
cs=mod(ms*G,2);

csig=cs; csig(csig==0)=-1;
syn_val=dec2bin(syn_array'); syn_val=reshape(syn_val,n-k,2^(n-k));
syn_dec=bin2dec(syn_val');

b=randi([0 1],Nb,1); %bit generation
m=reshape(b,k,N)';   %message word formation
x=mod(m*G,2)';       %block code - codeword generation
s=reshape(x,N*n,1);
s(s==0)=-1;          %converting to BPSK format

%BPSK:Binary Phase Shift Keying
EbNodB=0:1:15;
for ii=1:length(EbNodB)
    EbNodB(ii)
    SNRdB=EbNodB(ii)+3.01;
    rn=awgn(s,SNRdB,'measured'); %adding white noise
    xcat=rn;
    xcat(xcat>=0)=1; xcat(xcat<0)=0; %detection as '0' / '1'
    xcat=reshape(xcat,n,N);
    %BER computation without block codes
    BER0(ii)=sum(sum(xcat~=x))/(N*n); %BER w/o channel coder
    clear xcat;
    
    %BER computation with block codes - Hard decision
    SNRdB=EbNodB(ii)+3.01+10*log10(4/7);
    rn=awgn(s,SNRdB,'measured'); %adding white noise
    r=reshape(rn,n,N);
    y=r; y(y>=0)=1; y(y<0)=0;
    mH=[]; mE=[];
    
    syn=mod(y'*transpose(H),2); %syndrome computation
    %syn_val=binaryVectorToDecimal(syn);
    syn_val=dec2bin(syn'); syn_val=reshape(syn_val,n-k,N);
    syn_val=bin2dec(syn_val');
    
    for jj=1:N
        e_index(jj)=find(syn_val(jj)==syn_dec); %syndrome error pattern detection
    end
    
    e=E(e_index,:);
    scat=mod(y+e',2);  %correction of error in received seq
    bcat=scat(n-k+1:end,:);  %message bit collection
    bcat=reshape(bcat,Nb,1);
    BER_Synd(ii)=sum(bcat~=b)/Nb; %BER syndrome decoding
    %BER_Hard(ii)=sum(sum(mH~=n))/(N*k); %BER Hard decision channel decoder
end

%theoritical BER
EbNo=10.^(EbNodB/10);
BER=1/2*erfc(sqrt(EbNo));

semilogy(EbNodB, BER, 'r*'); hold on; grid on;
semilogy(EbNodB, BER0, 'b-');
semilogy(EbNodB, BER_Synd, 'm-');
%semilogy(EbNodB, BER_Hard, 'k-');
%semilogy(EbNodB, BER_Soft, 'r-');
xlabel(' E_b/N_o (dB)');
ylabel('Bit error probability(P_e)');
title('BER performance');
axis([0 15 10e-8 1]);
legend('BPSK w/o Ch.Coder (Th.)','BPSK w/o Ch. Coder (Sim)', '(7,4) Hamming Code-Syndrome');