B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

14. 13 MATLAB EXERCISES
14. 1 3 MATLAB Exercises 861
In this section, we provide MATLAB programs to illustrate simple examples of block encoders
and decoders. We focus on the simpler case of hard-decision decoding based on syndromes.
COMPUTER EXERCISE 14. 1
In the first experiment, we provide a program to decode the (6, 3) linear block code of Example 14.1.
% Matlab Program <Exl4 __ 1 .m>
% to illustrate encoding and decoding of (6,3) block code
% in ·Example 14 .1
%
G= [l 0 0 1 0 1 %Code Generator
0 1 0 0 1 1
0 0 1 1 1 0 ] ;
H= [l 0 1 %Parity Check Matrix
0 1 1
1 1 0
1 0 0
0 1 0
0 0 1] ';
E= [0 0 0 0 0 0 %List of correctable errors
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
1 0 0 0 1 0 ] ;
K=size (E,1);
Syndrome=mod (mtimes (E,H' ) ,2);
r= [l 1 1 0
display( ['Syndrome ' , 'Error
display (num2str ( [Syndrome
x=mod (r*H' ,2) ;
for kk=l :K,
if Syndrome (kk, :)==x,
idxe=kk ;
end
end
syndrome= Syndrome (idxe , :)
error=E ( idxe , : )
cword=xor (r,error)
1 1]
Pattern' ])
E] ))
%Find Syndrome List
%Received codeword
%Compute syndrome
%Find the syndrome index
%display the syndrome
%Error correction
The execution of this MATLAB program will generate the following results, which include the
erroneous codeword, the syndrome, the error pattern, and the corrected codeword.
Ex14 2
Syndrome Error Pattern
0 0 0 0 0 0 0 0 0
1 0 1 1 0 0 0 0 0
0 1 1 0 1 0 0 0 0
1 1 0 0 0 1 0 0 0