% Chapter 15 Error Correcting Codes
% In this section, we provide MATLAB programs to illustrate simple
% examples of block encoders and decodes. We focus on the simpler case
% of hard-decision decoding based on syndromes.
%
% In the first experiment, we provide a program to decode the(6,3)
% linear block code of Example 15.1.
%
% Matlab Program < Ex15_1.m >
% to illustrate encoding and decoding of (6,3) block code
% in Example 15.1
%
G=[1 0 0 1 0 1      % Code Generator
   0 1 0 0 1 1
   0 0 1 1 1 0];
H=[1 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);   % Find Syndrome List
r=[1 1 1 0 1 1]                 % Received codeword
display(['Syndrom ','Error Pattern'])
display(num2str([Syndrome E]))
x=mod(r*H',2);                  % Compute syndrome
for kk=1:K,
    if Syndrome(kk,:)==x,
        idxe=kk;
    end
end
syndrome=Syndrome(idxe,:)       % display the syndrome
error=E(idxe,:)
cword=xor(r,error)              % Error correction

%------------------------------------------------------------

% 参考文献 

% B.P.拉兹，丁峙. 现代数字与模拟通信系统[M]. 第4版. 北京：电子工业出版社，2011:966-967

1. % The linear block code is used to encode and the syndrome decoding i.

% 采用线性分组码进行编码，用伴随式译码。