% a function to realize a decoder, summation of some of the other functions
% the input 'r_x' is the output sequence of the function rs_channel()
% the output 'm_x' is the sequence after decoding
function m_x=rs_decoder(r_x);
disp('伴隨多項式：')
synd_x=rs_decode_syndrome(r_x);
% to view the results clearly, pause, press any key to continue
disp('Press any key to continue...')
pause
disp('錯誤位置多項式：')
sigma_x=rs_decode_iterate(synd_x);
disp('Press any key to continue...')
pause
disp('錯誤位置多項式的根：')
root=rs_decode_root(sigma_x);
disp('Press any key to continue...')
pause
% if number of error is more than t, cases of no root and few or more root will occur
if length(root)==0
   disp('檢測不到錯誤發生，解碼輸出：')
   m_x=r_x(7:31);
else
   disp('錯誤數值和錯誤位置：')
   [value,site]=rs_decode_forney(synd_x,sigma_x,root);
   disp('Press any key to continue...')
   pause
   temp=r_x;
   for i=1:length(site)
        temp(site(i)+1)=rs_add(r_x(site(i)+1),value(i));
   end
   if length(root)>3
       disp('Too many errors occur, can not correct them all')
       disp('部分糾錯解碼輸出：')
       m_x=temp(7:31);
   else
       disp('解碼輸出：')
       m_x=temp(7:31);
    end
end