rs.cpp

在GF（8）域内

        u++ ;
        if (d[u]==-1)
          { l[u+1] = l[u] ;
            for (i=0; i<=l[u]; i++)
             {  elp[u+1][i] = elp[u][i] ;
                elp[u][i] = index_of[elp[u][i]] ;
             }
          }
        else
/* search for words with greatest u_lu[q] for which d[q]!=0 */
          { q = u-1 ;
            while ((d[q]==-1) && (q>0)) q-- ;
/* have found first non-zero d[q]  */
            if (q>0)
             { j=q ;
               do
               { j-- ;
                 if ((d[j]!=-1) && (u_lu[q]<u_lu[j]))
                   q = j ;
               }while (j>0) ;
             } ;

/* have now found q such that d[u]!=0 and u_lu[q] is maximum */
/* store degree of new elp polynomial */
            if (l[u]>l[q]+u-q)  l[u+1] = l[u] ;
            else  l[u+1] = l[q]+u-q ;

/* form new elp(x) */
            for (i=0; i<nn-kk; i++)    elp[u+1][i] = 0 ;
            for (i=0; i<=l[q]; i++)
              if (elp[q][i]!=-1)
                elp[u+1][i+u-q] = alpha_to[(d[u]+nn-d[q]+elp[q][i])%nn] ;
            for (i=0; i<=l[u]; i++)
              { elp[u+1][i] ^= elp[u][i] ;
                elp[u][i] = index_of[elp[u][i]] ;  /*convert old elp value to index*/
              }
          }
        u_lu[u+1] = u-l[u+1] ;

/* form (u+1)th discrepancy */
        if (u<nn-kk)    /* no discrepancy computed on last iteration */
          {
            if (s[u+1]!=-1)
                   d[u+1] = alpha_to[s[u+1]] ;
            else
              d[u+1] = 0 ;
            for (i=1; i<=l[u+1]; i++)
              if ((s[u+1-i]!=-1) && (elp[u+1][i]!=0))
                d[u+1] ^= alpha_to[(s[u+1-i]+index_of[elp[u+1][i]])%nn] ;
            d[u+1] = index_of[d[u+1]] ;    /* put d[u+1] into index form */
          }
      } while ((u<nn-kk) && (l[u+1]<=tt)) ;

      u++ ;
      if (l[u]<=tt)         /* can correct error */
       {
/* put elp into index form */
         for (i=0; i<=l[u]; i++)   elp[u][i] = index_of[elp[u][i]] ;

/* find roots of the error location polynomial */
         for (i=1; i<=l[u]; i++)
           reg[i] = elp[u][i] ;
         count = 0 ;
         for (i=1; i<=nn; i++)
          {  q = 1 ;
             for (j=1; j<=l[u]; j++)
              if (reg[j]!=-1)
                { reg[j] = (reg[j]+j)%nn ;
                  q ^= alpha_to[reg[j]] ;
                } ;
             if (!q)        /* store root and error location number indices */
              { root[count] = i;
                loc[count] = nn-i ;
                count++ ;
              };
          } ;
         if (count==l[u])    /* no. roots = degree of elp hence <= tt errors */
          {
/* form polynomial z(x) */
           for (i=1; i<=l[u]; i++)        /* Z[0] = 1 always - do not need */
            { if ((s[i]!=-1) && (elp[u][i]!=-1))
                 z[i] = alpha_to[s[i]] ^ alpha_to[elp[u][i]] ;
              else if ((s[i]!=-1) && (elp[u][i]==-1))
                      z[i] = alpha_to[s[i]] ;
                   else if ((s[i]==-1) && (elp[u][i]!=-1))
                          z[i] = alpha_to[elp[u][i]] ;
                        else
                          z[i] = 0 ;
              for (j=1; j<i; j++)
                if ((s[j]!=-1) && (elp[u][i-j]!=-1))
                   z[i] ^= alpha_to[(elp[u][i-j] + s[j])%nn] ;
              z[i] = index_of[z[i]] ;         /* put into index form */
            } ;

  /* evaluate errors at locations given by error location numbers loc[i] */
           for (i=0; i<nn; i++)
             { err[i] = 0 ;
               if (recd[i]!=-1)        /* convert recd[] to polynomial form */
                 recd[i] = alpha_to[recd[i]] ;
               else  recd[i] = 0 ;
             }
           for (i=0; i<l[u]; i++)    /* compute numerator of error term first */
            { err[loc[i]] = 1;       /* accounts for z[0] */
              for (j=1; j<=l[u]; j++)
                if (z[j]!=-1)
                  err[loc[i]] ^= alpha_to[(z[j]+j*root[i])%nn] ;
              if (err[loc[i]]!=0)
               { err[loc[i]] = index_of[err[loc[i]]] ;
                 q = 0 ;     /* form denominator of error term */
                 for (j=0; j<l[u]; j++)
                   if (j!=i)
                     q += index_of[1^alpha_to[(loc[j]+root[i])%nn]] ;
                 q = q % nn ;
                 err[loc[i]] = alpha_to[(err[loc[i]]-q+nn)%nn] ;
                 recd[loc[i]] ^= err[loc[i]] ;  /*recd[i] must be in polynomial form */
               }
            }
          }
         else    /* no. roots != degree of elp => >tt errors and cannot solve */
           for (i=0; i<nn; i++)        /* could return error flag if desired */
               if (recd[i]!=-1)        /* convert recd[] to polynomial form */
                 recd[i] = alpha_to[recd[i]] ;
               else  recd[i] = 0 ;     /* just output received codeword as is */
       }
     else         /* elp has degree has degree >tt hence cannot solve */
       for (i=0; i<nn; i++)       /* could return error flag if desired */
          if (recd[i]!=-1)        /* convert recd[] to polynomial form */
            recd[i] = alpha_to[recd[i]] ;
          else  recd[i] = 0 ;     /* just output received codeword as is */
    }
   else       /* no non-zero syndromes => no errors: output received codeword */
    for (i=0; i<nn; i++)
       if (recd[i]!=-1)        /* convert recd[] to polynomial form */
         recd[i] = alpha_to[recd[i]] ;
       else  recd[i] = 0 ;
 }



main()
{
  register int i;

/* generate the Galois Field GF(2**mm) */
  generate_gf() ;
  printf("Look-up tables for GF(2**%2d)\n",mm) ;
  printf("  i   alpha_to[i]  index_of[i]\n") ;
  for (i=0; i<=nn; i++)
   printf("%3d      %3d         %3d\n",i,alpha_to[i],index_of[i]) ;
  printf("\n\n") ;

/* compute the generator polynomial for this RS code */
  gen_poly() ;
  for (i=0; i<=nn-kk; i++)
    printf("%3d    %3d\n",i, gg[i]) ;

/* for known data, stick a few numbers into a zero codeword. Data is in
   polynomial form.
*/
for  (i=0; i<212; i++)   data[i] = 0 ;

/* for example, say we transmit the following message (nothing special!) */
data[0] = 8 ;
data[1] = 6 ;
data[2] = 8 ;
data[3] = 1 ;
data[4] = 2 ;
data[5] = 4 ;
data[6] = 15 ;
data[7] = 9 ;
data[8] = 9 ;

/* encode data[] to produce parity in bb[].  Data input and parity output
   is in polynomial form
*/
  encode_rs() ;

/* put the transmitted codeword, made up of data plus parity, in recd[] */
  for (i=0; i<nn-kk; i++)  recd[i] = bb[i] ;
  for (i=0; i<kk; i++) recd[i+nn-kk] = data[i] ;

/* if you want to test the program, corrupt some of the elements of recd[]
   here. This can also be done easily in a debugger. */
/* Again, lets say that a middle element is changed */
  data[nn-nn/2] = 3 ;


  for (i=0; i<nn; i++)
     recd[i] = index_of[recd[i]] ;          /* put recd[i] into index form */

/* decode recv[] */
  decode_rs() ;         /* recd[] is returned in polynomial form */

/* print out the relevant stuff - initial and decoded {parity and message} */
//  printf("Results for Reed-Solomon code (n=%3d, k=%3d, t= %3d)\n\n",nn,kk,tt) ;
//  printf("  i  data[i]   recd[i](decoded)   (data, recd in polynomial form)\n");
//  for (i=0; i<nn-kk; i++)
//    printf("%3d    %3d      %3d\n",i, bb[i], recd[i]) ;
//  for (i=nn-kk; i<nn; i++)
//    printf("%3d    %3d      %3d\n",i, data[i-nn+kk], recd[i]) ;
 
}