只需要改变mm的值以及对应nn、kk、tt，就可以适应其他GF(2^m)空间的编码了。
//rs code
//m=8
#include <math.h>
#include <stdio.h>
#include <string.h>
#define mm 8 /* RS code over GF(2**4) - change to suit */
#define nn 255 /* nn=2**mm -1 length of codeword */
#define tt 10 /* number of errors that can be corrected */
#define kk 235 /* kk = nn-2*tt */
int pp[mm+1] = {1, 0, 1, 1, 1, 0, 0, 0, 1};
int alpha_to [nn+1], index_of [nn+1], gg [nn-kk+1] ;
int recd [nn], data [kk], bb [nn-kk] ;
void generate_gf()
/* 生成GF(2^m)空间 */
{
register int i, mask ;
mask = 1 ;
alpha_to[mm] = 0 ;
for (i=0; i<mm; i++)
{
alpha_to[i] = mask ;
index_of[alpha_to[i]] = i ;
if (pp[i]!=0)
alpha_to[mm] ^= mask ;
mask <<= 1 ;
}
index_of[alpha_to[mm]] = mm ;
mask >>= 1 ;
for (i=mm+1; i<nn; i++)
{
if (alpha_to[i-1] >= mask)
alpha_to[i] = alpha_to[mm] ^ ((alpha_to[i-1]^mask)<<1) ;
else
alpha_to[i] = alpha_to[i-1]<<1 ;
index_of[alpha_to[i]] = i ;
}
index_of[0] = -1 ;
//alpha_to[nn] = 1;
for(i=0;i<mm;i++)
printf("gf%d is%d\n",i,alpha_to[i]);
}
void gen_poly()
/* 生成---生成多项式*/
{
register int i,j ;
gg[0] = 2 ; /* primitive element alpha = 2 for GF(2**mm) */
gg[1] = 1 ; /* g(x) = (X+alpha) initially */
for (i=2; i<=nn-kk; i++)
{
gg[i] = 1 ;
for (j=i-1; j>0; j--)
if (gg[j] != 0)
gg[j] = gg[j-1]^ alpha_to[(index_of[gg[j]]+i)%nn];
else
gg[j] = gg[j-1] ;
gg[0] = alpha_to[(index_of[gg[0]]+i)%nn] ; /* gg[0] can never be zero */
}
//printf("polynomial:\n");
//for(i=0; i<=nn-kk; i++)
// printf("%d ", gg[i]);
//printf("\n");
/* convert gg[] to index form for quicker encoding */
for (i=0; i<=nn-kk; i++)
gg[i] = index_of[gg[i]];
//printf("polynomial:\n");
//for(i=0; i<=nn-kk; i++)
// printf("%d ", gg[i]);
//printf("\n");
}
void encode_rs()
/* 编码*/
{
register int i,j ;
int feedback ;
for (i=0; i<nn-kk; i++) bb[i] = 0 ;
for (i=kk-1; i>=0; i--)
{
//逐步的将下一步要减的，存入bb(i)
feedback = index_of[data[i]^bb[nn-kk-1]] ;
if(feedback != -1)
{
for (j=nn-kk-1; j>0; j--)
if (gg[j] != -1)
bb[j] = bb[j-1]^alpha_to[(gg[j]+feedback)%nn] ; //plus = ^
else
bb[j] = bb[j-1] ;
bb[0] = alpha_to[(gg[0]+feedback)%nn] ;
}
else
{
for (j=nn-kk-1; j>0; j--)
bb[j] = bb[j-1] ;
bb[0] = 0 ;
};
};
}
void decode_rs()
{/*解码*/
register int i,j,u,q ;
int elp[nn-kk+2][nn-kk], d[nn-kk+2], l[nn-kk+2], u_lu[nn-kk+2], s[nn-kk+1] ;
int count=0, syn_error=0, root[tt], loc[tt], z[tt+1], err[nn], reg[tt+1] ;
/* first form the syndromes */
for(i=0; i<nn; i++) //转换成GF空间的alpha幂次
if(recd[i] == -1)
recd[i] = 0;
else
recd[i] = index_of[recd[i]];
for (i=1; i<=nn-kk; i++)
{
s[i] = 0 ;
for (j=0; j<nn; j++)
if (recd[j]!=-1)
s[i] ^= alpha_to[(recd[j]+i*j)%nn] ; /* recd[j] in index form */
/* convert syndrome from polynomial form to index form */
if (s[i]!=0)
syn_error=1 ; /* set flag if non-zero syndrome => error */
printf("%3d", s[i]);
s[i] = index_of[s[i]] ;
printf("%3d", s[i]);
} ;
if (syn_error) /* if errors, try and correct */
{printf("*\n");
/* compute the error location polynomial via the Berlekamp iterative algorithm,
following the terminology of Lin and Costello : d[u] is the 'mu'th
discrepancy, where u='mu'+1 and 'mu' (the Greek letter!) is the step number
ranging from -1 to 2*tt (see L&C), l[u] is the
degree of the elp at that step, and u_l[u] is the difference between the
step number and the degree of the elp.*/
/* initialise table entries */
d[0] = 0 ; /* index form */
d[1] = s[1] ; /* index form */
elp[0][0] = 0 ; /* index form */
elp[1][0] = 1 ; /* polynomial form */
for (i=1; i<nn-kk; i++)
{
elp[0][i] = -1 ; /* index form */
elp[1][i] = 0 ; /* polynomial form */
}
l[0] = 0 ;
l[1] = 0 ;
u_lu[0] = -1 ;
u_lu[1] = 0 ;
u = 0 ;
do
{
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 */
/*求错误位置多项式的根*/
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++ ;
printf("根%d=%d\n", q, nn-i);
};
} ;
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] */
/*计算错误图样*/
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 */
{ /*错误太多，无法更正*/
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 */
{ /*错误太多，无法更正*/
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 ;
//printf("*");
}
}
int main()
{
int i, length;
char strSrc[255], strDst[255];
printf("请输入要编码的字符串：\n");
scanf("%s", strSrc);
length = strlen(strSrc);
if(length <= 0)
return 0;
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");
gen_poly();
for(i=0; i<kk; i++)
data[i] = 0;
/* for example, say we transmit the following message (nothing special!) */
for(i=0; i<length; i++)
data[i] = strSrc[i];
/* 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] = 55 ;*/
encode_rs();
data[0] = 19 ;
for (i=0; i<nn-kk; i++)
recd[i] = bb[i] ;
for (i=0; i<kk; i++)
recd[i+nn-kk] = data[i] ;
/* 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]) ;*/
decode_rs() ;
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]) ;
}
for(i=0; i<length; i++)
strDst[i] = recd[i+nn-kk];
strDst[length] = '\0';
printf("%s\n", strDst);
}
