Algorithm-FEC
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*
* THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR
* TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT
* OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
* OF SUCH DAMAGE.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <stdint.h>
#define MSDOS /* LEAVE THIS IN PLACE EVEN ON UNIX! */
/*
* compatibility stuff
*/
#ifdef MSDOS /* but also for others, e.g. sun... */
#define NEED_BCOPY
#define bcmp(a,b,n) memcmp(a,b,n)
#endif
#ifdef NEED_BCOPY
#define bcopy(s, d, siz) memcpy((d), (s), (siz))
#define bzero(d, siz) memset((d), '\0', (siz))
#endif
/*
* stuff used for testing purposes only
*/
#ifdef TEST
#define DEB(x)
#define DDB(x) x
#define DEBUG 0 /* minimal debugging */
#ifdef MSDOS
#include <time.h>
struct timeval {
unsigned long ticks;
};
#define gettimeofday(x, dummy) { (x)->ticks = clock() ; }
#define DIFF_T(a,b) (1+ 1000000*(a.ticks - b.ticks) / CLOCKS_PER_SEC )
typedef unsigned long u_long ;
typedef unsigned short u_short ;
#else /* typically, unix systems */
#include <sys/time.h>
#define DIFF_T(a,b) \
(1+ 1000000*(a.tv_sec - b.tv_sec) + (a.tv_usec - b.tv_usec) )
#endif
#define TICK(t) \
{struct timeval x ; \
gettimeofday(&x, NULL) ; \
t = x.tv_usec + 1000000* (x.tv_sec & 0xff ) ; \
}
#define TOCK(t) \
{ u_long t1 ; TICK(t1) ; \
if (t1 < t) t = 256000000 + t1 - t ; \
else t = t1 - t ; \
if (t == 0) t = 1 ;}
u_long ticks[10]; /* vars for timekeeping */
#else
#define DEB(x)
#define DDB(x)
#define TICK(x)
#define TOCK(x)
#endif /* TEST */
/*
* You should not need to change anything beyond this point.
* The first part of the file implements linear algebra in GF.
*
* gf is the type used to store an element of the Galois Field.
* Must constain at least GF_BITS bits.
*
* Note: unsigned char will work up to GF(256) but int seems to run
* faster on the Pentium. We use int whenever have to deal with an
* index, since they are generally faster.
*/
#if (GF_BITS < 2 && GF_BITS >16)
#error "GF_BITS must be 2 .. 16"
#endif
#if (GF_BITS <= 8)
typedef uint8_t gf;
#else
typedef uint16_t gf;
#endif
#define GF_SIZE ((1 << GF_BITS) - 1) /* powers of \alpha */
/*
* Primitive polynomials - see Lin & Costello, Appendix A,
* and Lee & Messerschmitt, p. 453.
*/
static char *allPp[] = { /* GF_BITS polynomial */
NULL, /* 0 no code */
NULL, /* 1 no code */
"111", /* 2 1+x+x^2 */
"1101", /* 3 1+x+x^3 */
"11001", /* 4 1+x+x^4 */
"101001", /* 5 1+x^2+x^5 */
"1100001", /* 6 1+x+x^6 */
"10010001", /* 7 1 + x^3 + x^7 */
"101110001", /* 8 1+x^2+x^3+x^4+x^8 */
"1000100001", /* 9 1+x^4+x^9 */
"10010000001", /* 10 1+x^3+x^10 */
"101000000001", /* 11 1+x^2+x^11 */
"1100101000001", /* 12 1+x+x^4+x^6+x^12 */
"11011000000001", /* 13 1+x+x^3+x^4+x^13 */
"110000100010001", /* 14 1+x+x^6+x^10+x^14 */
"1100000000000001", /* 15 1+x+x^15 */
"11010000000010001" /* 16 1+x+x^3+x^12+x^16 */
};
if (c == 0) {
fprintf(stderr, "singular matrix 2\n");
goto fail ;
}
if (c != 1 ) { /* otherwhise this is a NOP */
/*
* this is done often , but optimizing is not so
* fruitful, at least in the obvious ways (unrolling)
*/
DEB( pivswaps++ ; )
c = inverse[ c ] ;
pivot_row[icol] = 1 ;
for (ix = 0 ; ix < k ; ix++ )
pivot_row[ix] = gf_mul(c, pivot_row[ix] );
}
/*
* from all rows, remove multiples of the selected row
* to zero the relevant entry (in fact, the entry is not zero
* because we know it must be zero).
* (Here, if we know that the pivot_row is the identity,
* we can optimize the addmul).
*/
id_row[icol] = 1;
if (bcmp(pivot_row, id_row, k*sizeof(gf)) != 0) {
for (p = src, ix = 0 ; ix < k ; ix++, p += k ) {
if (ix != icol) {
c = p[icol] ;
p[icol] = 0 ;
addmul(p, pivot_row, c, k );
}
}
}
id_row[icol] = 0;
} /* done all columns */
for (col = k-1 ; col >= 0 ; col-- ) {
if (indxr[col] <0 || indxr[col] >= k)
fprintf(stderr, "AARGH, indxr[col] %d\n", indxr[col]);
else if (indxc[col] <0 || indxc[col] >= k)
fprintf(stderr, "AARGH, indxc[col] %d\n", indxc[col]);
else
if (indxr[col] != indxc[col] ) {
for (row = 0 ; row < k ; row++ ) {
SWAP( src[row*k + indxr[col]], src[row*k + indxc[col]], gf) ;
}
}
}
error = 0 ;
fail:
free(indxc);
free(indxr);
free(ipiv);
free(id_row);
free(temp_row);
return error ;
}
/*
* fast code for inverting a vandermonde matrix.
* XXX NOTE: It assumes that the matrix
* is not singular and _IS_ a vandermonde matrix. Only uses
* the second column of the matrix, containing the p_i's.
*
* Algorithm borrowed from "Numerical recipes in C" -- sec.2.8, but
* largely revised for my purposes.
* p = coefficients of the matrix (p_i)
* q = values of the polynomial (known)
*/
static int
invert_vdm(gf *src, int k)
{
int i, j, row, col ;
gf *b, *c, *p;
gf t, xx ;
if (k == 1) /* degenerate case, matrix must be p^0 = 1 */
return 0 ;
/*
* c holds the coefficient of P(x) = Prod (x - p_i), i=0..k-1
* b holds the coefficient for the matrix inversion
*/
c = NEW_GF_MATRIX(1, k);
b = NEW_GF_MATRIX(1, k);
p = NEW_GF_MATRIX(1, k);
for ( j=1, i = 0 ; i < k ; i++, j+=k ) {
c[i] = 0 ;
p[i] = src[j] ; /* p[i] */
}
/*
* construct coeffs. recursively. We know c[k] = 1 (implicit)
* and start P_0 = x - p_0, then at each stage multiply by
* x - p_i generating P_i = x P_{i-1} - p_i P_{i-1}
* After k steps we are done.
*/
c[k-1] = p[0] ; /* really -p(0), but x = -x in GF(2^m) */
for (i = 1 ; i < k ; i++ ) {
gf p_i = p[i] ; /* see above comment */
for (j = k-1 - ( i - 1 ) ; j < k-1 ; j++ )
c[j] ^= gf_mul( p_i, c[j+1] ) ;
c[k-1] ^= p_i ;
}
for (row = 0 ; row < k ; row++ ) {
/*
* synthetic division etc.
*/
xx = p[row] ;
t = 1 ;
b[k-1] = 1 ; /* this is in fact c[k] */
for (i = k-2 ; i >= 0 ; i-- ) {
b[i] = c[i+1] ^ gf_mul(xx, b[i+1]) ;
t = gf_mul(xx, t) ^ b[i] ;
}
for (col = 0 ; col < k ; col++ )
src[col*k + row] = gf_mul(inverse[t], b[col] );
}
free(c) ;
free(b) ;
free(p) ;
return 0 ;
}
static int fec_initialized = 0 ;
static void init_fec()
{
TICK(ticks[0]);
generate_gf();
TOCK(ticks[0]);
DDB(fprintf(stderr, "generate_gf took %ldus\n", ticks[0]);)
TICK(ticks[0]);
init_mul_table();
TOCK(ticks[0]);
DDB(fprintf(stderr, "init_mul_table took %ldus\n", ticks[0]);)
fec_initialized = 1 ;
}
/*
* This section contains the proper FEC encoding/decoding routines.
* The encoding matrix is computed starting with a Vandermonde matrix,
* and then transforming it into a systematic matrix.
*/
struct fec_parms {
int k, n ; /* parameters of the code */
gf *enc_matrix ;
} ;
void
fec_free(struct fec_parms *p)
{
if (p==NULL) {
fprintf(stderr, "bad parameters to fec_free\n");
return ;
}
free(p->enc_matrix);
free(p);
}
/*
* create a new encoder, returning a descriptor. This contains k,n and
* the encoding matrix.
*/
struct fec_parms *
fec_new(int k, int n)
{
int row, col ;
gf *p, *tmp_m ;
struct fec_parms *retval ;
if (fec_initialized == 0)
init_fec();
if (k > GF_SIZE + 1 || n > GF_SIZE + 1 || k > n ) {
fprintf(stderr, "Invalid parameters k %d n %d GF_SIZE %d\n",
k, n, GF_SIZE );
return NULL ;
}
retval = my_malloc(sizeof(struct fec_parms), "new_code");
retval->k = k ;
retval->n = n ;
retval->enc_matrix = NEW_GF_MATRIX(n, k);
tmp_m = NEW_GF_MATRIX(n, k);
/*
* fill the matrix with powers of field elements, starting from 0.
* The first row is special, cannot be computed with exp. table.
*/
tmp_m[0] = 1 ;
for (col = 1; col < k ; col++)
tmp_m[col] = 0 ;
for (p = tmp_m + k, row = 0; row < n-1 ; row++, p += k) {
for ( col = 0 ; col < k ; col ++ )
p[col] = gf_exp[modnn(row*col)];
}
/*
* quick code to build systematic matrix: invert the top
* k*k vandermonde matrix, multiply right the bottom n-k rows
( run in 0.644 second using v1.01-cache-2.11-cpan-39bf76dae61 )