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/*C
(c) 2005 bl0rg.net
**/
#include <stdlib.h>
#include <assert.h>
#include <string.h>
#include "fec.h"
#include "matrix.h"
#ifdef DEBUG
#include <stdio.h>
#endif
/*M
\emph{Free a FEC parameter structure.}
**/
void fec_free(fec_t *fec) {
assert(fec != NULL);
assert(fec->gen_matrix != NULL);
free(fec->gen_matrix);
free(fec);
}
/*M
\emph{Initialize a FEC parameter structure.}
Create a generator matrix.
% XXX Documentation for generator matrix
**/
fec_t *fec_new(unsigned int k, unsigned int n) {
assert((k <= n ) || "k is too big");
assert((k <= 256) || "k is too big");
assert((n <= 256) || "n is too big");
/*M
Init Galois arithmetic if not already initialized.
**/
static int gf_initialized = 0;
if (!gf_initialized) {
gf_init();
gf_initialized = 1;
}
fec_t *res;
res = malloc(sizeof(fec_t));
assert(res != NULL);
res->gen_matrix = malloc(sizeof(gf)*k*n);
assert(res->gen_matrix != NULL);
res->k = k;
res->n = n;
/*M
Fill the matrix with powers of field elements.
**/
gf tmp[k*n];
/* gf *tmp = res->gen_matrix; */
/*M
First row is special (powers of $0$).
**/
tmp[0] = 1;
unsigned int col;
for (col = 1; col < k; col++)
tmp[col] = 0;
gf *p;
unsigned int row;
for (p = tmp + k, row = 0; row < n - 1; row++, p += k) {
for (col = 0; col < k; col++)
p[col] = gf_polys[(row * col) % 255];
}
#ifdef DEBUG
fprintf(stderr, "first vandermonde matrix\n");
matrix_print(tmp, res->n, res->k);
#endif
/*M
Invert the upper $k \times k$ vandermonde matrix.
**/
matrix_inv_vandermonde(tmp, k);
#ifdef DEBUG
fprintf(stderr, "\ninverted vandermonde matrix\n");
matrix_print(tmp, res->n, res->k);
#endif
/*M
Multiply the inverted upper $k \times k$ vandermonde matrix with
the lower band of the matrix.
**/
matrix_mul(tmp + k * k, tmp, res->gen_matrix + k * k, n - k, k, k);
/*M
Fill the upper $k \times k$ matrix with the identity matrix to
generate a systematic matrix.
**/
for (row = 0; row < k; row++)
for (col = 0; col < k; col++)
if (col == row)
res->gen_matrix[row * k + col] = 1;
else
res->gen_matrix[row * k + col] = 0;
#ifdef DEBUG
fprintf(stderr, "\ngenerated matrix\n");
matrix_print(res->gen_matrix, res->n, res->k);
#endif
return res;
}
/*M
\emph{Produce encoded output packet.}
Encodes the \verb|idx|'th output data packet from the \verb|k| data
packets in \verb|src| and the generator matrix in \verb|fec|. For
\verb|idx| $<$ \verb|k|, we just copy the data (systematic matrix).
**/
void fec_encode(fec_t *fec,
gf *src[], gf *dst,
unsigned int idx, unsigned int len) {
assert((idx < fec->n) || "Index of output packet to high");
if (idx < fec->k) {
memcpy(dst, src[idx], len * sizeof(gf));
} else {
gf *p = fec->gen_matrix + idx * fec->k;
bzero(dst, len * sizeof(gf));
unsigned int i;
for (i = 0; i < fec->k; i++)
gf_add_mul(dst, src[i], p[i], len);
}
}
/*M
\emph{Builds the decoding matrix.}
Builds the decoding matrix into \verb|matrix| out of the indexes
stored in \verb|idxs|.
Returns 0 on error, 1 on success.
**/
int fec_decode_matrix(fec_t *fec,
gf *matrix,
unsigned int idxs[]) {
gf *p;
unsigned int i;
for (p = matrix, i = 0; i < fec->k; i++, p += fec->k) {
assert((idxs[i] < fec->n) || "index of packet to high for FEC");
memcpy(p, fec->gen_matrix + idxs[i] * fec->k, fec->k * sizeof(gf));
}
#ifdef DEBUG
matrix_print(matrix, fec->k, fec->k);
#endif
if (!matrix_inv(matrix, fec->k))
return 0;
return 1;
}
/*M
\emph{Put straight packets at the right place.}
Packets with index $<$ k are put at the right place.
**/
static int fec_shuffle(fec_t *fec, unsigned int idxs[]) {
unsigned int i;
for (i = 0; i < fec->k; ) {
if ((idxs[i] >= fec->k) ||
(idxs[i] == i)) {
i++;
} else {
unsigned int c = idxs[i];
/* check for conflicts */
if (idxs[c] == c)
return 0;
idxs[i] = idxs[c];
idxs[c] = c;
}
}
return 1;
}
/*M
\emph{Decode the received packets.}
% XXXX
**/
int fec_decode(fec_t *fec,
gf *pkts,
unsigned int idxs[], unsigned len) {
assert(fec != NULL);
if (!fec_shuffle(fec, idxs))
return 0;
/*M
Build decoding matrix.
**/
gf dec_matrix[fec->k * fec->k];
if (!fec_decode_matrix(fec, dec_matrix, idxs))
return 0;
unsigned int row;
for (row = 0; row < fec->k; row++) {
if (idxs[row] >= fec->k) {
gf *pkt = pkts + row * len;
bzero(pkt, len * sizeof(gf));
unsigned int col;
for (col = 0; col < fec->k; col++) {
gf_add_mul(pkt, pkts + idxs[col] * len,
dec_matrix[row * fec->k + col], len);
}
}
}
return 1;
}
/*C
**/
#ifdef FEC_TEST
#include <stdio.h>
void testit(char *name, unsigned int result, unsigned int should) {
if (result == should) {
printf("Test %s was successful\n", name);
} else {
printf("Test %s was not successful, %u should have been %u\n",
name, result, should);
}
}
int main(void) {
fec_t *fec;
gf_init();
fec = fec_new(4, 8);
printf("\n");
gf src_pkts[4][4] =
{ {1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16} };
gf dst_pkts[8 * 4];
gf *src_ptrs[4] = { src_pkts[0], src_pkts[1], src_pkts[2], src_pkts[3] };
unsigned int idxs[4] = {3, 5, 1, 0}; /* from 0 ?? */
int i;
for (i = 0; i < 8; i++) {
fec_encode(fec, src_ptrs, dst_pkts + i * 4, i, 4);
int j;
for (j = 0; j < 4; j++)
printf("%u ", dst_pkts[i * 4 + j]);
printf("\n");
}
memset(dst_pkts + 2 * 4, 0, 4);
memset(dst_pkts + 4 * 4, 0, 4);
memset(dst_pkts + 6 * 4, 0, 4);
memset(dst_pkts + 7 * 4, 0, 4);
testit("fec decode", fec_decode(fec, dst_pkts, idxs, 4), 1);
for (i = 0; i < 4; i++) {
int j;
for (j = 0; j < 4; j++)
testit("fec decode", dst_pkts[i * 4 + j], src_pkts[i][j]);
}
fec_free(fec);
return 0;
}
#endif /* FEC_TEST */
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