/* * fec.c -- forward error correction based on Vandermonde matrices * 980624 * (C) 1997-98 Luigi Rizzo (luigi@iet.unipi.it) * * Portions derived from code by Phil Karn (karn@ka9q.ampr.org), * Robert Morelos-Zaragoza (robert@spectra.eng.hawaii.edu) and Hari * Thirumoorthy (harit@spectra.eng.hawaii.edu), Aug 1995 * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above * copyright notice, this list of conditions and the following * disclaimer in the documentation and/or other materials * provided with the distribution. * * THIS SOFTWARE IS PROVIDED BY THE AUTHORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, * THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A * PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHORS * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, * OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, * OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY * 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. */ /* * The following parameter defines how many bits are used for * field elements. The code supports any value from 2 to 16 * but fastest operation is achieved with 8 bit elements * This is the only parameter you may want to change. */ #ifndef GF_BITS #define GF_BITS 8 /* code over GF(2**GF_BITS) - change to suit */ #endif #include <stdio.h> #include <stdlib.h> #include <string.h> /* * 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 ) #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) \ { unsigned long t1 ; TICK(t1) ; \ if (t1 < t) t = 256000000 + t1 - t ; \ else t = t1 - t ; \ if (t == 0) t = 1 ;} unsigned 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 unsigned char gf; #else typedef unsigned short 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 const 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 */ }; /* * To speed up computations, we have tables for logarithm, exponent * and inverse of a number. If GF_BITS <= 8, we use a table for * multiplication as well (it takes 64K, no big deal even on a PDA, * especially because it can be pre-initialized an put into a ROM!), * otherwhise we use a table of logarithms. * In any case the macro gf_mul(x,y) takes care of multiplications. */ static gf gf_exp[2*GF_SIZE]; /* index->poly form conversion table */ static int gf_log[GF_SIZE + 1]; /* Poly->index form conversion table */ static gf inverse[GF_SIZE+1]; /* inverse of field elem. */ /* inv[\alpha**i]=\alpha**(GF_SIZE-i-1) */ /* * modnn(x) computes x % GF_SIZE, where GF_SIZE is 2**GF_BITS - 1, * without a slow divide. */ static inline gf modnn(int x) { while (x >= GF_SIZE) { x -= GF_SIZE; x = (x >> GF_BITS) + (x & GF_SIZE); } return x; } #define SWAP(a,b,t) {t tmp; tmp=a; a=b; b=tmp;} /* * gf_mul(x,y) multiplies two numbers. If GF_BITS<=8, it is much * faster to use a multiplication table. * * USE_GF_MULC, GF_MULC0(c) and GF_ADDMULC(x) can be used when multiplying * many numbers by the same constant. In this case the first * call sets the constant, and others perform the multiplications. * A value related to the multiplication is held in a local variable * declared with USE_GF_MULC . See usage in addmul1(). */ #if (GF_BITS <= 8) static gf gf_mul_table[GF_SIZE + 1][GF_SIZE + 1]; #define gf_mul(x,y) gf_mul_table[x][y] #define USE_GF_MULC register gf * __gf_mulc_ #define GF_MULC0(c) __gf_mulc_ = gf_mul_table[c] #define GF_ADDMULC(dst, x) dst ^= __gf_mulc_[x] static void init_mul_table(void) { int i, j; for (i=0; i< GF_SIZE+1; i++) for (j=0; j< GF_SIZE+1; j++) gf_mul_table[i][j] = gf_exp[modnn(gf_log[i] + gf_log[j]) ] ; for (j=0; j< GF_SIZE+1; j++) gf_mul_table[0][j] = gf_mul_table[j][0] = 0; } #else /* GF_BITS > 8 */ static inline gf gf_mul(x,y) { if ( (x) == 0 || (y)==0 ) return 0; return gf_exp[gf_log[x] + gf_log[y] ] ; } #define init_mul_table() #define USE_GF_MULC register gf * __gf_mulc_ #define GF_MULC0(c) __gf_mulc_ = &gf_exp[ gf_log[c] ] #define GF_ADDMULC(dst, x) { if (x) dst ^= __gf_mulc_[ gf_log[x] ] ; } #endif /* * Generate GF(2**m) from the irreducible polynomial p(X) in p[0]..p[m] * Lookup tables: * index->polynomial form gf_exp[] contains j= \alpha^i; * polynomial form -> index form gf_log[ j = \alpha^i ] = i * \alpha=x is the primitive element of GF(2^m) * * For efficiency, gf_exp[] has size 2*GF_SIZE, so that a simple * multiplication of two numbers can be resolved without calling modnn */ /* * i use malloc so many times, it is easier to put checks all in * one place. */ static void * my_malloc(int sz, const char *err_string) { void *p = malloc( sz ); if (p == NULL) { fprintf(stderr, "-- malloc failure allocating %s\n", err_string); exit(1) ; } return p ; } #define NEW_GF_MATRIX(rows, cols) \ (gf *)my_malloc(rows * cols * sizeof(gf), " ## __LINE__ ## " ) /* * initialize the data structures used for computations in GF. */ static void generate_gf(void) { int i; gf mask; const char *Pp = allPp[GF_BITS] ; mask = 1; /* x ** 0 = 1 */ gf_exp[GF_BITS] = 0; /* will be updated at the end of the 1st loop */ /* * first, generate the (polynomial representation of) powers of \alpha, * which are stored in gf_exp[i] = \alpha ** i . * At the same time build gf_log[gf_exp[i]] = i . * The first GF_BITS powers are simply bits shifted to the left. */ for (i = 0; i < GF_BITS; i++, mask <<= 1 ) { gf_exp[i] = mask; gf_log[gf_exp[i]] = i; /* * If Pp[i] == 1 then \alpha ** i occurs in poly-repr * gf_exp[GF_BITS] = \alpha ** GF_BITS */ if ( Pp[i] == '1' ) gf_exp[GF_BITS] ^= mask; } /* * now gf_exp[GF_BITS] = \alpha ** GF_BITS is complete, so can als * compute its inverse. */ gf_log[gf_exp[GF_BITS]] = GF_BITS; /* * Poly-repr of \alpha ** (i+1) is given by poly-repr of * \alpha ** i shifted left one-bit and accounting for any * \alpha ** GF_BITS term that may occur when poly-repr of * \alpha ** i is shifted. */ mask = 1 << (GF_BITS - 1 ) ; for (i = GF_BITS + 1; i < GF_SIZE; i++) { if (gf_exp[i - 1] >= mask) gf_exp[i] = gf_exp[GF_BITS] ^ ((gf_exp[i - 1] ^ mask) << 1); else gf_exp[i] = gf_exp[i - 1] << 1; gf_log[gf_exp[i]] = i; } /* * log(0) is not defined, so use a special value */ gf_log[0] = GF_SIZE ; /* set the extended gf_exp values for fast multiply */ for (i = 0 ; i < GF_SIZE ; i++) gf_exp[i + GF_SIZE] = gf_exp[i] ; /* * again special cases. 0 has no inverse. This used to * be initialized to GF_SIZE, but it should make no difference * since noone is supposed to read from here. */ inverse[0] = 0 ; inverse[1] = 1; for (i=2; i<=GF_SIZE; i++) inverse[i] = gf_exp[GF_SIZE-gf_log[i]]; } /* * Various linear algebra operations that i use often. */ /* * addmul() computes dst[] = dst[] + c * src[] * This is used often, so better optimize it! Currently the loop is * unrolled 16 times, a good value for 486 and pentium-class machines. * The case c=0 is also optimized, whereas c=1 is not. These * calls are unfrequent in my typical apps so I did not bother. * * Note that gcc on */ #define addmul(dst, src, c, sz) \ if (c != 0) addmul1(dst, src, c, sz) #define UNROLL 16 /* 1, 4, 8, 16 */ static void addmul1(gf *dst1, gf *src1, gf c, int sz) { USE_GF_MULC ; register gf *dst = dst1, *src = src1 ; gf *lim = &dst[sz - UNROLL + 1] ; GF_MULC0(c) ; #if (UNROLL > 1) /* unrolling by 8/16 is quite effective on the pentium */ for (; dst < lim ; dst += UNROLL, src += UNROLL ) { GF_ADDMULC( dst[0] , src[0] ); GF_ADDMULC( dst[1] , src[1] ); GF_ADDMULC( dst[2] , src[2] ); GF_ADDMULC( dst[3] , src[3] ); #if (UNROLL > 4) GF_ADDMULC( dst[4] , src[4] ); GF_ADDMULC( dst[5] , src[5] ); GF_ADDMULC( dst[6] , src[6] ); GF_ADDMULC( dst[7] , src[7] ); #endif #if (UNROLL > 8) GF_ADDMULC( dst[8] , src[8] ); GF_ADDMULC( dst[9] , src[9] ); GF_ADDMULC( dst[10] , src[10] ); GF_ADDMULC( dst[11] , src[11] ); GF_ADDMULC( dst[12] , src[12] ); GF_ADDMULC( dst[13] , src[13] ); GF_ADDMULC( dst[14] , src[14] ); GF_ADDMULC( dst[15] , src[15] ); #endif } #endif lim += UNROLL - 1 ; for (; dst < lim; dst++, src++ ) /* final components */ GF_ADDMULC( *dst , *src ); } /* * computes C = AB where A is n*k, B is k*m, C is n*m */ static void matmul(gf *a, gf *b, gf *c, int n, int k, int m) { int row, col, i ; for (row = 0; row < n ; row++) { for (col = 0; col < m ; col++) { gf *pa = &a[ row * k ]; gf *pb = &b[ col ]; gf acc = 0 ; for (i = 0; i < k ; i++, pa++, pb += m ) acc ^= gf_mul( *pa, *pb ) ; c[ row * m + col ] = acc ; } } } #ifdef DEBUG /* * returns 1 if the square matrix is identiy * (only for test) */ static int is_identity(gf *m, int k) { int row, col ; for (row=0; row<k; row++) for (col=0; col<k; col++) if ( (row==col && *m != 1) || (row!=col && *m != 0) ) return 0 ; else m++ ; return 1 ; } #endif /* debug */ /* * invert_mat() takes a matrix and produces its inverse * k is the size of the matrix. * (Gauss-Jordan, adapted from Numerical Recipes in C) * Return non-zero if singular. */ DEB( int pivloops=0; int pivswaps=0 ; /* diagnostic */) static int invert_mat(gf *src, int k) { gf c, *p ; int irow, icol, row, col, i, ix ; int error = 1 ; int *indxc = my_malloc(k*sizeof(int), "indxc"); int *indxr = my_malloc(k*sizeof(int), "indxr"); int *ipiv = my_malloc(k*sizeof(int), "ipiv"); gf *id_row = NEW_GF_MATRIX(1, k); gf *temp_row = NEW_GF_MATRIX(1, k); memset(id_row, '\0', k*sizeof(gf)); DEB( pivloops=0; pivswaps=0 ; /* diagnostic */ ) /* * ipiv marks elements already used as pivots. */ for (i = 0; i < k ; i++) ipiv[i] = 0 ; for (col = 0; col < k ; col++) { gf *pivot_row ; /* * Zeroing column 'col', look for a non-zero element. * First try on the diagonal, if it fails, look elsewhere. */ irow = icol = -1 ; if (ipiv[col] != 1 && src[col*k + col] != 0) { irow = col ; icol = col ; goto found_piv ; } for (row = 0 ; row < k ; row++) { if (ipiv[row] != 1) { for (ix = 0 ; ix < k ; ix++) { DEB( pivloops++ ; ) if (ipiv[ix] == 0) { if (src[row*k + ix] != 0) { irow = row ; icol = ix ; goto found_piv ; } } else if (ipiv[ix] > 1) { fprintf(stderr, "singular matrix\n"); goto fail ; } } } } if (icol == -1) { fprintf(stderr, "XXX pivot not found!\n"); goto fail ; } found_piv: ++(ipiv[icol]) ; /* * swap rows irow and icol, so afterwards the diagonal * element will be correct. Rarely done, not worth * optimizing. */ if (irow != icol) { for (ix = 0 ; ix < k ; ix++ ) { SWAP( src[irow*k + ix], src[icol*k + ix], gf) ; } } indxr[col] = irow ; indxc[col] = icol ; pivot_row = &src[icol*k] ; c = pivot_row[icol] ; 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 (memcmp(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) */ 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(void) { 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. */ #define FEC_MAGIC 0xFECC0DEC struct fec_parms { unsigned long magic ; int k, n ; /* parameters of the code */ gf *enc_matrix ; } ; #define COMP_FEC_MAGIC(fec) \ (((FEC_MAGIC ^ (fec)->k) ^ (fec)->n) ^ (unsigned long)((fec)->enc_matrix)) void fec_free(struct fec_parms *p) { if (p==NULL || p->magic != COMP_FEC_MAGIC(p)) { 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); retval->magic = COMP_FEC_MAGIC(retval); 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 * by the inverse, and construct the identity matrix at the top. */ TICK(ticks[3]); invert_vdm(tmp_m, k); /* much faster than invert_mat */ matmul(tmp_m + k*k, tmp_m, retval->enc_matrix + k*k, n - k, k, k); /* * the upper matrix is I so do not bother with a slow multiply */ memset(retval->enc_matrix, '\0', k*k*sizeof(gf) ); for (p = retval->enc_matrix, col = 0 ; col < k ; col++, p += k+1 ) *p = 1 ; free(tmp_m); TOCK(ticks[3]); DDB(fprintf(stderr, "--- %ld us to build encoding matrix\n", ticks[3]);) DEB(pr_matrix(retval->enc_matrix, n, k, "encoding_matrix");) return retval ; } /* * fec_encode accepts as input pointers to n data packets of size sz, * and produces as output a packet pointed to by fec, computed * with index "index". */ void fec_encode(struct fec_parms *code, gf *src[], gf *fec, int index, int sz) { int i, k = code->k ; gf *p ; if (GF_BITS > 8) sz /= 2 ; if (index < k) memcpy(fec, src[index], sz*sizeof(gf) ) ; else if (index < code->n) { p = &(code->enc_matrix[index*k] ); memset(fec, '\0', sz*sizeof(gf)); for (i = 0; i < k ; i++) addmul(fec, src[i], p[i], sz ) ; } else fprintf(stderr, "Invalid index %d (max %d)\n", index, code->n - 1 ); } void fec_encode_linear(struct fec_parms *code, gf *src, gf *fec, int index, int sz) { int i, k = code->k ; gf *p ; if (GF_BITS > 8) sz /= 2 ; if (index < k) memcpy(fec, src + (index * sz), sz*sizeof(gf) ) ; else if (index < code->n) { p = &(code->enc_matrix[index*k] ); memset(fec, '\0', sz*sizeof(gf)); for (i = 0; i < k ; i++) addmul(fec, src + (i * sz), p[i], sz ) ; } else fprintf(stderr, "Invalid index %d (max %d)\n", index, code->n - 1 ); } /* * shuffle move src packets in their position */ static int shuffle(gf *pkt[], int index[], int k) { int i; for ( i = 0 ; i < k ; ) { if (index[i] >= k || index[i] == i) i++ ; else { /* * put pkt in the right position (first check for conflicts). */ int c = index[i] ; if (index[c] == c) { DEB(fprintf(stderr, "\nshuffle, error at %d\n", i);) return 1 ; } SWAP(index[i], index[c], int) ; SWAP(pkt[i], pkt[c], gf *) ; } } DEB( /* just test that it works... */ for ( i = 0 ; i < k ; i++ ) { if (index[i] < k && index[i] != i) { fprintf(stderr, "shuffle: after\n"); for (i=0; i<k ; i++) fprintf(stderr, "%3d ", index[i]); fprintf(stderr, "\n"); return 1 ; } } ) return 0 ; } /* * build_decode_matrix constructs the encoding matrix given the * indexes. The matrix must be already allocated as * a vector of k*k elements, in row-major order */ static gf * build_decode_matrix(struct fec_parms *code, int index[]) { int i , k = code->k ; gf *p, *matrix = NEW_GF_MATRIX(k, k); TICK(ticks[9]); for (i = 0, p = matrix ; i < k ; i++, p += k ) { #if 1 /* this is simply an optimization, not very useful indeed */ if (index[i] < k) { memset(p, '\0', k*sizeof(gf) ); p[i] = 1 ; } else #endif if (index[i] < code->n ) memcpy(p, &(code->enc_matrix[index[i]*k]), k*sizeof(gf) ); else { fprintf(stderr, "decode: invalid index %d (max %d)\n", index[i], code->n - 1 ); free(matrix) ; return NULL ; } } TICK(ticks[9]); if (invert_mat(matrix, k)) { free(matrix); matrix = NULL ; } TOCK(ticks[9]); return matrix ; } /* * fec_decode receives as input a vector of packets, the indexes of * packets, and produces the correct vector as output. * * Input: * code: pointer to code descriptor * pkt: pointers to received packets. They are modified * to store the output packets (in place) * index: pointer to packet indexes (modified) * sz: size of each packet */ int fec_decode(struct fec_parms *code, gf *pkt[], int index[], int sz) { gf *m_dec ; gf **new_pkt ; int row, col , k = code->k ; if (GF_BITS > 8) sz /= 2 ; if (shuffle(pkt, index, k)) /* error if true */ return 1 ; m_dec = build_decode_matrix(code, index); if (m_dec == NULL) return 1 ; /* error */ /* * do the actual decoding */ new_pkt = my_malloc (k * sizeof (gf * ), "new pkt pointers" ); for (row = 0 ; row < k ; row++ ) { if (index[row] >= k) { new_pkt[row] = my_malloc (sz * sizeof (gf), "new pkt buffer" ); memset(new_pkt[row], '\0', sz * sizeof(gf) ) ; for (col = 0 ; col < k ; col++ ) addmul(new_pkt[row], pkt[col], m_dec[row*k + col], sz) ; } } /* * move pkts to their final destination */ for (row = 0 ; row < k ; row++ ) { if (index[row] >= k) { memcpy(pkt[row], new_pkt[row], sz*sizeof(gf)); free(new_pkt[row]); } } free(new_pkt); free(m_dec); return 0; } /*********** end of FEC code -- beginning of test code ************/ #if (TEST || DEBUG) void test_gf(void) { int i ; /* * test gf tables. Sufficiently tested... */ for (i=0; i<= GF_SIZE; i++) { if (gf_exp[gf_log[i]] != i) fprintf(stderr, "bad exp/log i %d log %d exp(log) %d\n", i, gf_log[i], gf_exp[gf_log[i]]); if (i != 0 && gf_mul(i, inverse[i]) != 1) fprintf(stderr, "bad mul/inv i %d inv %d i*inv(i) %d\n", i, inverse[i], gf_mul(i, inverse[i]) ); if (gf_mul(0,i) != 0) fprintf(stderr, "bad mul table 0,%d\n",i); if (gf_mul(i,0) != 0) fprintf(stderr, "bad mul table %d,0\n",i); } } #endif /* TEST */