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gr-satnogs/lib/libfec/decode_rs.h

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/* The guts of the Reed-Solomon decoder, meant to be #included
* into a function body with the following typedefs, macros and variables supplied
* according to the code parameters:
* data_t - a typedef for the data symbol
* data_t data[] - array of NN data and parity symbols to be corrected in place
* retval - an integer lvalue into which the decoder's return code is written
* NROOTS - the number of roots in the RS code generator polynomial,
* which is the same as the number of parity symbols in a block.
Integer variable or literal.
* NN - the total number of symbols in a RS block. Integer variable or literal.
* PAD - the number of pad symbols in a block. Integer variable or literal.
* ALPHA_TO - The address of an array of NN elements to convert Galois field
* elements in index (log) form to polynomial form. Read only.
* INDEX_OF - The address of an array of NN elements to convert Galois field
* elements in polynomial form to index (log) form. Read only.
* MODNN - a function to reduce its argument modulo NN. May be inline or a macro.
* FCR - An integer literal or variable specifying the first consecutive root of the
* Reed-Solomon generator polynomial. Integer variable or literal.
* PRIM - The primitive root of the generator poly. Integer variable or literal.
* DEBUG - If set to 1 or more, do various internal consistency checking. Leave this
* undefined for production code
* The memset(), memmove(), and memcpy() functions are used. The appropriate header
* file declaring these functions (usually <string.h>) must be included by the calling
* program.
*/
#if !defined(NROOTS)
#error "NROOTS not defined"
#endif
#if !defined(NN)
#error "NN not defined"
#endif
#if !defined(PAD)
#error "PAD not defined"
#endif
#if !defined(ALPHA_TO)
#error "ALPHA_TO not defined"
#endif
#if !defined(INDEX_OF)
#error "INDEX_OF not defined"
#endif
#if !defined(MODNN)
#error "MODNN not defined"
#endif
#if !defined(FCR)
#error "FCR not defined"
#endif
#if !defined(PRIM)
#error "PRIM not defined"
#endif
#if !defined(NULL)
#define NULL ((void *)0)
#endif
#undef MIN
#define MIN(a,b) ((a) < (b) ? (a) : (b))
#undef A0
#define A0 (NN)
{
int deg_lambda, el, deg_omega;
int i, j, r, k;
data_t u, q, tmp, num1, num2, den, discr_r;
data_t lambda[NROOTS + 1], s[NROOTS]; /* Err+Eras Locator poly
* and syndrome poly */
data_t b[NROOTS + 1], t[NROOTS + 1], omega[NROOTS + 1];
data_t root[NROOTS], reg[NROOTS + 1], loc[NROOTS];
int syn_error, count;
/* form the syndromes; i.e., evaluate data(x) at roots of g(x) */
for (i = 0; i < NROOTS; i++)
{
s[i] = data[0];
}
for (j = 1; j < NN - PAD; j++)
{
for (i = 0; i < NROOTS; i++) {
if (s[i] == 0) {
s[i] = data[j];
}
else {
s[i] = data[j] ^ ALPHA_TO[MODNN(INDEX_OF[s[i]] + (FCR + i) * PRIM)];
}
}
}
/* Convert syndromes to index form, checking for nonzero condition */
syn_error = 0;
for (i = 0; i < NROOTS; i++)
{
syn_error |= s[i];
s[i] = INDEX_OF[s[i]];
}
if (!syn_error)
{
/* if syndrome is zero, data[] is a codeword and there are no
* errors to correct. So return data[] unmodified
*/
count = 0;
goto finish;
}
memset(&lambda[1], 0, NROOTS * sizeof(lambda[0]));
lambda[0] = 1;
if (no_eras > 0)
{
/* Init lambda to be the erasure locator polynomial */
lambda[1] = ALPHA_TO[MODNN(PRIM * (NN - 1 - eras_pos[0]))];
for (i = 1; i < no_eras; i++) {
u = MODNN(PRIM * (NN - 1 - eras_pos[i]));
for (j = i + 1; j > 0; j--) {
tmp = INDEX_OF[lambda[j - 1]];
if (tmp != A0) {
lambda[j] ^= ALPHA_TO[MODNN(u + tmp)];
}
}
}
#if DEBUG >= 1
/* Test code that verifies the erasure locator polynomial just constructed
Needed only for decoder debugging. */
/* find roots of the erasure location polynomial */
for (i = 1; i <= no_eras; i++) {
reg[i] = INDEX_OF[lambda[i]];
}
count = 0;
for (i = 1, k = IPRIM - 1; i <= NN; i++, k = MODNN(k + IPRIM)) {
q = 1;
for (j = 1; j <= no_eras; j++)
if (reg[j] != A0) {
reg[j] = MODNN(reg[j] + j);
q ^= ALPHA_TO[reg[j]];
}
if (q != 0) {
continue;
}
/* store root and error location number indices */
root[count] = i;
loc[count] = k;
count++;
}
if (count != no_eras) {
printf("count = %d no_eras = %d\n lambda(x) is WRONG\n", count, no_eras);
count = -1;
goto finish;
}
#if DEBUG >= 2
printf("\n Erasure positions as determined by roots of Eras Loc Poly:\n");
for (i = 0; i < count; i++) {
printf("%d ", loc[i]);
}
printf("\n");
#endif
#endif
}
for (i = 0; i < NROOTS + 1; i++)
{
b[i] = INDEX_OF[lambda[i]];
}
/*
* Begin Berlekamp-Massey algorithm to determine error+erasure
* locator polynomial
*/
r = no_eras;
el = no_eras;
while (++r <= NROOTS) /* r is the step number */
{
/* Compute discrepancy at the r-th step in poly-form */
discr_r = 0;
for (i = 0; i < r; i++) {
if ((lambda[i] != 0) && (s[r - i - 1] != A0)) {
discr_r ^= ALPHA_TO[MODNN(INDEX_OF[lambda[i]] + s[r - i - 1])];
}
}
discr_r = INDEX_OF[discr_r]; /* Index form */
if (discr_r == A0) {
/* 2 lines below: B(x) <-- x*B(x) */
memmove(&b[1], b, NROOTS * sizeof(b[0]));
b[0] = A0;
}
else {
/* 7 lines below: T(x) <-- lambda(x) - discr_r*x*b(x) */
t[0] = lambda[0];
for (i = 0 ; i < NROOTS; i++) {
if (b[i] != A0) {
t[i + 1] = lambda[i + 1] ^ ALPHA_TO[MODNN(discr_r + b[i])];
}
else {
t[i + 1] = lambda[i + 1];
}
}
if (2 * el <= r + no_eras - 1) {
el = r + no_eras - el;
/*
* 2 lines below: B(x) <-- inv(discr_r) *
* lambda(x)
*/
for (i = 0; i <= NROOTS; i++) {
b[i] = (lambda[i] == 0) ? A0 : MODNN(INDEX_OF[lambda[i]] - discr_r + NN);
}
}
else {
/* 2 lines below: B(x) <-- x*B(x) */
memmove(&b[1], b, NROOTS * sizeof(b[0]));
b[0] = A0;
}
memcpy(lambda, t, (NROOTS + 1)*sizeof(t[0]));
}
}
/* Convert lambda to index form and compute deg(lambda(x)) */
deg_lambda = 0;
for (i = 0; i < NROOTS + 1; i++)
{
lambda[i] = INDEX_OF[lambda[i]];
if (lambda[i] != A0) {
deg_lambda = i;
}
}
/* Find roots of the error+erasure locator polynomial by Chien search */
memcpy(&reg[1], &lambda[1], NROOTS * sizeof(reg[0]));
count = 0; /* Number of roots of lambda(x) */
for (i = 1, k = IPRIM - 1; i <= NN; i++, k = MODNN(k + IPRIM))
{
q = 1; /* lambda[0] is always 0 */
for (j = deg_lambda; j > 0; j--) {
if (reg[j] != A0) {
reg[j] = MODNN(reg[j] + j);
q ^= ALPHA_TO[reg[j]];
}
}
if (q != 0) {
continue; /* Not a root */
}
/* store root (index-form) and error location number */
#if DEBUG>=2
printf("count %d root %d loc %d\n", count, i, k);
#endif
root[count] = i;
loc[count] = k;
/* If we've already found max possible roots,
* abort the search to save time
*/
if (++count == deg_lambda) {
break;
}
}
if (deg_lambda != count)
{
/*
* deg(lambda) unequal to number of roots => uncorrectable
* error detected
*/
count = -1;
goto finish;
}
/*
* Compute err+eras evaluator poly omega(x) = s(x)*lambda(x) (modulo
* x**NROOTS). in index form. Also find deg(omega).
*/
deg_omega = deg_lambda - 1;
for (i = 0; i <= deg_omega; i++)
{
tmp = 0;
for (j = i; j >= 0; j--) {
if ((s[i - j] != A0) && (lambda[j] != A0)) {
tmp ^= ALPHA_TO[MODNN(s[i - j] + lambda[j])];
}
}
omega[i] = INDEX_OF[tmp];
}
/*
* Compute error values in poly-form. num1 = omega(inv(X(l))), num2 =
* inv(X(l))**(FCR-1) and den = lambda_pr(inv(X(l))) all in poly-form
*/
for (j = count - 1; j >= 0; j--)
{
num1 = 0;
for (i = deg_omega; i >= 0; i--) {
if (omega[i] != A0) {
num1 ^= ALPHA_TO[MODNN(omega[i] + i * root[j])];
}
}
num2 = ALPHA_TO[MODNN(root[j] * (FCR - 1) + NN)];
den = 0;
/* lambda[i+1] for i even is the formal derivative lambda_pr of lambda[i] */
for (i = MIN(deg_lambda, NROOTS - 1) & ~1; i >= 0; i -= 2) {
if (lambda[i + 1] != A0) {
den ^= ALPHA_TO[MODNN(lambda[i + 1] + i * root[j])];
}
}
#if DEBUG >= 1
if (den == 0) {
printf("\n ERROR: denominator = 0\n");
count = -1;
goto finish;
}
#endif
/* Apply error to data */
if (num1 != 0 && loc[j] >= PAD) {
data[loc[j] - PAD] ^= ALPHA_TO[MODNN(INDEX_OF[num1] + INDEX_OF[num2] + NN -
INDEX_OF[den])];
}
}
finish:
if (eras_pos != NULL)
{
for (i = 0; i < count; i++) {
eras_pos[i] = loc[i];
}
}
retval = count;
}
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