// Top level decoder module
void rs_decode (unsigned char n, unsigned char t, unsigned char in_d[nn],
unsigned char *k, unsigned char out_d[kk])
{
unsigned char temp_k = n - 2*t;
unsigned char s[2*tt];
unsigned char c[tt+2];
unsigned char w[tt+2];
unsigned char lambda[tt];
unsigned char omega[tt];
unsigned char err_no;
unsigned char err_loc[kk];
unsigned char alpha_inv[tt];
unsigned char err[kk];
unsigned char in_data[kk];
unsigned char in_d_2[nn];
Simple_rs1: for (int i = 0; i < nn; i++)
in_d_2[i] = in_d[i];
*k = temp_k;
rs_fifo(temp_k, in_d, in_data);
syndrome(temp_k, t, in_d_2, s);
berlekamp(t, s, lambda, omega);
chien_search(kk, tt, lambda, &err_no, err_loc, alpha_inv);
error_mag(kk, lambda, omega, err_no, err_loc, alpha_inv, err);
error_correct(temp_k, in_data, err, out_d);
}
void Hamming_Code::decode(const bvec &coded_bits, bvec &decoded_bits)
{
int length = coded_bits.length();
int Itterations = floor_i(static_cast<double>(length) / n);
ivec Hindexes(n);
bvec temp(n - k);
bvec coded(n), syndrome(n - k);
int isynd, errorpos = 0;
int i, j;
decoded_bits.set_size(Itterations*k, false);
for (i = 0; i < n; i++) {
for (j = 0; j < n - k; j++)
temp(j) = H(j, i);
Hindexes(i) = bin2dec(temp);
}
//Decode all codewords
for (i = 0; i < Itterations; i++) {
coded = coded_bits.mid(i * n, n);
syndrome = H * coded;
isynd = bin2dec(syndrome);
if (isynd != 0) {
for (j = 0; j < n; j++)
if (Hindexes(j) == isynd) {
errorpos = j;
};
coded(errorpos) += 1;
}
decoded_bits.replace_mid(k*i, coded.right(k));
}
}
void ReedSolomonDecoder::decode(ArrayRef<int> received, int twoS) {
Ref<GenericGFPoly> poly(new GenericGFPoly(field, received));
#ifdef DEBUG
cout << "decoding with poly " << *poly << "\n";
#endif
ArrayRef<int> syndromeCoefficients(new Array<int> (twoS));
#ifdef DEBUG
cout << "syndromeCoefficients array = " <<
syndromeCoefficients.array_ << "\n";
#endif
bool dataMatrix = (field.object_ == GenericGF::DATA_MATRIX_FIELD_256.object_);
bool noError = true;
for (int i = 0; i < twoS; i++) {
int eval = poly->evaluateAt(field->exp(dataMatrix ? i + 1 : i));
syndromeCoefficients[syndromeCoefficients->size() - 1 - i] = eval;
if (eval != 0) {
noError = false;
}
}
if (noError) {
return;
}
Ref<GenericGFPoly> syndrome(new GenericGFPoly(field, syndromeCoefficients));
Ref<GenericGFPoly> monomial = field->buildMonomial(twoS, 1);
vector<Ref<GenericGFPoly> > sigmaOmega = runEuclideanAlgorithm(monomial, syndrome, twoS);
ArrayRef<int> errorLocations = findErrorLocations(sigmaOmega[0]);
ArrayRef<int> errorMagitudes = findErrorMagnitudes(sigmaOmega[1], errorLocations, dataMatrix);
for (unsigned i = 0; i < errorLocations->size(); i++) {
int position = received->size() - 1 - field->log(errorLocations[i]);
//TODO: check why the position would be invalid
if (position < 0 || (size_t)position >= received.size())
throw IllegalArgumentException("Invalid position (ReedSolomonDecoder)");
received[position] = GenericGF::addOrSubtract(received[position], errorMagitudes[i]);
}
}
void ReedSolomonDecoder::decode(ArrayRef<int> received, int twoS) {
Ref<GF256Poly> poly(new GF256Poly(field, received));
#ifdef DEBUG
cout << "decoding with poly " << *poly << "\n";
#endif
ArrayRef<int> syndromeCoefficients(new Array<int>(twoS));
#ifdef DEBUG
cout << "syndromeCoefficients array = " <<
syndromeCoefficients.array_ << "\n";
#endif
bool noError = true;
for (int i = 0; i < twoS; i++) {
int eval = poly->evaluateAt(field.exp(i));
syndromeCoefficients[syndromeCoefficients->size() - 1 - i] = eval;
if (eval != 0) {
noError = false;
}
}
if (noError) {
return;
}
Ref<GF256Poly> syndrome(new GF256Poly(field, syndromeCoefficients));
Ref<GF256Poly> monomial(field.buildMonomial(twoS, 1));
vector<Ref<GF256Poly> > sigmaOmega
(runEuclideanAlgorithm(monomial, syndrome, twoS));
ArrayRef<int> errorLocations = findErrorLocations(sigmaOmega[0]);
ArrayRef<int> errorMagitudes = findErrorMagnitudes(sigmaOmega[1],
errorLocations);
for (unsigned i = 0; i < errorLocations->size(); i++) {
int position = received->size() - 1 - field.log(errorLocations[i]);
received[position] = GF256::addOrSubtract(received[position],
errorMagitudes[i]);
}
}
/*
* Full implementation of the three error correcting Peterson decoder. For
* t<6, it is faster than Massey - Berlekamp. It is also somewhat more
* intuitive.
*/
extern void ecc_decode(uint8_t code[ECC_CAPACITY], uint8_t mesg[ECC_CAPACITY], int *errcode)
{
REVERSE(code, ECC_CAPACITY);
uint8_t syn[ECC_OFFSET + 1], deter, z[4], e0, e1, e2, n0, n1, n2, w0, w1, w2, x0, x[3];
int sols;
*errcode = 0;
/*
* First, get the message out of the code, so that even if we can't correct
* it, we return an estimate.
*/
for (int i = 0; i < ECC_PAYLOAD; i++)
mesg[i] = code[(ECC_CAPACITY - 1) - i];
syndrome(code, syn);
if (syn[0] == 0)
return;
/*
* We now know we have at least one error. If there are no errors detected,
* we assume that something funny is going on, and so return with errcode 4,
* else pass the number of errors back via errcode.
*/
errnum(syn, &deter, errcode);
if (*errcode == 4)
return;
/* Having obtained the syndrome, the number of errors, and the determinant,
* we now proceed to correct the block. If we do not find exactly the
* number of solutions equal to the number of errors, we have exceeded our
* error capacity, and return with the block uncorrected, and errcode 4.
*/
switch (*errcode)
{
case 1:
x0 = GF_MUL(syn[2], GF_INV(syn[1]));
w0 = GF_MUL(GF_EXP(syn[1], 2), GF_INV(syn[2]));
if (v2e[x0] > 5)
mesg[(ECC_CAPACITY - 1) - v2e[x0]] = GF_ADD(mesg[(ECC_CAPACITY - 1) - v2e[x0]], w0);
return;
case 2:
z[0] = GF_MUL(GF_ADD(GF_MUL(syn[1], syn[3]), GF_EXP(syn[2], 2)), GF_INV(deter));
z[1] = GF_MUL(GF_ADD(GF_MUL(syn[2], syn[3]), GF_MUL(syn[1], syn[4])), GF_INV(deter));
z[2] = 1;
z[3] = 0;
polysolve(z, x, &sols);
if (sols != 2)
{
*errcode = 4;
return;
}
w0 = GF_MUL(z[0], syn[1]);
w1 = GF_ADD(GF_MUL(z[0], syn[2]), GF_MUL(z[1], syn[1]));
n0 = (ECC_CAPACITY - 1) - v2e[GF_INV(x[0])];
n1 = (ECC_CAPACITY - 1) - v2e[GF_INV(x[1])];
e0 = GF_MUL(GF_ADD(w0, GF_MUL(w1, x[0])), GF_INV(z[1]));
e1 = GF_MUL(GF_ADD(w0, GF_MUL(w1, x[1])), GF_INV(z[1]));
if (n0 < ECC_PAYLOAD)
mesg[n0] = GF_ADD(mesg[n0], e0);
if (n1 < ECC_PAYLOAD)
mesg[n1] = GF_ADD(mesg[n1], e1);
return;
case 3:
z[3] = 1;
z[2] = GF_MUL(syn[1], GF_MUL(syn[4], syn[6]));
z[2] = GF_ADD(z[2], GF_MUL(syn[1], GF_MUL(syn[5], syn[5])));
z[2] = GF_ADD(z[2], GF_MUL(syn[5], GF_MUL(syn[3], syn[3])));
z[2] = GF_ADD(z[2], GF_MUL(syn[3], GF_MUL(syn[4], syn[4])));
z[2] = GF_ADD(z[2], GF_MUL(syn[2], GF_MUL(syn[5], syn[4])));
z[2] = GF_ADD(z[2], GF_MUL(syn[2], GF_MUL(syn[3], syn[6])));
z[2] = GF_MUL(z[2], GF_INV(deter));
z[1] = GF_MUL(syn[1], GF_MUL(syn[3], syn[6]));
z[1] = GF_ADD(z[1], GF_MUL(syn[1], GF_MUL(syn[5], syn[4])));
z[1] = GF_ADD(z[1], GF_MUL(syn[4], GF_MUL(syn[3], syn[3])));
z[1] = GF_ADD(z[1], GF_MUL(syn[2], GF_MUL(syn[4], syn[4])));
z[1] = GF_ADD(z[1], GF_MUL(syn[2], GF_MUL(syn[3], syn[5])));
z[1] = GF_ADD(z[1], GF_MUL(syn[2], GF_MUL(syn[2], syn[6])));
z[1] = GF_MUL(z[1], GF_INV(deter));
z[0] = GF_MUL(syn[2], GF_MUL(syn[3], syn[4]));
z[0] = GF_ADD(z[0], GF_MUL(syn[3], GF_MUL(syn[2], syn[4])));
z[0] = GF_ADD(z[0], GF_MUL(syn[3], GF_MUL(syn[5], syn[1])));
z[0] = GF_ADD(z[0], GF_MUL(syn[4], GF_MUL(syn[4], syn[1])));
z[0] = GF_ADD(z[0], GF_MUL(syn[3], GF_MUL(syn[3], syn[3])));
z[0] = GF_ADD(z[0], GF_MUL(syn[2], GF_MUL(syn[2], syn[5])));
z[0] = GF_MUL(z[0], GF_INV(deter));
polysolve (z, x, &sols);
if (sols != 3)
{
*errcode = 4;
return;
}
w0 = GF_MUL(z[0], syn[1]);
w1 = GF_ADD(GF_MUL(z[0], syn[2]), GF_MUL(z[1], syn[1]));
w2 = GF_ADD(GF_MUL(z[0], syn[3]), GF_ADD(GF_MUL(z[1], syn[2]), GF_MUL(z[2], syn[1])));
n0 = (ECC_CAPACITY - 1) - v2e[GF_INV(x[0])];
n1 = (ECC_CAPACITY - 1) - v2e[GF_INV(x[1])];
n2 = (ECC_CAPACITY - 1) - v2e[GF_INV(x[2])];
e0 = GF_ADD(w0, GF_ADD(GF_MUL(w1, x[0]), GF_MUL(w2, GF_EXP(x[0], 2))));
e0 = GF_MUL(e0, GF_INV(GF_ADD(z[1], GF_EXP(x[0], 2))));
e1 = GF_ADD(w0, GF_ADD(GF_MUL(w1, x[1]), GF_MUL(w2, GF_EXP(x[1], 2))));
e1 = GF_MUL(e1, GF_INV(GF_ADD(z[1], GF_EXP(x[1], 2))));
e2 = GF_ADD(w0, GF_ADD(GF_MUL(w1, x[2]), GF_MUL(w2, GF_EXP(x[2], 2))));
e2 = GF_MUL(e2, GF_INV(GF_ADD(z[1], GF_EXP(x[2], 2))));
if (n0 < ECC_PAYLOAD)
mesg[n0] = GF_ADD(mesg[n0], e0);
if (n1 < ECC_PAYLOAD)
mesg[n1] = GF_ADD(mesg[n1], e1);
if (n2 < ECC_PAYLOAD)
mesg[n2] = GF_ADD(mesg[n2], e2);
return;
}
}
