Atmel SAM9X25, Manual

Page: 353 / 1145

353
11054A–ATARM–27-Jul-11
SAM9X25
28.5 Software Implementation
28.5.1 Remainder Substitution Procedure
The substitute function evaluates the polynomial remainder, with different values of the field
primitive elements. The finite field arithmetic addition operation is performed with the Exclusive
or. The finite field arithmetic multiplication operation is performed through the gf_log, gf_antilog
lookup tables.
The REM2NP1 and REMN2NP3 fields of the PMECC_REMx registers contain only odd remain-
ders. Each bit indicates whether the coefficient of the polynomial remainder is set to zero or not.
NB_ERROR_MAX defines the maximum value of the error correcting capability.
NB_ERROR defines the error correcting capability selected at encoding/decoding time.
NB_FIELD_ELEMENTS defines the number of elements in the field.
si[] is a table that holds the current syndrome value, an element of that table belongs to the field.
This is also a shared variable for the next step of the decoding operation.
oo[] is a table that contains the degree of the remainders.
int substitute()
{
int i;
int j;
for (i = 1; i < 2 * NB_ERROR_MAX; i++)
{
si[i] = 0;
}
for (i = 1; i < 2*NB_ERROR; i++)
{
for (j = 0; j < oo[i]; j++)
{
if (REM2NPX[i][j])
{
si[i] = gf_antilog[(i * j)%NB_FIELD_ELEMENTS] ^ si[i];
}
}
}
return 0;
}
28.5.2 Find the Error Location Polynomial Sigma(x)
The sample code below gives a Berlekamp iterative procedure for finding the value of the error
location polynomial.
The input of the procedure is the si[] table defined in the remainder substitution procedure.