Patent ID: 7472333

Claim:
An encoding method for encoding a codeword to obtain a corresponding parity code, the parity code being embedded in the codeword and dividing the codeword to have intermediate symbol locations between a first and a second set of data symbols, each data symbol forming a coefficient, the first set of data symbols, the second set of data symbols, and the parity code respectively forming a first polynomial (M 1 (x)), a second polynomial (M 2 (x)), and a parity code polynomial (R(x)), the encoding method comprising the following steps: designing a first code generator polynomial (G 1 (x)) according to a desired parity resolution; multiplying the first polynomial (M 1 (x)) by x 4 and dividing a product of M 1 (x) * x 4 by the first code generator polynomial (G 1 (x)), so as to obtain a first remainder polynomial (R 1 (x)); generating a second code generator polynomial (G 2 (x)) from the first code generator polynomial (G 1 (x)) according to a reciprocal substitution procedure; generating a third polynomial (M 3 (x)), wherein the coefficients of the third polynomial (M 3 (x)) in the ascending order are the reverse permuted order of the coefficients of the second polynomial (M 2 (x)) in the ascending order; multiplying the third polynomial (M 3 (x)) by x 4 and dividing a product of M 3 (x) * x 4 by the second code generator polynomial (G 2 (x)), so as to obtain a second remainder polynomial (R 2 (x)); performing an adding procedure to the first remainder polynomial (R 1 (x)) and the second remainder polynomial (R 2 (x)), so as to obtain the parity code polynomial (R(x)); and obtaining the parity code from each coefficient of the parity code polynomial (R(x)).