Patent ID: 7185258

Claim:
A signal processing method for a digital signal comprising the steps of: establishing a Yule-Walker equation having the following form by using a matrix that includes, as components, the elements of a Galois field GF(2 m ) applied to Reed-Solomon codes having an odd minimum distance, and a vector that includes, as components, said elements of said Galois field GF(2 m ) ( S 0 S 1 ⋯ S l - 1 S 1 S 2 ⋯ S l ⋮ ⋰ ⋮ S l - 1 S l ⋯ S 2 ⁢ l - 2 ) ⁢ ( Λ l ( l ) ⋮ ⋮ Λ 1 ( l ) ) = ( S l ⋮ ⋮ S 2 ⁢ l - 1 ) ; obtaining the solution of said Yule-Walker equation as the following determinants Λ ~ i - ( l ) =  S 0 S 1 ⋯ S l - 1 ⋮ ⋯ ⋰ ⋮ S l - i - 1 S l - i ⋯ S 2 ⁢ l - i - 2 S l - i + 1 S l - i + 2 ⋯ S 2 ⁢ l - i ⋮ ⋯ ⋰ ⋮ S l S l + 1 ⋯ S 2 ⁢ l - 1  , i = 1 , … ⁢ , l - 1 ; employing Jacobi's formula, Γ i (l+1) Λ 0 hat(l) +(Λ 1 hat(l) ) 2 =Λ 0 hat(i+1) Γ i l , to enable the calculation of the solution {tilde over (Λ)} i (l) (hereinafter referred to as Λ i hat(l) ) to result in the calculation of the following determinants of the symmetric matrices Γ i ( l + 1 ) =  S 0 ⋯ S l - 1 - i S l + 1 - i ⋯ S l ⋮ ⋮ ⋮ ⋮ S l - 1 - i ⋯ S 2 ⁢ ( l - 1 - i ) S 2 ⁢ ( l - i ) ⋯ S 2 ⁢ l - 1 - i S l + 1 - i ⋯ S 2 ⁢ ( l - i ) S 2 ⁢ ( l + 1 - i ) ⋯ S 2 ⁢ l + 1 - i ⋮ ⋮ ⋮ ⋮ S l ⋯ S 2 ⁢ l - 1 - i S 2 ⁢ l + 1 - i ⋯ S 2 ⁢ l  (where i=0, . . . , 1); determining the number of errors to be the maximum matrix size that corresponds to said obtained solution that is not zero; determining whether said number of errors equals the maximum number of correctable errors in the digital signal; and correcting at least one error in the digital signal.