Patent ID: 8132083

Claim:
A method of generating an updated error indicator in a Reed-Solomon decoder capable of decoding an n-symbol decision-codeword to produce a k-symbol dataword, the method comprising: receiving existing syndromes S 0 , . . . , S 2t−1 for a decision-codeword, where t=(n−k)/2; generating modified syndromes S 0 (e l ) , . . . , S t+δ (e l ) based on the existing syndromes, where δ is a positive integer; receiving existing error indicator polynomials Λ(x) and B(x) associated with the decision-codeword; and generating updated error indicator polynomials based on the modified syndromes, wherein said generating comprises: computing quotient polynomials Q Λ (x), Q xΛ (x), Q B (x), Q xB (x), Q x 2 B (x) based on Λ(x) and B(x), computing remainder values r Λ , r xΛ , r B , r xB , r x 2 B based on Λ(x) and B(x), and computing at least one of quantities d 1 , d 2 , d 3 , and d 4 , where d 1 = ⁢ ∑ i = 0 ⁢ ⁢ S t + δ - i ( e 1 ) ⁡ ( Q Λ ) i , d 2 = ⁢ ∑ i = 0 ⁢ ⁢ S t + δ - i ( e 1 ) ⁢ ( Q x ⁢ ⁢ Λ ) i , d 3 = ⁢ ∑ i = 0 ⁢ ⁢ S t + δ - i ( e 1 ) ⁡ ( Q x ⁢ ⁢ B ) i , ⁢ and d 4 = ⁢ ∑ i = 0 ⁢ ⁢ S t + δ - i ( e 1 ) ⁡ ( Q x 2 ⁢ ⁢ B ) i .