Patent ID: 7694207

Claim:
A method of processing a signal, comprising the steps of: a) receiving a codeword vector, the codework vector having a BCH code with binary vectors of a user-definable length n; b) establishing a generator polynomial g(x) having g(α i )=0, for 1≦i≦2t, where α is an element of a Galois field GF(2 m ); c) establishing a check polynomial, h ⁡ ( x ) = ( x n - 1 ) g ⁡ ( x ) , where n=2 m −1; d) calculating a binary-matrix with respect to H = [ h k h k - 1 h k - 2 … h 0 0 0 … 0 0 h k h k - 1 … h 1 h 0 0 … 0 … … … … … … 0 0 0 … h k h k - 1 h k - 2 … h 0 0 0 0 … 0 h k h k - 1 … h 1 h 0 ] , the binary-matrix syndrome calculated by performing an exclusive-OR function on (n−k)-long segments of the coefficients of the binary vector with the coefficients of the polynomial established in step (c), where k is the dimension of the received binary vector; e) calculating the binary syndrome S=Hr t , the binary syndrome calculated by matrix-multiplying the received codework vector by the binary-matrix calculated in step (d); f) if the result of step (e) is an all-zero vector, then reporting no errors exist in the received codeword vector and proceeding to step (k), otherwise proceeding to step (g); g) establishing a tm x (N−k) binary matrix, m rows at a time, for the odd values in 1≦i≦2t; h) calculating the power-basis expansion of (r(α 1 ), r(α 3 ), r(α 5 ), . . . r(α 2t−1 )), the power basis expansion calculated by applying the binary matrix established in step (g) to the binary syndrome calculated in step (e); i) solving the syndrome sequence using s 2i =r(α 2i )=r(α i ) 2 =s i 2 ; j) correcting errors in a communication signal using the calculated syndrome sequence; and k) repeating step (a) through step (f) for each codeword vector received.