Correcting DFT Codes with a Modified Berlekamp-Massey Algorithm and Kalman Recursive Syndrome Extension

Real number block codes derived from the discrete Fourier transform (DFT) are corrected by coupling a very modified Berlekamp-Massey (BM) algorithm with a syndrome extension process. The modified BM algorithm determines recursively the locations of any large errors whose number is within the capability of the DFT code. It evolves a connection polynomial which is changed when a discrepancy is above a threshold which is adjusted during each iteration. The large error locations are repositioned to exact location indices to combat low-level noise effects. The syndromes are extended using the refined connection polynomial taps. Alternately, enhanced extension recursions based on Kalman syndrome extensions are developed and simulated.