A fault-tolerant decoding procedure for real cyclic codes

Real number cyclic codes which are constructed by imposing constraints in the discrete Fourier (DFT) domain are decoded by new estimation procedures. The codewords are assumed corrupted by small levels of roundoff noise and possibly by a few large excursions of random disturbances that represent the effects of failures. Error correction is separated into two parts, large activity detection followed by error value estimation particularly for the larger errors. The activity-detecting part determines locations for large increases in the Wiener estimator's gain, and an efficient modified Berlekamp-Massey algorithm is developed for this purpose.