Decoding real block codes: Activity detection Wiener estimation

New decoding procedures for real-number block codes which are constructed by imposing constraints in the discrete Fourier transform (DFT) domain are examined. The codewords are corrupted by small levels of roundoff noise and possibly occasionally by a few large excursions of random disturbances. The error-correcting procedure is separated into two parts, large activity detection followed by error value estimation, particularly the larger errors. The first part determines if large excursions are present, roughly identifying their locations, while the second part is a Wiener minimum mean-squared error estimation technique providing a stochastic correction to the corrupted components. The activity-detecting part determines locations for large increases in the Wiener estimator's gain. A computationally intensive Bayes hypothesis testing approach is shown to be very effective at locating large activity positions, but a more efficient modified Berlekamp-Massey (1969) algorithm is developed which leads to excellent mean-squared error performance. Extensive simulations demonstrate individual codeword corrective actions and compare the average mean-squared error performance between coded and unprotected data. The error level improvement ranges from three to four orders of magnitude.