Digital Communications

Tufts (1965), Smith (1965), and Berger and Tufts (1967). “Faster than Nyquist” transmission has been studied by Mazo (1975) and Foschini (1984). Channel equalization for digital communications was developed by Lucky (1965, 1966), who focused on linear equalizers that were optimized using the peak distortion criterion. The mean-square-error criterion for optimization of the equalizer coefficients was proposed by Widrow (1966). Decision-feedback equalization was proposed and analyzed by Austin (1967). Analyses of the performance of the DFE can be found in the papers by Monsen (1971), George et al. (1971), Price (1972), Salz (1973), Duttweiler et al. (1974), and Altekar and Beaulieu (1993). The use of the Viterbi algorithm as the optimal maximum-likelihood sequence estimator for symbols corrupted by ISI was proposed and analyzed by Forney (1972) and Omura (1971). Its use for carrier-modulated signals was considered by Ungerboeck (1974) and MacKenchnie (1973). The use of iterative MAP algorithms in suppressing ISI in coded systems, called turbo equalization, represents a major new advance in suppression of intersymbol interference in signal transmission through band-limited channels. It is anticipated that iterative MAP equalization algorithms will be incorporated in future communication systems. The implementation of turbo equalization, described in the paper by Hagenauer et al. (1999), is the first attempt at implementing an iterative MAP equalization algorithm in a coded system.