Delayed decision-feedback sequence estimation (DDFSE) is a detection algorithm that prpvides a direct tradeoff between complexity and performance in digital co~munications over intersymbol interference channels. The complexity of the algorithm is controlled by a pqrameter p and can be varied from zero tfl the lpemory of the channel (which can be infinite). The algorithq is based on a trellis with the number of states exponential in p. Whey p = Q, QDFSE requces to the decision-feedback detector. When the qemory of the channel is finite, PDFSE with maximal complexity i w equivaleat to the Viterbi slgoritbm. Of course, if the channel has infinite mepory, the Viterbi algorithm cannot be implemented. Far the intermediate values of p, the algorithm can be described as a reduced-state Viterbi algorithm with feedback incorporated into the structure of path metric computations.We first consider DDFSE for uncoded PAM signals. Estimates on the performance of the algorithm are given, and simulation results are provided for several examples. A more general form of DDFSE applicable to coded modulation systems is also presented. As an example, detection of trellis coded QPSK signals over intersymbol interference channels is discussed., m f -, , xi-into u, = ( m f -, , mj-,) and u, = x,-I . The dranch metric is ( y , -t, 1 where t, = x, + G,-,, and from (10) and (1 I), the partial state estimator is given by v^(u,, m ! , m f ) = x,(x, = x ( m ! , m2, u,) J J J is determined by (36), and w,- = -pu(u,)). Fig. 10 shows results of computer simulations for this channel ( p = 1/2). It gives error rates of the DDFSE and the