Tight upper bounds to the error probability of decision feedback equalization

The authors derive some upper bounds to the error probability of decision feedback equalization (DFE). The bounds are valid for the same conditions as the bounds of D.L. Duttweiler et al. (1974). The bounds are as much as 2.8 dB tighter in signal-to-noise ratio (SNR) than those of Duttweiler for certain channels. An upper bound based on considering distinct single error states is derived. A second bound based on examining distinct single and distinct double consecutive error states is presented. Worthwhile improvement over the second bound is obtained by adding all distinct double error states to the reduced state model. Triple consecutive error state bounds are considered, and a revised comparison of DFE with linear equalization is made using the tighter bounds