Lower Bounds on Error Probability in the Presence of Large Intersymbol Interference

A lower bound on the symbol error probability achieved by any estimator of a digital pulse-amplitude-modulated sequence in the presence of white Gaussian noise and intersymbol interference is presented. The bound reduces to the well-known single-pulse error probability bound when intersymbol interference is small, but is tighter when interference is large. For example, on the singlepole (RC) channel, the effective signal-to-noise ratio for any estimator is shown to decrease by at least 3 dB for every doubling in pulse rate T^-1asT rightarrow 0and, on the double-pole channel, by at least 9 dB, thus disproving a recent conjecture [2] on the performance of nonlinear receivers.