Error Probability of a Multilevel Digital System with Intersymbol Interference and Gaussian Noise

In a recent paper 1 we have developed a new method to calculate the error probability of a binary digital data system in the presence of intersymbol interference and additive gaussian noise. A similar method has also been reported by M. I. Celebiler and 0. Shimbo. 2 The purpose of this paper is to extend the previous results to multilevel systems. The existing methods for the estimation of the error probability are the Chernoff bound or the worst case bound, 3 " 4 the results of which are generally too loose. Another alternative is the time-consuming exhaustive method. 3 For example, it would require 4 1 0 ( ^ 10'') calculations of the error function to find the error probability of a four-level digital system where intersymbol interference resulted from ten nonzero samples of the channel impulse response.