Does a Larger Intersymbol Interference Result in a Higher Probability of Error?

In this correspondence, we investigate an intuitive conjecture on data communication studies that a larger intersymbol interference (ISI) would result in a higher error probability. It is proved that if: 1) the eye is open, and 2) the additive noise has a symmetric probability density function and its complementary distribution function is concave upward (i.e., convex
\cup
) on the positive real line, then the system with a larger ISI will have a higher probability of error.