A lower bound on the error probability for signals in white Gaussian noise

The performance of specific signal constellations in digital communications problems is often described through use of the union bound, an upper bound which is asymptotically tight with respect to the signal-to-noise ratio. It is not unnatural to ask how tight this result is for small to medium values of signal-to-noise ratio; one way to answer this question is to develop an asymptotically tight lower bound. Such is the goal of the present paper