 
Summary: Performance Bounds of NonUniform Signaling
over AWGN Channels \Lambda
Hongyan Kuai, Fady Alajaji and Glen Takahara
Mathematics and Engineering
Department of Mathematics and Statistics
Queen's University
Kingston, Ontario, Canada K7L 3N6
Abstract  In this work, we present two bounds (one
lower bound and one upper bound) on the probability
of a union of a finite number of events. The bounds
 which are expressed in terms of only the individual
event probabilities and the pairwise event probabili
ties  are applied to examine the symbol error (Ps)
and bit error (P b
) probabilities of an uncoded com
munication system used in conjunction with Mary
PSK/QAM modulations and maximum a posteriori
(MAP) decoding over AWGN channels. It is shown
that both bounds provide a good, and often excel
lent, estimate of the error probabilities over the entire
