Tight Lower Bounds on the Symbol Error Rate of Uncoded Nonuniform Signaling over AWGN Channel

Abstract

Using a recent Bonferroni-type inequality proposed by Cohen and Merhav, we develop new tight lower bounds on the word error probability of uncoded systems with optimal Maximum A Posteriori (MAP) coherent detection for nonuniform signaling over additive white Gaussian noise channels. Our results are compared to the state-of-the-art KAT lower bounds and it is shown that the superiority of one bound to another is dependent on the signal constellation, the amount of nonuniformity of the Bernoulli source to be communicated, and the SNR range of interest. For instance, for smaller deviations from the uniform case, which are in fact more plausible, and at low SNRs, the new bounds are tighter than KAT lower bounds for all the constellations studied.Index Terms-Additive white Gaussian noise (AWGN) channels, communication theory, error probability, lower bound, maximum a posteriori (MAP) decoding, nonuniform signaling, probability of a union, symbol error rate, word error probability.