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Tight error bounds for nonuniform signaling over AWGN channels

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3 Author(s)
Hongyan Kuai ; Dept. of Math. & Stat., Queen''s Univ., Kingston, Ont., Canada ; Alajaji, F. ; Takahara, G.

We consider a Bonferroni-type lower bound due to Kounias (1968) on the probability of a finite union. The bound is expressed in terms of only the individual and pairwise event probabilities; however, it suffers from requiring an exponentially complex search for its direct implementation. We address this problem by presenting a practical algorithm for its evaluation. This bound is applied together with two other bounds, a recent lower bound (the KAT bound) and a greedy algorithm implementation of an upper bound due to Hunter (1976), to examine the symbol error (Pa) and bit error (Pb) probabilities of an uncoded communication system used in conjunction with M-ary phase-shift keying (PSK)/quadrature amplitude (QAM) (PSK/QAM) modulations and maximum a posteriori (MAP) decoding over additive white Gaussian noise (AWGN) channels. It is shown that the bounds-which can be efficiently computed-provide an excellent estimate of the error probabilities over the entire range of the signal-to-noise ratio (SNR) E b/N0. The new algorithmic bound and the greedy bound are particularly impressive as they agree with the simulation results even during very severe channel conditions

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Information Theory, IEEE Transactions on  (Volume:46 ,  Issue: 7 )