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—We consider a Bonferroni-type lower bound due to Kounias 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… (More)

A new lower bound on the probability P(A1 ∪ · · · ∪ AN) is established in terms of only the individual event probabilities P(Ai)'s and the pairwise event probabilities P(Ai ∩ Aj)'s. This bound is shown to be always at least as good as two similar lower bounds: one by de Caen (1997) and the other by Dawson and Sankoo (1967). Numerical examples for the… (More)

—The design of two-dimensional constellation map-pings for the transmission of binary nonuniform memoryless sources over additive white Gaussian noise channels using standard -ary PSK and QAM modulation schemes is investigated. The main application of this problem is the incorporation of an adaptive mapping assignment in modem devices that employ fixed… (More)

- H. Kuai, F. Alajaji
- 1998

A new lower bound on the probability P(A 1 A N) is established in terms of only the individual event probabilities P(A i)'s and the pairwise event probabilities P(A i \ A j)'s. This bound is shown to be always at least as good as two similar lower bounds: one by de Caen (1997) and the other by Dawson and Sankoo (1967). Numerical examples for the computation… (More)

- Hongyan Kuai, Fady Alajaji
- 2007

| In this work, we present two bounds (one lower bound and one upper bound) on the probability of a union of a nite number of events. The bounds { which are expressed in terms of only the individual event probabilities and the pairwise event probabilities { are applied to examine the symbol error (Ps) and bit error (P b) probabilities of an uncoded… (More)

- Hongyan Kuai, Fady Alajaji
- 2000

A new lower bound on the probability of P(A 1 A N) is established in terms of only the individual event probabilities P(A i)'s and the pairwise event probabilities P(A i \ A j)'s. This bound is shown to be always at least as good as two similar lower bounds, one by de Caen (1997) and the other by Dawson and Sankoo (1967). Numerical examples for the… (More)

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