New bounds on the probability of a finite union of events
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New bounds on the probability of a finite union of events. / Yang, Jun; Alajaji, Fady; Takahara, Glen.
2014 IEEE International Symposium on Information Theory, ISIT 2014. Institute of Electrical and Electronics Engineers Inc., 2014. p. 1271-1275 6875037 (IEEE International Symposium on Information Theory - Proceedings).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - New bounds on the probability of a finite union of events
AU - Yang, Jun
AU - Alajaji, Fady
AU - Takahara, Glen
PY - 2014
Y1 - 2014
N2 - The classes of all lower/upper bounds on the probability of a finite union of events which are expressed only in terms of the individual event probabilities and the sums of the pairwise event probabilities are considered. The optimal lower and upper bounds in each class are given numerically by solving a linear programming (LP) problem. Furthermore, a suboptimal analytical lower bound is established by solving a relaxed LP problem, which is at least as good as an existing bound due to Kuai, et al. [1]. Note that the new lower bounds can be further improved algorithmically by optimizing them over subsets [2], [3], and can be applied to general estimation problems involving the probability of a finite union. Finally, the new lower/upper bounds are illustrated by examining the symbol and bit error rates of an uncoded communication system used in conjunction with Mary phase-shift keying (PSK) modulation over additive white Gaussian noise (AWGN) channels under maximum a posteriori (MAP) decoding.
AB - The classes of all lower/upper bounds on the probability of a finite union of events which are expressed only in terms of the individual event probabilities and the sums of the pairwise event probabilities are considered. The optimal lower and upper bounds in each class are given numerically by solving a linear programming (LP) problem. Furthermore, a suboptimal analytical lower bound is established by solving a relaxed LP problem, which is at least as good as an existing bound due to Kuai, et al. [1]. Note that the new lower bounds can be further improved algorithmically by optimizing them over subsets [2], [3], and can be applied to general estimation problems involving the probability of a finite union. Finally, the new lower/upper bounds are illustrated by examining the symbol and bit error rates of an uncoded communication system used in conjunction with Mary phase-shift keying (PSK) modulation over additive white Gaussian noise (AWGN) channels under maximum a posteriori (MAP) decoding.
UR - http://www.scopus.com/inward/record.url?scp=84906538048&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2014.6875037
DO - 10.1109/ISIT.2014.6875037
M3 - Article in proceedings
AN - SCOPUS:84906538048
SN - 9781479951864
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1271
EP - 1275
BT - 2014 IEEE International Symposium on Information Theory, ISIT 2014
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2014 IEEE International Symposium on Information Theory, ISIT 2014
Y2 - 29 June 2014 through 4 July 2014
ER -
ID: 362747506