On bounding the union probability
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On bounding the union probability. / Yang, Jun; Alajaji, Fady; Takahara, Glen.
Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1761-1765 7282758 (IEEE International Symposium on Information Theory - Proceedings, Vol. 2015-June).Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review
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TY - GEN
T1 - On bounding the union probability
AU - Yang, Jun
AU - Alajaji, Fady
AU - Takahara, Glen
N1 - Funding Information: This work was supported in part by NSERC of Canada. Publisher Copyright: © 2015 IEEE.
PY - 2015/9/28
Y1 - 2015/9/28
N2 - We present new results on bounding the probability of a finite union of events, equation for a fixed positive integer N, using partial information on the events joint probabilities. We first consider bounds that are established in terms of {P(Ai)} and {ΣjcjP(Ai ∩ Aj)} where c1,⋯, cN are given weights. We derive a new class of lower bounds of at most pseudo-polynomial computational complexity. This class of lower bounds generalizes the recent bounds in [1], [2] and can be tighter in some cases than the Gallot-Kounias [3]-[5] and Prékopa-Gao [6] bounds which require more information on the events probabilities. We next consider bounds that fully exploit knowledge of {P(Ai)} and {P(Ai ∩ Aj)}. We establish new numerical lower/upper bounds on the union probability by solving a linear programming problem with equation variables. These bounds coincide with the optimal lower/upper bounds when N ≤ 7 and are guaranteed to be sharper than the optimal lower/upper bounds of [1], [2] that use {P(Ai)} and {Σj P(Ai ∩ Aj)}.
AB - We present new results on bounding the probability of a finite union of events, equation for a fixed positive integer N, using partial information on the events joint probabilities. We first consider bounds that are established in terms of {P(Ai)} and {ΣjcjP(Ai ∩ Aj)} where c1,⋯, cN are given weights. We derive a new class of lower bounds of at most pseudo-polynomial computational complexity. This class of lower bounds generalizes the recent bounds in [1], [2] and can be tighter in some cases than the Gallot-Kounias [3]-[5] and Prékopa-Gao [6] bounds which require more information on the events probabilities. We next consider bounds that fully exploit knowledge of {P(Ai)} and {P(Ai ∩ Aj)}. We establish new numerical lower/upper bounds on the union probability by solving a linear programming problem with equation variables. These bounds coincide with the optimal lower/upper bounds when N ≤ 7 and are guaranteed to be sharper than the optimal lower/upper bounds of [1], [2] that use {P(Ai)} and {Σj P(Ai ∩ Aj)}.
KW - communication systems
KW - linear programming
KW - probability of error analysis
KW - Union probability
KW - upper and lower bounds
UR - http://www.scopus.com/inward/record.url?scp=84969815923&partnerID=8YFLogxK
U2 - 10.1109/ISIT.2015.7282758
DO - 10.1109/ISIT.2015.7282758
M3 - Article in proceedings
AN - SCOPUS:84969815923
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1761
EP - 1765
BT - Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - IEEE International Symposium on Information Theory, ISIT 2015
Y2 - 14 June 2015 through 19 June 2015
ER -
ID: 362747061