Supertight algebraic bounds on the Gaussian Q-function

Authors:
Giuseppe Thadeu Freitas De Abreu
Affiliations:
CWC, University of Oulu, Finland
Venue:
Asilomar'09 Proceedings of the 43rd Asilomar conference on Signals, systems and computers
Year:
2009

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Abstract

We present a pair of new tight and very simple lower and upper bounds on the Gaussian Q-function. The new bounds contain only two exponential terms with a constant and a rational coefficient. Despite having only two algebraic terms, the bounds are as tight as multi-term alternatives obtained from Exponential [1] and Jensen-Cotes [2], [3] families of bounds. An important consequent result is that integer powers of Q(x) can also be tightly bounded both below and above by sums of n + 1 algebraic terms. In addition to offering remarkable accuracy and mathematical tractability combined, the new bounds are very consistent, in which both lower and upper counterparts are similarly tight over the entire domain.