Jensen-Cotes Upper and Lower Bounds on the Gaussian -Function and Related Functions Giuseppe Thadeu Freitas de Abreu, Senior Member, IEEE

[1]  Chintha Tellambura,et al.  Efficient computation of erfc(x) for large arguments , 2000, IEEE Trans. Commun..

[2]  B. K. Ghosh,et al.  Some Monotonicity Theorems for χ2, F and T Distributions with Applications , 1973 .

[3]  A. Laforgia,et al.  An inequality for the product of two integrals relating to the incomplete gamma function. , 2000 .

[4]  Mohamed-Slim Alouini,et al.  Digital Communication Over Fading Channels: A Unified Approach to Performance Analysis , 2000 .

[5]  Dariush Divsalar,et al.  Some new twists to problems involving the Gaussian probability integral , 1998, IEEE Trans. Commun..

[6]  Marvin K. Simon,et al.  The Nuttall Q function - its relation to the Marcum Q function and its application in digital communication performance evaluation , 2002, IEEE Trans. Commun..

[7]  Yin Sun,et al.  Inequalities for the generalized Marcum Q-function , 2008, Appl. Math. Comput..

[8]  J. Nicholas Laneman,et al.  Modulation and demodulation for cooperative diversity in wireless systems , 2006, IEEE Transactions on Wireless Communications.

[9]  S. Yousefi,et al.  A simple form for the two-dimensional Q-function suitable for performance evaluation of communication systems , 2005, 2005 IEEE 61st Vehicular Technology Conference.

[10]  J. Craig.  A new, simple and exact result for calculating the probability of error for two-dimensional signal constellations , 1991, MILCOM 91 - Conference record.

[11]  Árpád Baricz,et al.  Mills' ratio: Monotonicity patterns and functional inequalities , 2008 .

[12]  Norman C. Beaulieu.  A simple series for personal computer computation of the error function Q(·) , 1989, IEEE Trans. Commun..

[13]  Marvin K. Simon,et al.  Single integral representations of certain integer powers of the Gaussian Q-function and their application , 2002, IEEE Communications Letters.

[14]  W. Gautschi.  Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function , 1959 .

[15]  George K. Karagiannidis,et al.  An Improved Approximation for the Gaussian Q-Function , 2007, IEEE Communications Letters.

[16]  Per Ola Börjesson,et al.  Simple Approximations of the Error Function Q(x) for Communications Applications , 1979, IEEE Trans. Commun..

[17]  Rong Li,et al.  A New Geometric View of the First-Order Marcum Q-Function and Some Simple Tight Erfc-Bounds , 2006, 2006 IEEE 63rd Vehicular Technology Conference.

[18]  Marco Chiani,et al.  New exponential bounds and approximations for the computation of error probability in fading channels , 2003, IEEE Trans. Wirel. Commun..

[19]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[20]  Seungkeun Park,et al.  A Generic Craig Form for the Two-Dimensional Gaussian Q-Function , 2007 .

[21]  Horst Alzer,et al.  On some inequalities for the incomplete gamma function , 1997, Math. Comput..

[22]  Mary Beth Ruskai,et al.  Study of a Class of Regularizations of 1/|x| Using Gaussian Integrals , 2000, SIAM J. Math. Anal..

[23]  D. Owen.  Handbook of Mathematical Functions with Formulas , 1965 .

[24]  Rong Li,et al.  Generic Exponential Bounds on the Generalized Marcum Q-Function via the Geometric Approach , 2007, IEEE GLOBECOM 2007 - IEEE Global Telecommunications Conference.

[25]  George K. Karagiannidis,et al.  On the Monotonicity of the Generalized Marcum and Nuttall ${Q}$ -Functions , 2007, IEEE Transactions on Information Theory.

[26]  Rong Li,et al.  Computing and Bounding the Generalized Marcum Q-Function via a Geometric Approach , 2006, 2006 IEEE International Symposium on Information Theory.

[27]  George K. Karagiannidis,et al.  Lower and upper bounds for the generalized Marcum and Nuttall Q-functions , 2008, 2008 3rd International Symposium on Wireless Pervasive Computing.

[28]  Hongbin Li,et al.  Differential Modulation for Cooperative Wireless Systems , 2007, IEEE Transactions on Signal Processing.