V. M. Zolotarev, One-Dimensional Stable Distributions, 1986.

J. L. Jensen, Saddlepoint Approximations, 1995.

W. Feller, An Introduction to Probability Theory and Its Applications, vol.2, 1971.

H. E. Daniels, Saddlepoint approximations in statistics, vol.25, p.631650, 1954.

H. E. Daniels, Exact saddlepoint approximations, Biometrika, vol.67, issue.1, p.5963, 1980.

H. E. Daniels, Tail probability approximations, International Statistical Review / Revue Internationale de Statistique, vol.55, p.3748, 1987.

N. Temme, The uniform asymptotic expansion of a class of integrals related to cumulative distribution functions, SIAM J. Math. Anal, vol.13, issue.2, p.239253, 1982.

R. Lugannani and S. Rice, Saddle point approximation for the distribution of the sum of independent random variables, Advances in Applied Probability, vol.12, p.475490, 1980.

F. Esscher, On the probability function in the collective theory of risk, Skand. Aktuarie Tidskr, vol.15, p.175195, 1932.

Y. Polyanskiy, H. V. Poor, and S. Verdú, Channel coding rate in the nite blocklength regime, IEEE Transactions on Information Theory, vol.56, p.23072359, 2010.

E. Molavianjazi and J. N. Laneman, A second-order achievable rate region for Gaussian multi-access channels via a central limit theorem for functions, IEEE Transactions on Information Theory, vol.61, p.67196733, 2015.

E. Molavianjazi, A Unied Approach to Gaussian Channels with Finite Blocklength, 2014.

T. Erseghe, Coding in the nite-blocklength regime: Bounds based on Laplace integrals and their asymptotic approximations, IEEE Transactions on Information Theory, vol.62, p.68546883, 2016.

J. Font-segura, G. Vazquez-vilar, A. Martinez, A. G. Fàbregas, and A. Lancho, Saddlepoint approximations of lower and upper bounds to the error probability in channel coding, Proc. of the 52nd Annual Conference on Information Sciences and Systems (CISS), p.16, 2018.

A. Martinez, J. Scarlett, M. Dalai, and A. G. Fàbregas, A complex-integration approach to the saddlepoint approximation for random-coding bounds, Proc. of the 11th International Symposium on Wireless Communications Systems (ISWCS), pp.618-621, 2014.

I. Shevtsova, On the absolute constants in the Berry-Esseen type inequalities for identically distributed summands, 2011.

Y. Polyanskiy, Channel coding: non-asymptotic fundamental limits, 2010.

R. Rr and . Centre-grenoble--rhône-alpes, Inovallée 655 avenue de l'Europe Montbonnot 38334 Saint Ismier Cedex Publisher Inria Domaine de Voluceau -Rocquencourt BP 105 -78153 Le Chesnay Cedex inria, pp.249-6399