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An upper bound on the error induced by saddlepoint approximations - Applications to information theory

Dadja Anade 1 Jean-Marie Gorce 1 Philippe Mary 2 Samir Perlaza 3
1 MARACAS - Modèle et algorithmes pour des systèmes de communication fiables
CITI - CITI Centre of Innovation in Telecommunications and Integration of services, Inria Grenoble - Rhône-Alpes
3 NEO - Network Engineering and Operations
CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This report introduces an upper bound on the absolute difference between: $(a)$~the cumulative distribution function (CDF) of the sum of a finite number of independent and identically distributed random variables; and $(b)$~a saddlepoint approximation of such CDF. This upper bound, which is particularly precise in the regime of large deviations is used to study the dependence testing (DT) bound and the meta converse (MC) bound on the decoding error probability (DEP) in point-to-point memoryless channels. Often, these bounds cannot be analytically calculated and thus, lower and upper bounds become particularly useful. Within this context, the main results include new upper bounds and lower bounds on the DT and MC bounds. A numerical analysis of these bounds is presented in the case of the binary symmetric channel, the additive white Gaussian noise channel, and the additive symmetric $\alpha$-stable noise channel, in which the new bounds are observed to be tight.
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https://hal.inria.fr/hal-02557887
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Submitted on : Tuesday, May 12, 2020 - 3:53:11 PM
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  • HAL Id : hal-02557887, version 3

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Dadja Anade, Jean-Marie Gorce, Philippe Mary, Samir Perlaza. An upper bound on the error induced by saddlepoint approximations - Applications to information theory. [Research Report] RR-9329, INRIA Grenoble - Rhône-Alpes. 2020, pp.1-55. ⟨hal-02557887v3⟩

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