Saddlepoint Approximation of the Error Probability of Binary Hypothesis Testing

We propose a saddlepoint approximation of the error probability of a binary hypothesis test between two i.i.d. distributions. The approximation is accurate, simple to compute, and yields a unified analysis in different asymptotic regimes. The proposed formulation is used to efficiently compute the meta-converse lower bound for moderate block-lengths in several cases of interest. This work has been funded in part by the European Research Council (ERC) under grants 714161 and 725411, by the Spanish Ministry of Economy and Competitiveness under grants TEC2013-41718-R, RYC-201416332, IJCI-2015-27020 and TEC2016-78434-C3 (AEI/FEDER, EU), by the Madrid Autonomous Community under grant S2103/ICE-2845 and by the Spanish Ministry of Education, Culture and Sport under grant FPU14/01274.