## Computing the Meta-Converse Bound: A Saddlepoint Approximation of Hypothesis Testing

### Gonzalo Vazquez Vilar (Universidad Carlos III de Madrid)

**Abstract: **

In channel coding, binary hypothesis testing has been instrumental in the derivation of several lower bounds to the error probability, one prominent example the meta-converse bound. In this talk, we propose a saddlepoint approximation to the error probability of a binary hypothesis test with certain parameters. This approximation is then used to efficiently compute the metaconverse bound for moderate block-lengths in several cases of interest. The resulting expression can be numerically optimized when operating far from capacity, e.g., when the pay-load is small in a machine-to-machine transmission. Joint work with: Albert Guillén i Fàbregas (ICREA, Universitat Pompeu Fabra, University of Cambridge)