Full off-shell NLO QCD predictions for $t\bar{t}b\bar{b}$ at the LHC

We report on state-of-the-art theoretical predictions for $pp\to t\bar{t}b\bar{b}$ including full off-shell effects in the di-lepton decay channel at NLO QCD accuracy. We briefly discuss the impact of NLO QCD corrections on differential distributions and also asses theoretical uncertainties from scale and PDF dependence. Furthermore, we propose a simple kinematic reconstruction in order to distinguish $b$ jets originating from top-quark decays from arising from gluon splittings.