  We report on our recent calculation for the off-shell $t\bar{t}b\bar{b}$
process in the di-lepton decay channel at the LHC. Our results take into
account NLO QCD corrections for the complete $pp\to e^+\nu_e\mu^- \bar{\nu}_\mu
b\bar{b}b\bar{b}$ process, and include all double, single and non-resonant
contributions. We investigate the size of the corrections and their associated
theoretical uncertainties. We also briefly comment on the impact of different
$b$ jet definitions on our results.
