  In this article, we report on the computation of the NLO QCD corrections to
${\rm p}{\rm p} \to \mu^-\bar\nu_{\mu}{\rm e}^+\nu_{\rm e}\bar{\rm b}{\rm
b}\bar{\rm b}{\rm b}$ at the LHC, which is an irreducible background to ${\rm
p}{\rm p}\to{\rm t}\bar{\rm t}{\rm H}\bigl(\to{\rm b}\bar{\rm b}\bigr)$. This
is the first time that a full NLO computation for a $2\to8$ process with 6
external strongly-interacting partons is made public. No approximations are
used, and all off-shell and interference effects are taken into account. Cross
sections and differential distributions from the full computation are compared
to results obtained by using a double-pole approximation for the top quarks.
The difference between the full calculation and the one using the double-pole
approximation is in general below 5\% but can reach 10\% in some regions of
phase space.
