We analyse the production of a Higgs boson in association with a top--antitop-quark pair in the Standard Model at the LHC. Considering the final state consisting of four b jets, two jets, one identified charged lepton and missing energy, we examine the irreducible background for the production rate and several kinematical distributions. While ttH production and decay is roughly a fourth of the full process for the final state specified above, ttbb production constitutes the main contribution with about $92%$. Surprisingly, interference effects result in a reduction of the cross-section by five per cent. Furthermore, we consider NLO QCD corrections for the production of a Higgs boson, two charged leptons, two neutrinos, and two b jets. We discuss the size of the corrections and the scale dependence for the integrated cross section and different distributions. For the integrated cross section we find a $K$ factor of 1.17 and a reduction of the scale dependence from $30%$ at leading order to $5%$ at next-to-leading order.
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