  We study the contributions from radiation to $p_{\perp}$-broadening of a high
energy parton traversing a QCD medium with a finite length $L$. The interaction
between the parton and the medium is described by decorrelated static multiple
scattering. Amplitudes of medium-induced gluon emission and parton self-energy
diagrams are evaluated in the soft gluon limit in the BDMPS formalism. We find
both the double-logarithmic correction from incoherent scattering, which is
parametrically the same as that in single scattering, and the logarithmic
correction from the LPM effect. Therefore, we expect a parametrically large
correction from radiation to the medium-induced $p_\perp$-broadening in
perturbative QCD.
