  We investigate the effect of interactions on shot noise in $\nu=2$ quantum
Hall edges, where a repulsive coupling between co-propagating edge modes is
expected to give rise to charge fractionalization. Using the method of
non-equilibrium bosonization, we find that even asymptotically the edge
distribution function depends in a sensitive way on the interaction strength
between the edge modes. We compute shot noise and Fano factor from the
asymptotic distribution function, and from comparison with a reference model of
fractionalized excitations we find that the Fano factor can be close to the
value of the fractionalized charge.
