  We explore the low-frequency noise of interacting electrons in a
one-dimensional structure (quantum wire or interaction-coupled edge states)
with counterpropagating modes, assuming a single channel in each direction. The
system is driven out of equilibrium by a quantum point contact (QPC) with an
applied voltage, which induces a double-step energy distribution of incoming
electrons on one side of the device. A second QPC serves to explore the
statistics of outgoing electrons. We show that measurement of a low-frequency
noise in such a setup allows one to extract the Luttinger liquid constant $K$
which is the key parameter characterizing an interacting 1D system. We evaluate
the dependence of the zero-frequency noise on $K$ and on parameters of both
QPCs (transparencies and voltages).
