  The first repeating fast radio burst source, FRB 121102, is observed to emit
bursts periodically. We show that FRB 121102 can be interpreted as an
interacting neutron star binary system with an orbital period of 159 days. We
develop a binary comb model by introducing an eccentricity in the orbit.
Besides the original funnel mode of the binary comb model, which was applied to
FRB 180916.J0158+65 by Ioka and Zhang 2020, we also identify two new modes of
the binary comb model, i.e. the tau-crossing mode and the inverse funnel mode,
and apply them to interpret FRB 121102. These new developments expand the
applicable parameter space, allowing the companion star to be a massive star, a
massive black hole, or a supermassive black hole, with the latter two having
larger parameter spaces. These models are also consistent with other
observations, such as the persistent bright radio counterpart associated with
the source. We also argue that the observed frequency dependence of the active
window does not disfavor the binary comb model, in contrast to recent claims,
and propose two possible scenarios to interpret the data.
