We consider the problem of two transmitters wishing to exchange
information through a relay in the middle. The channels between the
transmitters and the relay are assumed to be synchronized, average
power constrained additive white Gaussian noise channels with a
complex input with complex fading coefficients. In an earlier work,
we considered the case when the channel gains are the same on all
the links and we showed that lattice coding is near-optimal for
high signal-to-noise ratios (SNR). In this work, we consider the case when
the channel gains are asymmetric, i.e. the links are fading independently.
We consider a protocol in which the two nodes first transmit to the realy 
simulataneously during a MAC phase and then the relay broadcasts to the 
two nodes during a broadcast phase. For such a protocol, an upper
bound on the capacity under the sum power constraint on the relays
is obtained as a solution to a convex optimization problem. We show
that a scheme using channel inversion  and lattice decoding can
obtain a rate within 0.09 bits from the upper bound,
under the high SNR approximation. We also consider variations in the
problem setup such as using individual power constraints and suggest
some schemes. These schemes show the advantage of using nested
lattices for the bidirectional relaying problem even in the case of
asymmetric channel gains.