  The basic problem of secure bidirectional relaying involves two users who
want to exchange messages via an intermediate "honest-but-curious" relay node.
There is no direct link between the users, all communication must take place
via the relay node. The links between the user nodes and the relay are wireless
links with Gaussian noise. It is required that the users' messages be kept
secure from the relay. In prior work, we proposed coding schemes based on
nested lattices for this problem, assuming that the channel gains from the two
user nodes to the relay are identical. We also analyzed the power-rate tradeoff
for secure and reliable message exchange using our coding schemes. In this
paper, we extend our prior work to the case when the channel gains are not
necessarily identical, and are known to the relay node but perhaps not to the
users. We show that using our scheme, perfect secrecy can be obtained only for
certain values of the channel gains, and analyze the power-rate tradeoff in
these cases. We also make similar observations for our strongly-secure scheme.
