  In a three-node network a half-duplex relay node enables bidirectional
communication between two nodes with a spectral efficient two phase protocol.
In the first phase, two nodes transmit their message to the relay node, which
decodes the messages and broadcast a re-encoded composition in the second
phase. In this work we determine the capacity region of the broadcast phase. In
this scenario each receiving node has perfect information about the message
that is intended for the other node. The resulting set of achievable rates of
the two-phase bidirectional relaying includes the region which can be achieved
by applying XOR on the decoded messages at the relay node. We also prove the
strong converse for the maximum error probability and show that this implies
that the $[\eps_1,\eps_2]$-capacity region defined with respect to the average
error probability is constant for small values of error parameters $\eps_1$,
$\eps_2$.
