  We show that polar codes asymptotically achieve the whole
capacity-equivocation region for the wiretap channel when the wiretapper's
channel is degraded with respect to the main channel, and the weak secrecy
notion is used. Our coding scheme also achieves the capacity of the physically
degraded receiver-orthogonal relay channel. We show simulation results for
moderate block length for the binary erasure wiretap channel, comparing polar
codes and two edge type LDPC codes.
