Nested Polar Codes for Wiretap and Relay Channels

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.