Polar coding for the broadcast channel with confidential messages

We develop a low-complexity and secrecy capacity achieving polar coding scheme for the discrete memoryless wiretap channel. Our scheme extends previous work by using a nearly optimal amount of uniform randomness in the stochastic encoder, and avoiding assumptions regarding the symmetry or degraded nature of the channels. The price paid for these extensions is that the encoder and decoder are required to share a secret seed of negligible size. We also highlight a close conceptual connection between the proposed polar coding scheme and a random binning proof of the secrecy capacity.