Polar Coding for the Wiretap Channel With Shared Key

The wiretap channel with shared key (WTC-K) refers to the classic wiretap channel with a secret key of arbitrary rate shared between the transmitter and the legitimate receiver. While the secrecy capacity of WTC-K has been obtained using random coding arguments, in this paper, we propose a low-complexity polar coding scheme achieving the secrecy capacity under the strong secrecy condition. Our construction consists of choosing the sets of information indices and using the shared key properly. Specifically, we utilize the structure of superposition coding in the proposed scheme.