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On the optimality of polar codes for the deterministic wiretap channel

The wiretap channel introduced by Wyner [1] in 1975 consists of a transmitter with a confidential message for an intended receiver that needs to be kept secret from an eavesdropper. The secrecy capacity of the wiretap channel quantifies the maximum rate at which a transmitter can reliably send a secret message to its intended recipient without it being decoded by an eavesdropper. While the secrecy capacity is achievable based upon a random-coding argument, constructing channel coding schemes that achieve the secrecy capacity for a general wiretap channel is still an open problem. In this paper, we show that polar coding is an optimal coding scheme in achieving the secrecy capacity for the deterministic wiretap channel, where the channel between the transmitter and the intended receiver and the channel between the transmitter and the eavesdropper are arbitrary and deterministic.