Differentially Pre-coded Polar Codes for Physical Layer Security

Polar codes can be utilized to enhance physical layer security (PLS) over wiretap channels. Most of the polar-coding based PLS schemes require the channel state information (CSI) of the main channel and that of the eavesdropper's channel. However, the CSI of the eavesdropper's channel is generally unavailable in practice. In this paper, we propose a differentially pre-coded polar coding (DPPC) scheme for systems where the CSI of the eavesdropper's channel is unavailable. The main idea of DPPC is to add a differential pre-coding operation prior to polar coding. In classical polar coding scheme, a legitimate transmitter (Alice) transmits K information bits to a legitimate receiver (Bob), where K is the number of good sub-channels of the main channel. For Bob, all bits transmitted on good sub-channels can be decoded correctly. On the other hand, some of the K information bits lie in the bad sub-channels of the eavesdropper (Eve) and thus cannot be decoded correctly by Eve, given the assumption that the eavesdropper's channel is degraded compared to the main channel. The pre-coding operation introduced in the DPPC scheme XORs a "good"information bit (i.e., the bit that will be decoded correctly by Eve) with a "bad"information bit (i.e., the bit that will not be decoded correctly by Eve), yielding an error propagation at Eve after the inverse operation of the pre-coding. This results in a high BER at Eve. Meanwhile, the error performance of Bob remains unchanged because the pre-coding operation is applied to the K information bits, all of which will be received correctly with polar coding. Simulation results demonstrate that the proposed scheme can achieve transmission reliability and security simultaneously. Moreover, our scheme outperforms the existing candidates in terms of transmission reliability in the high-SNR regime.