Design of the Gaussian wiretap channel with punctured polar codes

A physical layer secrecy coding scheme based on punctured polar codes is proposed in the paper, which aims at the physical layer secure problem under Gaussian wiretap channel, where the punctured position is calculated by the reliability of code-bit. Considering different effects of channel noise on the decoding results, the recovery-error probability of information-bits related to the Bhattacharyya parameter of Gaussian channel is useful for calculating the reliability of code-bit, which contributes to the decision of the punctured positions. Theoretical analysis shows that the eavesdropper has high bit error rate (BER) under SNR threshold, while the authorized user can keep low BER when the noise is over the SNR threshold. Numerical simulation results show that the proposed puncturing scheme reduces the security gap efficiently. The BER of eavesdropper gets close to 0.5 rapidly even though his channel is only a little worse than the authorized channel, while the BER for the authorized channel could fall below a 10-5 . The gap for security between Bob and Eve reduces greatly.