Construction of Polar Codes Combined with Physical Layer Security on Impulsive Noise Channels

Polar codes are the first proven capacity-achieving codes for any symmetric binary input discrete memoryless channel (B-DMC) and their has been recent interest in their combination with the popular area of physical layer security. Previous work on error-correcting codes and physical layer security has assumed a wiretap channel where each user experiences Gaussian noise, but this paper presents the first results evaluating the performance of polar codes on wiretap channels where both the intended recipient and eavesdropper experience varying levels of impulsive noise. The impulsive noise has a symmetric alpha-stable probability density function (pdf) and density evolution is employed with knowledge of this pdf to construct optimal polar codes for an impulsive environment. Simulation results confirm that the bit error rate (BER) at the eavesdropper is always 0.5 for all signal-to-noise ratios, thus always ensuring secure communication, and we present the very interesting result where this is still achieved when the main channel is more impulsive than the eavesdropper's channel.