LDPC codes for physical layer security

Abstract

This paper presents a coding scheme for the Gaussian wiretap channel based on low-density parity-check (LDPC) codes. The messages are transmitted over punctured bits to hide data from eavesdroppers. It is shown that this method is asymptotically effective in the sense that it yields a BER very close to 0.5 for an eavesdropper whose SNR is lower than the threshold SNRE, even if the eavesdropper has the ability to use a bitwise MAP decoder. Such codes also achieve high reliability for the friendly parties provided they have an SNR above a second threshold SNRB. It is shown how asymptotically optimized LDPC codes can be designed with differential evolution where the goal is to achieve high reliability between friendly parties and security against a passive eavesdropper while keeping the security gap SNRB/SNRE as small as possible. The proposed coding scheme is applicable at finite block lengths and can be combined with existing cryptographic schemes to deliver improved data security by taking advantage of the stochastic nature of many communication channels.