LDPC Codes for the Gaussian Wiretap Channel

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. The proposed coding scheme is asymptotically effective in the sense that it yields a bit-error rate (BER) very close to 0.5 for an eavesdropper whose signal-to-noise ratio (SNR) is lower than the threshold SNR <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> , even if the eavesdropper has the ability to use a bitwise maximum a posteriori (MAP) decoder. Such codes also achieve high reliability for the friendly parties provided they have an SNR above a second threshold SNR <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> . It is shown how asymptotically optimized LDPC codes are designed with differential evolution where the goal is to achieve high reliability between friendly parties while keeping the security gap SNR <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> /SNR <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</i> as small as possible to protect against passive eavesdroppers. The proposed coding scheme is encodable in linear time, 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.