LDPC Codes over Gaussian Multiple Access Wiretap Channel

TL;DR

This paper proposes a secure coding scheme using LDPC codes for the Gaussian multiple access wiretap channel, effectively reducing the security gap and approaching the secrecy rate region under various power conditions.

Contribution

It introduces a novel LDPC-based secure coding scheme with optimized puncturing for GMAC-WT, enhancing secrecy performance compared to existing methods.

Findings

Achieves a small security gap close to the secrecy rate region.

Effectively applies optimized puncturing using EXIT chart analysis.

Performs well under both equal and unequal power conditions.

Abstract

We study the problem of two-user Gaussian multiple access channel (GMAC) in the presence of an external eavesdropper. In this problem, an eavesdropper receives a signal with a lower signal-to-noise ratio (SNR) compared to the legitimate receiver and all transmitted messages should be kept confidential against the eavesdropper. For this purpose, we propose a secure coding scheme on this channel which utilizes low-density parity-check (LDPC) codes by employing random bit insertion and puncturing techniques. At each encoder, the confidential message with some random bits as a random message are systematically encoded, and then the associated bits to the confidential message are punctured. Next, the encoders send their unpunctured bits over a Gaussian multiple access wiretap channel (GMAC-WT). The puncturing distribution applied to the LDPC code is considered in two cases: random and optimized. We utilize a modified extrinsic information transfer (EXIT) chart analysis to optimize the puncturing distribution for each encoder. The security gap is used as a measure of secrecy for the sent messages over GMAC-WT which should be made as small as possible. We compare the achieved secure rate pair with an achievable secrecy rate region of GMAC-WT to show the effective performance of the proposed scheme. In this paper, equal and unequal power conditions at the transmitters are investigated. For both cases, we attain a fairly small security gap which is equivalent to achieve the points near the secrecy rate region of GMAC-WT.