LDPC Codes over Gaussian Multiple Access Wiretap Channel

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.