MAC Wiretap Channels with Confidential and Open Messages: Improved Achievable Region and Low-complexity Precoder Design
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This paper investigates the achievable region and precoder design for multiple access wiretap (MAC-WT) channels, where each user transmits both secret and open (i.e., non-confidential) messages. All these messages are intended for the legitimate receiver (or Bob for brevity) and the eavesdropper (Eve) is interested only in the secret messages of all users. By allowing users with zero secret message rate to act as conventional MAC channel users with no wiretapping, we show that the achievable region of the discrete memoryless (DM) MAC-WT channel given in [1] can be enlarged. In [1], the achievability was proven by considering the two-user case, making it possible to prove a key auxiliary lemma by directly using the Fourier-Motzkin elimination procedure. However, this approach does not generalize to the case with any number of users. In this paper, we provide a new region that generally enlarges that in [1] and provide general achievability proof. Furthermore, we consider the Gaussian vector (GV) MAC-WT channel and maximize the sum secrecy rate by precoder design. Although this non-convex problem can be solved by the majorization minimization (MM) technique, this suffers from an extremely high computational complexity. Instead, we propose a simultaneous diagonalization based low-complexity (SDLC) method to maximize the secrecy rate of a simple single-user wiretap channel, and then use this method to iteratively optimize the covariance matrix of each user in the GV MAC-WT channel at hand. Simulation results show that, compared with existing approaches, the SDLC scheme achieves similar secrecy performance but requires much lower complexity. It is also shown that the system spectral efficiency can be significantly increased by simultaneously transmitting secret and open messages.
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