Self-Secure Capacity-Achieving Feedback Schemes of Gaussian Multiple-Access Wiretap Channels with Degraded Message Sets

The Schalkwijk-Kailath (SK) scheme, which achieves the capacity of the point-to-point white Gaussian channel with feedback, is secure by itself and also achieves the secrecy capacity of the Gaussian wiretap channel with feedback, i.e., the SK scheme is a self-secure capacity-achieving (SSCA) feedback scheme for the Gaussian wiretap channel. For the multi-user wiretap channels, recently, it has been shown that Ozarow's capacity-achieving feedback scheme for the two-user Gaussian multiple-access channel (GMAC) is the SSCA feedback scheme for the two-user Gaussian multiple-access wiretap channel (GMAC-WT). In this paper, first, we propose a capacity-achieving feedback scheme for the two-user GMAC with degraded message sets (GMAC-DMS), and show that this scheme is the SSCA feedback scheme for the two-user GMAC-WT with degraded message sets (GMAC-WT-DMS). Next, we extend the above scheme to the two-user GMAC-DMS with noncausal channel state information at the transmitters (NCSIT), and show that the extended scheme is capacity-achieving and also a SSCA feedback scheme for the two-user GMAC-WT-DMS with NCSIT. Finally, we derive outer bounds on the secrecy capacity regions of the two-user GMAC-WT-DMS with or without NCSIT, and numerical results show the rate gains by the feedback.