On the Secure Degrees-of-Freedom of the Multiple-Access-Channel

Abstract

A $K$-user secure Gaussian Multiple-Access-Channel (MAC) with an external eavesdropper is considered in this paper. An achievable rate region is established for the secure discrete memoryless MAC. The secrecy sum capacity of the degraded Gaussian MIMO MAC is proven using Gaussian codebooks. For the non-degraded Gaussian MIMO MAC, an algorithm inspired by interference alignment technique is proposed to achieve the largest possible total Secure-Degrees-of-Freedom (S-DoF). When all the terminals are equipped with a single antenna, Gaussian codebooks have shown to be inefficient in providing a positive S-DoF. Instead, a novel secure coding scheme is proposed to achieve a positive S-DoF in the single antenna MAC. This scheme converts the single-antenna system into a multiple-dimension system with fractional dimensions. The achievability scheme is based on the alignment of signals into a small sub-space at the eavesdropper, and the simultaneous separation of the signals at the intended receiver. Tools from the field of Diophantine Approximation in number theory are used to analyze the probability of error in the coding scheme. It is proven that the total S-DoF of $\frac{K-1}{K}$ can be achieved for almost all channel gains. For the other channel gains, a multi-layer coding scheme is proposed to achieve a positive S-DoF. As a function of channel gains, therefore, the achievable S-DoF is discontinued.

arXiv commentThe conference version of this work has been submitted to ISIT 2010

References in corpus (4)

• Secure Transmission with Multiple Antennas II: The MIMOME Wiretap Channel
• Cooperation with an Untrusted Relay: A Secrecy Perspective
• Real Interference Alignment with Real Numbers
• Providing Secrecy With Structured Codes: Tools and Applications to Two-User Gaussian Channels

Cited by in corpus (8)

• Secure Degrees of Freedom of One-hop Wireless Networks
• Secure Degrees of Freedom of MIMO X-Channels with Output Feedback and Delayed CSIT
• Secure Degrees of Freedom of Wireless X Networks Using Artificial Noise Alignment
• Secure Degrees of Freedom Regions of Multiple Access and Interference Channels: The Polytope Structure
• Secure Communication in Uplink Transmissions: User Selection and Multiuser Secrecy Gain
• Adding Common Randomness Can Remove the Secrecy Constraints in Communication Networks
• Blind MIMOME Wiretap Channel with Delayed CSIT
• MIMO Multiple Access Channel with an Arbitrarily Varying Eavesdropper