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

TL;DR

This paper investigates the secure degrees-of-freedom in multi-user Gaussian MACs with eavesdroppers, proposing novel coding schemes and algorithms to maximize secure communication rates, especially in single-antenna scenarios.

Contribution

It introduces new secure coding schemes and an interference alignment inspired algorithm to achieve positive S-DoF in various Gaussian MAC configurations.

Findings

Achieves total S-DoF of (K-1)/K for almost all channel gains.

Proposes a multi-layer coding scheme for certain channel gains.

Demonstrates the inefficiency of Gaussian codebooks in single-antenna MACs.

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.