Gaussian Multiuser Wiretap Channels in the Presence of a Jammer-Aided Eavesdropper

Abstract

This paper considers secure communication in the presence of an eavesdropper and a malicious jammer. The jammer is assumed to be oblivious of the communication signals emitted by the legitimate transmitter(s) but can employ any jamming strategy subject to a given power constraint and shares her jamming signal with the eavesdropper. Four such models are considered: (i) the Gaussian point-to-point wiretap channel; (ii) the Gaussian multiple-access wiretap channel; (iii) the Gaussian broadcast wiretap channel; and (iv) the Gaussian symmetric interference wiretap channel. The use of pre-shared randomness between the legitimate users is not allowed in our models. Inner and outer bounds are derived for these four models. For (i), the secrecy capacity is obtained. For (ii) and (iv) under a degraded setup, the optimal secrecy sum-rate is characterized. Finally, for (iii), ranges of model parameter values for which the inner and outer bounds coincide are identified.

Keywords: Gaussian broadcast wiretap channel; Gaussian multiple-access wiretap channel; Gaussian wiretap channel; jamming; secure communication.

Figure 1

The Gaussian wiretap channel in the presence of a jammer-aided eavesdropper.

Figure 2

The Gaussian multiple-access wiretap channel in the presence of a jammer-aided eavesdropper.

Figure 3

The Gaussian broadcast wiretap channel in the presence of a jammer-aided eavesdropper.

Figure 4

The shaded area represents ${\mathcal{R}}_{1,2}^{\mathrm{M}\mathrm{A}\mathrm{C}}(P_1,P_2)$, where $(P_1,P_2,\mathsf{\Lambda },h_1,h_2)=(4,3.3,1.5,0.12,0.11)$. The solid segments represent the rate pairs achievable with Proposition 1.

Figure 5

Region ${\mathcal{R}}_{1,2}(P_1,P_2)$.