Recently, Geng et al. have shown that from the perspective of generalized degrees of freedom (GDoF), power control and treating interference as noise (TIN) is optimal for a broad class of Gaussian interference channels. In this work, we show that for TIN-optimal interference channels identified by Geng et al., secrecy constraints on unintended messages incur no GDoF penalty, which leads us to a secure capacity region characterization within a constant gap.
Secure GDoF of K -User Gaussian Interference Channels: When Secrecy Incurs No Penalty
Recently, Geng et al. have shown that from the perspective of generalized degrees of freedom (GDoF), power control and treating interference as noise (TIN) is optimal for a broad class of Gaussian interference channels. In this work, we show that for TIN-optimal interference channels identified by Geng et al., secrecy constraints on unintended messages incur no GDoF penalty, which leads us to a secure capacity region characterization within a constant gap.
We consider a secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. For the symmetric case, this simple scheme is optimal when the interference-to-signal ratio (all link strengths in decibel scale) is no more than 2/3. However, when the ratio is more than 2/3, we show that this simple scheme is not optimal anymore and a scheme with cooperative jamming is proposed to achieve the optimal secure sum generalized degrees-of-freedom (GDoF). Specifically, for the symmetric case, we complete the optimal secure sum GDoF characterization for any interference regimes.
We consider a secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. For the symmetric case, this simple scheme is optimal when the interference-to-signal ratio (all link strengths in decibel scale) is no more than 2/3. However, when the ratio is more than 2/3, we show that this simple scheme is not optimal anymore and a scheme with cooperative jamming is proposed to achieve the optimal secure sum generalized degrees-of-freedom (GDoF). Specifically, for the symmetric case, we complete the optimal secure sum GDoF characterization for all the interference regimes, for almost all channel gains (except for a set of channel gains of measure zero).
We consider a secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. For the symmetric case, this simple scheme is optimal when the interference-to-signal ratio (all link strengths in decibel scale) is no more than 2/3. However, when the ratio is more than 2/3, we show that this simple scheme is not optimal anymore and a scheme with cooperative jamming is proposed to achieve the optimal secure sum generalized degrees-of-freedom (GDoF). Specifically, for the symmetric case, we complete the optimal secure sum GDoF characterization for all the interference regimes.
In many communication networks, secrecy constraints usually incur an extra limit in capacity (or generalized degrees-of-freedom, GDoF), in the sense that a penalty in capacity (or GDoF) is incurred due to the secrecy constraints. Over the past decades a significant amount of effort has been made by the researchers to understand the limits of secrecy constraints in communication networks. In this work, we focus on how to break the limits of secrecy constraints in communication networks, i.e., how to remove the penalty in GDoF due to the secrecy constraints. We begin with three basic settings: a two-user symmetric Gaussian interference channel with confidential messages, a symmetric Gaussian wiretap channel with a helper, and a two-user symmetric Gaussian multiple access wiretap channel. Interestingly, in this work we show that adding common randomness at the transmitters can totally remove the penalty in sum GDoF or GDoF region of the three settings considered here. The results reveal that adding common randomness at the transmitters is a powerful way to break the limits of secrecy constraints in communication networks. Common randomness can be generated offline. The role of the common randomness is to jam the information signal at the eavesdroppers, without causing too much interference at the legitimate receivers. To accomplish this role, a new method of Markov chain-based interference neutralization is proposed in the achievability schemes utilizing common randomness. From the practical point of view, we hope to use less common randomness to break the limits of secrecy constraints. With this motivation, for most of the cases we characterize the minimal GDoF of common randomness to break the limits of secrecy constraints, based on our derived converses.
The sum secure degrees of freedom (s.d.o.f.) of the K-user interference channel (IC) with secrecy constraints has been determined recently as equation [1], [2]. In this paper, we determine the entire s.d.o.f. region of this channel model. The converse includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. The extreme points of the converse region are achieved by a (K - m)-user IC with confidential messages, m helpers, and N external eavesdroppers, for m ≥ 1 and a finite N. A byproduct of our results in this paper is that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point.
The achievable rate region and degrees of freedom are studied for interference channels with confidential messages under strong secrecy constraints. The problem is studied based on the framework of Han and Verdacutetextrmu's channel resolvability theory. It is shown that if the random binning rate for securing a confidential message is slightly above the resolution of its corresponding wiretapped channel, strong secrecy can be guaranteed. At first, the information-spectrum method introduced by Han and Verdacutetextrmu is generalized to an arbitrary interference channel to obtain a direct channel resolvability result. After specifying the channel transition probability, the derived resolvability results are shown to be the achievable strong secrecy rates for the stationary and memoryless interference channel. As an application, the secure degrees of freedom (SDOF) for the K-user Gaussian interference channel with confidential messages are investigated under strong secrecy constraints. It is shown that the optimal SDOF of the considered network is fracK−12K−1 for each user, which equals to its counterpart with weak secrecy constraints. The optimal SDOF scheme is achieved by combining the resolvability-based secrecy coding and artificial noise alignment on the real line. A suboptimal ergodic secure alignment is also proposed for the time-varying interference channels to achieve a sum SDOF of fracK−32K−2 for each user. Following the footsteps of Hayashi and of Bloch and Laneman, our results provide further evidence that channel resolvability can be a powerful and general framework for strong secrecy analysis in multiuser networks.