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Strong secrecy for interference channels : Achievable rate region and degrees of freedom

Zhao Wang, Rafael F. Schaefer, Mikael Skoglund, Ming Xiao, H. Vincent Poor

Published Jan 1, 2015• 2 citations
OpenAlex

Abstract

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 Verd$\\acute{\\textrm{u}}$'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 Verd$\\acute{\\textrm{u}}$ 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 $\\frac{K-1}{2K-1}$ 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 $\\frac{K-3}{2K-2}$ 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.

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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\\acute{\\textrm{u}}acutetextrmu'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\\acute{\\textrm{u}}acutetextrmu 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 KKK-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\\frac{K-1}{2K-1}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\\frac{K-3}{2K-2}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.
Interference channels with confidential messages are studied under strong secrecy constraints, based on the framework of channel resolvability theory. It is shown that if the random binning rate for securing a confidential message is above the resolution of its corresponding wiretapped channel, strong secrecy can be guaranteed. The information-spectrum method introduced by Han and Verdú is generalized to an arbitrary interference channel to obtain a direct channel resolvability result as a first step. For stationary and memoryless channels with discrete output alphabets, the results show that the achievable rates under weak and strong secrecy constraints are the same. This result is then generalized to channels with continuous output alphabets by deriving a reverse direction of Pinsker's inequality to bound the secrecy measure from above by a function of the variational distance of relevant distributions. As an application, Gaussian interference channels are studied in which the agreement between the best known weak and strong secrecy rate regions also appear. Following the footsteps of Csiszár, Hayashi and of Bloch and Laneman, these results provide further evidence that channel resolvability is a powerful and general framework for strong secrecy analysis in multiuser networks.
The achievable rate region is studied for interference channels with confidential messages under strong secrecy constraints. The problem is investigated based on the framework of the channel resolvability theory. The information-spectrum method introduced by Han and Verdu is first generalized to an arbitrary interference channel to obtain a direct channel resolvability result. The derived resolvability results are then shown to be the achievable strong secrecy rates for the stationary and memoryless interference channel. Our results provide further evidence that channel resolvability can be a powerful and general framework for strong secrecy analysis in multiuser networks.
This paper studies the frequency/time selectiveK-user Gaussian interference channel with secrecy constraints. Two distinct models, namely the interference channel with confidential messages and the interference channel with an external eavesdropper, are analyzed. The key difference between the two models is the lack of channel state information (CSI) of the external eavesdropper. Using interference alignment along with secrecy precoding, it is shown that each user can achieve non-zero secure degrees of freedom (DoF) for both cases. More precisely, the proposed coding scheme achieves [(K-2)/(2K-2)] secure DoF with probability one per user in the confidential messages model. For the external eavesdropper scenario, on the other hand, it is shown that each user can achieve [(K-2)/(2K)] secure DoF in the ergodic setting. Remarkably, these results establish the positive impact of interference on the secrecy capacity region of wireless networks.
Previous work showed that the X network with M transmitters, N receivers has MN/M+N−1 degrees of freedom. In this work we study the degrees of freedom of the X network with secrecy constraints, i.e. the X network where some/all messages are confidential. We consider the M × N network where all messages are secured and show that N(M−1)/M+N−1 degrees of freedom can be achieved. Secondly, we show that if messages from only M − 1 transmitters are confidential, then MN/M+N−1 degrees of freedom can be achieved meaning that there is no loss of degrees of freedom because of secrecy constraints. We also consider the achievable secure degrees of freedom under a more conservative secrecy constraint. We require that messages from any subset of transmitters are secure even if other transmitters are compromised, i.e., messages from the compromised transmitter are revealed to the unintended receivers. We also study the achievable secure degrees of freedom of the K user Gaussian interference channel under two different secrecy constraints where 1/2 secure degrees of freedom per message can be achieved. The achievable scheme in all cases is based on random binning combined with interference alignment.
In this paper, we determine the entire secure degrees of freedom (s.d.o.f.) regions of the K-user Gaussian multiple access (MAC) wiretap channel and the K-user interference channel (IC) with secrecy constraints. For the IC, we consider three secrecy constraints: K-user IC with an external eavesdropper (ICEE), K-user IC with confidential messages (IC-CM), and their combination Kuser IC with confidential messages and external eavesdropper (IC-CM-EE). The converse for the IC includes constraints both due to secrecy as well as due to interference. For the IC, 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 four-user case, i.e., the twoor three-user cases do not illustrate the full generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. In particular, the extreme points of the MAC region are achieved by an m-user MAC wiretap channel with K - m helpers, i.e., by setting K - m users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC 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, for both MAC and IC channel models.
This paper studies the K-user Gaussian interference channel with secrecy constraints. Two distinct network models, namely the interference channel with confidential messages and the one with an external eavesdropper, are analyzed. Using interference alignment along with secrecy pre-coding at each transmitter, it is shown that each user in the network can achieve non-zero secure Degrees of Freedoms (DoFs) in both scenarios. In particular, the proposed coding scheme achieves K−2/2K−2 secure DoFs for each user in the interference channel with confidential messages model, and K−2/2K secure DoFs in the case of an external eavesdropper. The fundamental difference between the two scenarios stems from the lack of channel state information (CSI) about the external eavesdropper. Remarkably, the results establish the positive impact of interference on the secrecy capacity of wireless networks.