Conference Paper

On the Secure Degrees of Freedom of Wireless X Networks

Electr. Eng. & Comput. Sci., Univ. of California, Irvine, CA
DOI: 10.1109/ALLERTON.2008.4797643 Conference: Communication, Control, and Computing, 2008 46th Annual Allerton Conference on
Source: IEEE Xplore


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 times 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.

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    • "Therefore, it is necessary to develop an IA scheme that is capable of guaranteeing secure wireless communications by explicitly taking into account the secrecy constraints imposed by the eavesdropper. The existing contributions on the joint study of IA and secure communications mainly focused on the analysis and design of secure interference networks based on the informationtheoretic concept of achieving a certain maximum degrees of freedom (DoF) [28]–[31]. In contrast to these DoF-based studies , the authors of [32] studied the achievable rate regions of the MIMO interference channel where confidential messages are sent to two receivers. "
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    ABSTRACT: In this paper, we consider the problem of joint transmit precoding (TPC) matrix and receive filter matrix design subject to both secrecy and per-transmitter power constraints in the MIMO interference channel, where $K$ legitimate transmitter-receiver pairs communicate in the presence of an external eavesdropper. Explicitly, we jointly design the TPC and receive filter matrices based on the minimum total mean-squared error (MT-MSE) criterion under a given and feasible information-theoretic degrees of freedom. More specifically, we formulate this problem by minimizing the total MSEs of the signals communicated between the legitimate transmitter-receiver pairs, whilst ensuring that the MSE of the signals decoded by the eavesdropper remains higher than a certain threshold. We demonstrate that the joint design of the TPC and receive filter matrices subject to both secrecy and transmit power constraints can be accomplished by an efficient iterative distributed algorithm. The convergence of the proposed iterative algorithm is characterized as well. Furthermore, the performance of the proposed algorithm, including both its secrecy rate and MSE, is characterized with the aid of numerical results. We demonstrate that the proposed algorithm outperforms the traditional interference alignment (IA) algorithm in terms of both the achievable secrecy rate and the MSE. As a benefit, secure communications can be guaranteed by the proposed algorithm for the MIMO interference channel even in the presence of a "sophisticated/strong" eavesdropper, whose number of antennas is much higher than that of each legitimate transmitter and receiver.
    IEEE Transactions on Information Forensics and Security 10/2015; DOI:10.1109/TIFS.2015.2493888 · 2.41 Impact Factor
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    • ", [22] and artificial noise transmission. We note that the achieved SDOF K(M−1) K+M−1 overlaps with the results in [23]. However, we prove it using a new approach: by proposing an ANA scheme we show that K(M−1) K+M−1 can be achieved for the M ×K XNCM with an external eavesdropper (EE), which implies the same SDOF for the considered network without the EE. 3) The achieved sum SDOF of the XNCM with reconfigurable antennas: Following a similar principle, we generalize the ANA scheme into a blind approach, where CSIT is not required with the help of reconfigurable antennas at the receivers. "
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    ABSTRACT: The problem of transmitting confidential messages in $M \times K$ wireless X networks is considered, in which each transmitter intends to send one confidential message to every receiver. In particular, the secrecy degrees of freedom (SDOF) of the considered network achieved by an artificial noise alignment (ANA) approach, which integrates interference alignment and artificial noise transmission, are studied. At first, an SDOF upper bound is derived for the $M \times K$ X network with confidential messages (XNCM) to be $\frac{K(M-1)}{K+M-2}$. By proposing an ANA approach, it is shown that the SDOF upper bound is tight when either $K=2$ or $M=2$ for the considered XNCM with time/frequency varying channels. For $K,M \geq 3$, it is shown that an SDOF $\frac{K(M-1)}{K+M-1}$ can be achieved, even when an external eavesdropper appears. The key idea of the proposed scheme is to inject artificial noise to the network, which can be aligned in the interference space at receivers for confidentiality. Moreover, for the network with no channel state information at transmitters, a blind ANA scheme is proposed to achieve the SDOF $\frac{K(M-1)}{K+M-1}$ for $K,M \geq 2$, with reconfigurable antennas at receivers. The proposed method provides a linear approach to handle secrecy coding and interference alignment.
    IEEE Transactions on Communications 10/2014; 63(7). DOI:10.1109/TCOMM.2015.2434378 · 1.99 Impact Factor
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    • "The model consists of a sender which transmits information to a legitimate receiver; and this information is meant to be kept secret from an external wiretapper that overhears the transmission. Wyner's basic setup has been extended to study the secrecy capacity of various multiuser channels, such as the broadcast channel [18], [19], the multi-antennas wiretap channel [20]–[23], the multiple access wiretap channel [24]–[28], the relay channel [29]–[31], the interference channel [32], [33] and X networks [34] (the reader may also refer to [35] for a review of many other related contributions). In [36], the authors study a K-user interference channel with security constraints, from a SDoF perspective. "
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    ABSTRACT: We investigate the problem of secure transmission over a two-user multi-input multi-output (MIMO) X-channel in which channel state information is provided with one-unit delay to both transmitters (CSIT), and each receiver feeds back its channel output to a different transmitter. We refer to this model as MIMO X-channel with asymmetric output feedback and delayed CSIT. The transmitters are equipped with M-antennas each, and the receivers are equipped with N-antennas each. For this model, accounting for both messages at each receiver, we characterize the optimal sum secure degrees of freedom (SDoF) region. We show that, in presence of asymmetric output feedback and delayed CSIT, the sum SDoF region of the MIMO X-channel is same as the SDoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver and delayed CSIT. This result shows that, upon availability of asymmetric output feedback and delayed CSIT, there is no performance loss in terms of sum SDoF due to the distributed nature of the transmitters. Next, we show that this result also holds if only output feedback is conveyed to the transmitters, but in a symmetric manner, i.e., each receiver feeds back its output to both transmitters and no CSIT. We also study the case in which only asymmetric output feedback is provided to the transmitters, i.e., without CSIT, and derive a lower bound on the sum SDoF for this model. Furthermore, we specialize our results to the case in which there are no security constraints. In particular, similar to the setting with security constraints, we show that the optimal sum DoF region of the (M,M,N,N)--MIMO X-channel with asymmetric output feedback and delayed CSIT is same as the DoF region of a two-user MIMO BC with 2M-antennas at the transmitter, N-antennas at each receiver, and delayed CSIT. We illustrate our results with some numerical examples.
    IEEE Transactions on Information Forensics and Security 09/2013; 8(11). DOI:10.1109/TIFS.2013.2278936 · 2.41 Impact Factor
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