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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    • ", [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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    • ". The Gaussian wiretap channel with M helpers. [20], Gaussian wiretap channel with helpers [1], [2], [21]– [23], Gaussian multiple access wiretap channel [24] in ergodic fading setting [25], multiple antenna compound wiretap channel [26], and wireless X network [27]. The exact sum secure d.o.f. was found for a large class of one-hop wireless networks, including the wiretap channel with M helpers, twouser interference channel with confidential messages, and Kuser multiple access wiretap channel in [2], and for all twounicast layered wireless networks in [28], [29]. "
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    ABSTRACT: We consider the Gaussian wiretap channel with M helpers, where no eavesdropper channel state information (CSI) is available at the legitimate entities. The exact secure d.o.f. of the Gaussian wiretap channel with M helpers with perfect CSI at the transmitters was found in [1], [2] to be M/(M+1). One of the key ingredients of the optimal achievable scheme in [1], [2] is to align cooperative jamming signals with the information symbols at the eavesdropper to limit the information leakage rate. This required perfect eavesdropper CSI at the transmitters. Motivated by the recent result in [3], we propose a new achievable scheme in which cooperative jamming signals span the entire space of the eavesdropper, but are not exactly aligned with the information symbols. We show that this scheme achieves the same secure d.o.f. of M/(M+1) in [1], [2] but does not require any eavesdropper CSI; the transmitters blindly cooperative jam the eavesdropper.
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