Semantically Secure Lattice Codes for Compound MIMO Channels

We consider compound multi-input multi-output (MIMO) wiretap channels where minimal channel state information at the transmitter (CSIT) is assumed. Code construction is given for the special case of isotropic mutual information, which serves as a conservative strategy for general cases. Using the flatness factor for MIMO channels, we propose lattice codes universally achieving the secrecy capacity of compound MIMO wiretap channels up to a constant gap (measured in nats) that is equal to the number of transmit antennas. The proposed approach improves upon existing works on secrecy coding for MIMO wiretap channels from an error probability perspective, and establishes information theoretic security (in fact semantic security). We also give an algebraic construction to reduce the code design complexity, as well as the decoding complexity of the legitimate receiver. Thanks to the algebraic structures of number fields and division algebras, our code construction for compound MIMO wiretap channels can be reduced to that for Gaussian wiretap channels, up to some additional gap to secrecy capacity.Comment: IEEE Trans. Information Theory, to appea

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201

Precoded Integer-Forcing Universally Achieves the MIMO Capacity to Within a Constant Gap

An open-loop single-user multiple-input multiple-output communication scheme is considered where a transmitter, equipped with multiple antennas, encodes the data into independent streams all taken from the same linear code. The coded streams are then linearly precoded using the encoding matrix of a perfect linear dispersion space-time code. At the receiver side, integer-forcing equalization is applied, followed by standard single-stream decoding. It is shown that this communication architecture achieves the capacity of any Gaussian multiple-input multiple-output channel up to a gap that depends only on the number of transmit antennas.Comment: to appear in the IEEE Transactions on Information Theor

Capacity of Compound MIMO Gaussian Channels with Additive Uncertainty

This paper considers reliable communications over a multiple-input multiple-output (MIMO) Gaussian channel, where the channel matrix is within a bounded channel uncertainty region around a nominal channel matrix, i.e., an instance of the compound MIMO Gaussian channel. We study the optimal transmit covariance matrix design to achieve the capacity of compound MIMO Gaussian channels, where the channel uncertainty region is characterized by the spectral norm. This design problem is a challenging non-convex optimization problem. However, in this paper, we reveal that this problem has a hidden convexity property, which can be exploited to map the problem into a convex optimization problem. We first prove that the optimal transmit design is to diagonalize the nominal channel, and then show that the duality gap between the capacity of the compound MIMO Gaussian channel and the min-max channel capacity is zero, which proves the conjecture of Loyka and Charalambous (IEEE Trans. Inf. Theory, vol. 58, no. 4, pp. 2048-2063, 2012). The key tools for showing these results are a new matrix determinant inequality and some unitarily invariant properties.Comment: 8 pages, submitted to IEEE Transactions on Information Theor

On the Secrecy Degress of Freedom of the Multi-Antenna Block Fading Wiretap Channels

We consider the multi-antenna wiretap channel in which the transmitter wishes to send a confidential message to its receiver while keeping it secret to the eavesdropper. It has been known that the secrecy capacity of such a channel does not increase with signal-to-noise ratio when the transmitter has no channel state information (CSI) under mild conditions. Motivated by Jafar's robust interference alignment technique, we study the so-called staggered multi-antenna block-fading wiretap channel where the legitimate receiver and the eavesdropper have different temporal correlation structures. Assuming no CSI at transmitter, we characterize lower and upper bounds on the secrecy degrees of freedom (s.d.o.f.) of the channel at hand. Our results show that a positive s.d.o.f. can be ensured whenever two receivers experience different fading variation. Remarkably, very simple linear precoding schemes provide the optimal s.d.o.f. in some cases of interest.Comment: to appear in Proc. of IEEE International Symposium on Information Theory (ISIT2010