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

On the Secrecy Capacity of MIMO Wiretap Channels: Convex Reformulation and Efficient Numerical Methods

This paper presents novel numerical approaches to finding the secrecy capacity of the multiple-input multiple-output (MIMO) wiretap channel subject to multiple linear transmit covariance constraints, including sum power constraint, per antenna power constraints and interference power constraint. An analytical solution to this problem is not known and existing numerical solutions suffer from slow convergence rate and/or high per-iteration complexity. Deriving computationally efficient solutions to the secrecy capacity problem is challenging since the secrecy rate is expressed as a difference of convex functions (DC) of the transmit covariance matrix, for which its convexity is only known for some special cases. In this paper we propose two low-complexity methods to compute the secrecy capacity along with a convex reformulation for degraded channels. In the first method we capitalize on the accelerated DC algorithm which requires solving a sequence of convex subproblems, for which we propose an efficient iterative algorithm where each iteration admits a closed-form solution. In the second method, we rely on the concave-convex equivalent reformulation of the secrecy capacity problem which allows us to derive the so-called partial best response algorithm to obtain an optimal solution. Notably, each iteration of the second method can also be done in closed form. The simulation results demonstrate a faster convergence rate of our methods compared to other known solutions. We carry out extensive numerical experiments to evaluate the impact of various parameters on the achieved secrecy capacity

Simultaneous Wireless Information and Power Transfer Based on Generalized Triangular Decomposition

The rapidly growing number of wireless devices has raised the need for designing self-sustained wireless systems. Simultaneous wireless information and power transfer (SWIPT) has been advocated as a promising solution. Various approaches have emerged to design wireless systems that enable SWIPT. In this thesis, we propose a novel approach for spatial switching (SS) based SWIPT using the generalized triangular decomposition (GTD) for point-to-point multiple-input-multiple-output (MIMO) systems. The GTD structure allows the transmitter to use the highest gain subchannels jointly for energy and information transmissions and these joint transmissions can be separated at the receiver. We first derive the optimal GTD structure to attain optimal performance in SS based SWIPT systems. This structure is then extended to design three novel transceivers where each transceiver achieves a certain objective and meets specific constraints. The first transceiver focuses on minimizing the total transmitted power while satisfying the energy harvesting and data rate constraints at the receiver. The second transceiver targets the data rate maximization while meeting a certain amount of energy at the receiver. The third transceiver considers the energy harvesting maximization and guarantees to satisfy the required data rate constraint. The proposed transceivers are designed assuming two transmitted power constraints at the transmitter; the instantaneous total transmit power and the limited transmit power per subchannel. For each designed transceiver, optimal and/or suboptimal solutions are developed to obtain joint power allocation and subchannel assignment under a linear energy harvesting model. Additionally, a novel extension to the SS based SWIPT system is proposed considering a non-linear energy harvesting model. Thereafter, the case of maximizing the energy harvesting for a given data rate and instantaneous total transmitted power constraints is studied. A solution is developed that obtains jointly the optimal power allocation and the subchannel assignment alongside the optimal and/or suboptimal split ratios at the energy harvesters. The theoretical and simulation results show that our novel proposed GTD designs for both linear and non-linear energy harvesting models outperform the state-of-the-art singular value decomposition (SVD) based SWIPT designs

The MIMO Wiretap Channel Decomposed

The problem of sending a secret message over the Gaussian multiple-input multiple-output (MIMO) wiretap channel is studied. While the capacity of this channel is known, it is not clear how to construct optimal coding schemes that achieve this capacity. In this work, we use linear operations along with successive interference cancellation to attain effective parallel single-antenna wiretap channels. By using independent scalar Gaussian wiretap codebooks over the resulting parallel channels, the capacity of the MIMO wiretap channel is achieved. The derivation of the schemes is based upon joint triangularization of the channel matrices.We find that the same technique can be used to re-derive capacity expressions for the MIMO wiretap channel in a way that is simple and closely connected to a transmission scheme. This technique allows to extend the previously proven strong security for scalar Gaussian channels to the MIMO case. We further consider the problem of transmitting confidential messages over a two-user broadcast MIMO channel. For that problem, we find that derivation of both the capacity and a transmission scheme is a direct corollary of the proposed analysis for the MIMO wiretap channel