10 research outputs found
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
The Secrecy Capacity of The Gaussian Wiretap Channel with Rate-Limited Help
The Gaussian wiretap channel with rate-limited help, available at the
legitimate receiver (Rx) or/and transmitter (Tx), is studied under various
channel configurations (degraded, reversely degraded and non-degraded). In the
case of Rx help and all channel configurations, the rate-limited help results
in a secrecy capacity boost equal to the help rate irrespective of whether the
help is secure or not, so that the secrecy of help does not provide any
capacity increase. The secrecy capacity is positive for the reversely-degraded
channel (where the no-help secrecy capacity is zero) and no wiretap coding is
needed to achieve it. More noise at the legitimate receiver can sometimes
result in higher secrecy capacity. The secrecy capacity with Rx help is not
increased even if the helper is aware of the message being transmitted. The
same secrecy capacity boost also holds if non-secure help is available to the
transmitter (encoder), in addition to or instead of the same Rx help, so that,
in the case of the joint Tx/Rx help, one help link can be omitted without
affecting the capacity. If Rx/Tx help links are independent of each other, then
the boost in the secrecy capacity is the sum of help rates and no link can be
omitted without a loss in the capacity. Non-singular correlation of the
receiver and eavesdropper noises does not affect the secrecy capacity and
non-causal help does not bring in any capacity increase over the causal one.Comment: An extended version of the paper presented at the IEEE International
Symposium on Information Theory, Helsinki, Finland, June 26 - July 1, 2022;
submitted to IEEE Trans. Info. Theor
On the secrecy performance of transmit-receive diversity and spatial multiplexing systems
Emerging from the information-theoretic characterization of secrecy, physical-layer security exploits the physical properties of the wireless channel for security purpose. In recent years, a great deal of attention has been paid to investigating the physical-layer security issues in multiple-input multiple-output (MIMO) wireless communications. This paper analyzes the secrecy performance of transmit-receive diversity system and spatial multiplexing systems with zero-forcing equalization and minimum mean-square-error equalization. Specifically, exact and asymptotic closed-form expressions are derived for the secrecy outage probability of such MIMO systems in a Rayleigh fading environment, and the corresponding secrecy diversity orders and secrecy array gains are determined. Numerical results are presented to corroborate the analytical results and to examine the impact of various system parameters, including the numbers of antennas at the transmitter, the legitimate receiver, and the eavesdropper. These contributions bring about valuable insights into the physical-layer security in MIMO wireless systems
Algorithms for Globally-Optimal Secure Signaling over Gaussian MIMO Wiretap Channels Under Interference Constraints
Multi-user Gaussian MIMO wiretap channel is considered under interference
power constraints (IPC), in addition to the total transmit power constraint
(TPC). Algorithms for \textit{global} maximization of its secrecy rate are
proposed. Their convergence to the secrecy capacity is rigorously proved and a
number of properties are established analytically. Unlike known algorithms, the
proposed ones are not limited to the MISO case and are proved to converge to a
\textit{global} rather than local optimum in the general MIMO case, even when
the channel is not degraded. In practice, the convergence is fast as only a
small to moderate number of Newton steps is required to achieve a high
precision level. The interplay of TPC and IPC is shown to result in an unusual
property when an optimal point of the max-min problem does not provide an
optimal transmit covariance matrix in some (singular) cases. To address this
issue, an algorithm is developed to compute an optimal transmit covariance
matrix in those singular cases. It is shown that this algorithm also solves the
dual (nonconvex) problems of \textit{globally} minimizing the total transmit
power subject to the secrecy and interference constraints; it provides the
minimum transmit power and respective signaling strategy needed to achieve the
secrecy capacity, hence allowing power savings.Comment: accepted for publicatio
Effects of Correlation of Channel Gains on the Secrecy Capacity in the Gaussian Wiretap Channel
Secrecy capacity is one of the most important characteristic of a wireless communication channel. Therefore, the study of this characteristic wherein the system has correlated channel gains and study them for different line-of-sight (LOS) propagation scenarios is of ultimate importance.
The primary objective of this thesis from the mathematical side is to determine the secrecy capacity (SC) for correlated channel gains for the main and eavesdropper channels in a Gaussian Wiretap channel as a function from main parameters (μ, Σ, ρ). f(h1, h2) is the joint distribution of the two channel gains at channel use (h1, h2), fi(hi) is the main distribution of the channel gain hi. The results are based on assumption of the Gaussian distribution of channel gains (gM, gE). The main task of estimating the secrecy capacity is reduced to the problem of solving linear partial differential equations (PDE). Different aspects of the analysis of secrecy capacity considered in this research are the Estimation of SC mathematically and numerically for correlated SISO systems and a mathematical example for MIMO systems with PDE.
The variations in Secrecy Capacity are studied for Rayleigh (NLOS) distribution and Rician (LOS) distribution. Suitable scenarios are identified in which secure communication is possible with correlation of channel gains. Also, the new algorithm using PDE has a higher speed and than analog algorithms constructed on the classical statistical Monte Carlo methods. Taking into account the normality of the distribution of system parameters, namely the channel gain (gM, gE), the algorithm is constructed for systems of partial differential equations which satisfies the secrecy criterion.
Advisor: H. Andrew Harm