We consider joint optimization of artificial noise (AN) and information signals in a MIMO wiretap interference network, wherein the transmission of each link may be overheard by several MIMO-capable eavesdroppers. Each information signal is accompanied with AN, generated by the same user to confuse nearby eavesdroppers. Using a noncooperative game, a distributed optimization mechanism is proposed to maximize the secrecy rate of each link. The decision variables here are the covariance matrices for the information signals and ANs. However, the nonconvexity of each link's optimization problem (i.e., best response) makes conventional convex games inapplicable, even to find whether a Nash Equilibrium (NE) exists. To tackle this issue, we analyze the proposed game using a relaxed equilibrium concept, called quasi-Nash equilibrium (QNE). Under a constraint qualification condition for each player's problem, the set of QNEs includes the NE of the proposed game. We also derive the conditions for the existence and uniqueness of the resulting QNE. It turns out that the uniqueness conditions are too restrictive, and do not always hold in typical network scenarios. Thus, the proposed game often has multiple QNEs, and convergence to a QNE is not always guaranteed. To overcome these issues, we modify the utility functions of the players by adding several specific terms to each utility function. The modified game converges to a QNE even when multiple QNEs exist. Furthermore, players have the ability to select a desired QNE that optimizes a given social objective (e.g., sum-rate or secrecy sum-rate). Depending on the chosen objective, the amount of signaling overhead as well as the performance of resulting QNE can be controlled. Simulations show that due to the QNE selection mechanism, we can achieve a significant improvement in terms of secrecy sum-rate and power efficiency.
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. In this paper, we first revisit the rank property of the optimal input covariance matrix that achieves the secrecy capacity of the multiple antenna MIMO Gaussian wiretap channel under the average power constraint. Next, we obtain necessary and sufficient conditions on the MIMO wiretap channel parameters such that the optimal input covariance matrix is full-rank, and we fully characterize t…
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 t…
Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of a wiretapper who also makes channel observations that are different from but correlated to those made by the destination. An interactive authenticated unrestricted public channel is also available for use by the source and destination in the secret sharing process. This falls under the "channel-type model with wiretapper" considered by Ahlswede and Csiszar. A minor extension of their result (to continuous channel a…
In this paper, we consider the problem of power allocation in MIMO wiretap channel for secrecy in the presence of multiple eavesdroppers. Perfect knowledge of the destination channel state information (CSI) and only the statistical knowledge of the eavesdroppers CSI are assumed. We first consider the MIMO wiretap channel with Gaussian input. Using Jensen's inequality, we transform the secrecy rate max-min optimization problem to a single maximization problem. We use generalized singular value decomposition and transform the problem to a concave maximization problem which maximizes the sum secr…
A Gaussian multiple-input multiple-output (MIMO) wiretap channel model is considered. The input is a two-antenna transmitter, while the outputs are the legitimate receiver and an eavesdropper, both equipped with multiple antennas. All channels are assumed to be known. The problem of obtaining the optimal input covariance matrix that achieves secrecy capacity subject to a power constraint is addressed, and a closed-form expression for the secrecy capacity is obtained.
In this work, a class of information theoretic secrecy problems is addressed where the eavesdropper channel states are completely unknown to the legitimate parties. In particular, MIMO wiretap channel models are considered where the channel of the eavesdropper is arbitrarily varying over time. Assuming that the number of antennas of the eavesdropper is limited, the secrecy rate of the MIMO wiretap channel in the sense of strong secrecy is derived, and shown to match with the converse in secure degrees of freedom. It is proved that there exists a universal coding scheme that secures the confide…
We consider MIMO (Multiple Input Multiple Output) wiretap channels, where a legitimate transmitter Alice is communicating with a legitimate receiver Bob in the presence of an eavesdropper Eve, and communication is done via MIMO channels. We suppose that Alice's strategy is to use a codebook which has a lattice structure, which then allows her to perform coset encoding. We analyze Eve's probability of correctly decoding the message Alice meant to Bob, and from minimizing this probability, we derive a code design criterion for MIMO lattice wiretap codes. The case of block fading channels is trea…
This paper considers a multiple-input multiple-output (MIMO) Gaussian wiretap channel model, where there exists a transmitter, a legitimate receiver and an eavesdropper, each equipped with multiple antennas. Perfect secrecy is achieved when the transmitter and the legitimate receiver can communicate at some positive rate, while ensuring that the eavesdropper gets zero bits of information. In this paper, the perfect secrecy capacity of the multiple antenna MIMO wiretap channel is found for aribtrary numbers of antennas under the assumption that the transmitter performs beamforming based on the …
The growth of interest in massive MIMO systems is accompanied with hardware cost and computational complexity. Antenna selection is an efficient approach to overcome this cost-plus-complexity issue which also enhances the secrecy performance in wiretap settings. Optimal antenna selection requires exhaustive search which is computationally infeasible for settings with large dimensions. This paper develops an iterative algorithm for antenna selection in massive multiuser MIMO wiretap settings. The algorithm takes a stepwise approach to find a suitable subset of transmit antennas. Numerical inves…
We investigate the secure degrees of freedom (SDoF) of the wiretap and the K user Gaussian broadcast channels with multiple antennas at the transmitter, the legitimate receivers and an unknown number of eavesdroppers each with a number of antennas less than or equal to a known value NE. The channel matrices between the legitimate transmitter and the receivers are available everywhere, while the legitimate pair have no information about the eavesdroppers' channels. We provide the exact sum SDoF for the considered system. A new comprehensive upperbound is deduced and a new achievable scheme base…
We consider the MIMO wiretap channel, that is a MIMO broadcast channel where the transmitter sends some confidential information to one user which is a legitimate receiver, while the other user is an eavesdropper. Perfect secrecy is achieved when the the transmitter and the legitimate receiver can communicate at some positive rate, while insuring that the eavesdropper gets zero bits of information. In this paper, we compute the perfect secrecy capacity of the multiple antenna MIMO broadcast channel, where the number of antennas is arbitrary for both the transmitter and the two receivers.
The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior performance of coset codes constructed from well-rounded lattices has been illustrated in several simulations. In the present article, this work is extended to fading multiple-input multiple-output (MIMO) wiretap channels, and similar design criteria as…
The classic MIMO wiretap channel comprises a passive eavesdropper that attempts to intercept communications between an authorized transmitter-receiver pair, each node being equipped with multiple antennas. In a dynamic network, it is imperative that the presence of an eavesdropper be determined before the transmitter can deploy robust secrecyencoding schemes as a countermeasure. This is a difficult task in general, since by definition the eavesdropper is passive and never transmits. In this work we adopt a method that allows the legitimate nodes to detect the passive eavesdropper from the loca…
We study the Gaussian MIMO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, each equipped with multiple antennas. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. We obtain a closed-form expression for the structure of the artificial noise covariance matrix that guarantees no decrease in the secrecy capacity of the w…
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 MI…
Capacity-achieving signaling strategies for the Gaussian wiretap MIMO channel are investigated without the degradedness assumption. In addition to known solutions, a number of new rank-deficient solutions for the optimal transmit covariance matrix are obtained. The case of a weak eavesdropper is considered in detail and the optimal covariance is established in an explicit, closed form with no extra assumptions. This provides lower and upper bounds to the secrecy capacity in the general case with a bounded gap, which are tight for a weak eavesdropper or/and low SNR. Closed form solutions are al…
We study the Gaussian multiple-input multiple-output (MIMO) wiretap channel, which consists of a transmitter, a legitimate user, and an eavesdropper. In this channel, the transmitter sends a common message to both the legitimate user and the eavesdropper. In addition to this common message, the legitimate user receives a private message, which is desired to be kept hidden as much as possible from the eavesdropper. We obtain the entire capacity-equivocation region of the Gaussian MIMO wiretap channel. This region contains all achievable common message, private message, and private message's equ…
This paper shows determining the secrecy capacity of a unicast network with uniform wiretap sets is at least as difficult as the k-unicast problem. In particular, we show that a general k-unicast problem can be reduced to the problem of finding the secrecy capacity of a corresponding single unicast network with uniform link capacities and one arbitrary wiretap link.
While the wiretap secret key capacity remains unknown for general source models even in the two-user case, we obtained a single-letter characterization for a large class of multi-user source models with a linear wiretapper who can observe any linear combinations of the source. We introduced the idea of irreducible sources to show existence of an optimal communication scheme that achieves perfect omniscience with minimum leakage of information to the wiretapper. This implies a duality between the problems of wiretap secret key agreement and secure omniscience, and such duality potentially holds…
This paper investigates reliable and covert transmission strategies in a multiple-input multiple-output (MIMO) wiretap channel with a transmitter, receiver and an adversarial wiretapper, each equipped with multiple antennas. In a departure from existing work, the wiretapper possesses a novel capability to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data, or broadcasting artificial interference along with the information signal in an attempt to jam the eavesdropper (…
Secrecy Capacity Analysis and Beamforming Optimization for MIMO-VLC Wiretap Channels
China Mobile Research Institute（中国移动研究院）；SJTU Paris Elite Institute of Technology, Shanghai Jiao Tong University（上海交通大学巴黎卓越工程师学院）；Beijing National Research Center for Information Science and Technology (BNRist), Tsinghua University（清华大学北京信息科学与技术国家研究中心）；Department of Electronic Engineering, Tsinghua University（清华大学电子工程系）；Research Institute, Tsinghua University in Shenzhen（清华大学深圳研究院）
In this paper, we study the impacts of transmit antenna selection on the secrecy performance of massive MIMO systems. We consider a wiretap setting in which a fixed number of transmit antennas are selected and then confidential messages are transmitted over them to a multi-antenna legitimate receiver while being overheard by a multi-antenna eavesdropper. For this setup, we derive an accurate approximation of the instantaneous secrecy rate. Using this approximation, it is shown that in some wiretap settings under antenna selection the growth in the number of active antennas enhances the secrecy…
In this paper, we propose a strategy for making DNA-based data storage information-theoretically secure through the use of wiretap channel coding. This motivates us to extend the shuffling-sampling channel model of Shomorony and Heckel (2021) to include a wiretapper. Our main result is a characterization of the secure storage capacity of our DNA wiretap channel model, which is the maximum rate at which data can be stored within a pool of DNA molecules so as to be reliably retrieved by an authorized party (Bob), while ensuring that an unauthorized party (Eve) gets almost no information from her…
Several gaps and errors in [1] are identified and corrected. While accommodating these corrections, a rigours proof is given that the successive convex approximation algorithm in [1] for secrecy rate maximization (SRM) does generate an increasing and bounded sequence of true secrecy rates and hence converges. It is further shown that its convergence point is a KKT point of the original SRM problem and, if the original problem is convex, this convergence point is globally-optimal, which is not necessarily the case in general. An interlacing property of the sequences of the true and approximate …
One key metric for physical layer security is the secrecy capacity. This is the maximum rate that a system can transmit with perfect secrecy. For a Multiple Input Multiple Output (MIMO) system (a newer technology for 5G, 6G and beyond) the secrecy capacity is not fully understood. For a Gaussian MIMO channel, the secrecy capacity is a non-convex optimisation problem for which a general solution is not available. Previous work by the authors showed that the secrecy capacity of a MIMO system with a single eavesdrop antenna is concave to a cut off point. In this work, which extends the previous p…
In this paper, we consider the problem of secure and reliable communication with uncertain channel state information (CSI) and present a new solution named active secure coding which combines the machine learning methods with the traditional physical layer secure coding scheme. First, we build a detectable wiretap channel model by combining the hidden Markov model with the compound wiretap channel model, in which the varying of channel block CSI is a Markov process and the detected information is a stochastic emission from the current CSI. Next, we present a CSI learning scheme to learn the CS…
We consider the problem of securing a multicast network against a wiretapper that can intercept the packets on a limited number of arbitrary network edges of its choice. We assume that the network employs the network coding technique to simultaneously deliver the packets available at the source to all the receivers. We show that this problem can be looked at as a network generalization of the wiretap channel of type II introduced in a seminal paper by Ozarow and Wyner. In particular, we show that the transmitted information can be secured by using the Ozarow-Wyner approach of coset coding at t…
This paper examines linear beamforming methods for secure communications in a multiuser wiretap channel with a single transmitter, multiple legitimate receivers, and a single eavesdropper, where all nodes are equipped with multiple antennas. No information regarding the eavesdropper is presumed at the transmitter, and we examine both the broadcast MIMO downlink with independent information, and the multicast MIMO downlink with common information for all legitimate receivers. In both cases the information signal is transmitted with just enough power to guarantee a certain SINR at the desired re…
This paper considers a Gaussian multi-input multi-output (MIMO) multiple access wiretap (MAC-WT) channel, where an eavesdropper (Eve) wants to extract the confidential information of all users. Assuming that both the legitimate receiver and Eve jointly decode their interested messages, we aim to maximize the sum secrecy rate of the system by precoder design. Although this problem could be solved by first using the iterative majorization minimization (MM) based algorithm to get a sequence of convex log-determinant optimization subproblems and then using some general tools, e.g., the interior po…
Optimal signalling over the Gaussian MIMO wire-tap channel is studied under the total transmit power constraint. A closed-form solution for an optimal transmit covariance matrix is obtained when the channel is strictly degraded. In combination with the rank-1 solution, this provides the complete characterization of the optimal covariance for the case of two transmit antennas. The cases of weak eavesdropper and high SNR are considered. It is shown that the optimal covariance does not converge to a scaled identity in the high-SNR regime. Necessary optimality conditions and a tight upper bound on…
We consider linear precoder design for a multiple-input multiple-output (MIMO) Gaussian wiretap channel, which comprises two legitimate nodes, i.e., Alice and Bob, operating in Full-Duplex (FD) mode and exchanging confidential messages in the presence of a passive eavesdropper. Using the sum secrecy degrees of freedoms (sum S.D.o.F.) as reliability measure, we formulate an optimization problem with respect to the precoding matrices. In order to solve this problem, we first propose a cooperative secrecy transmission scheme, and prove that its feasible set is sufficient to achieve the maximum su…
The secrecy capacity of a network, for a given collection of permissible wiretap sets, is the maximum rate of communication such that observing links in any permissible wiretap set reveals no information about the message. This paper considers secure network coding with nonuniform or restricted wiretap sets, for example, networks with unequal link capacities where a wiretapper can wiretap any subset of $k$ links, or networks where only a subset of links can be wiretapped. Existing results show that for the case of uniform wiretap sets (networks with equal capacity links/packets where any $k$ c…
In this paper, we investigate the secure coding issue for a wiretap channel model with fixed main channel and varying wiretap channel, by assuming that legitimate parties can obtain the wiretapping channel state information (CSI) after some time delay. For the symmetric degraded delay CSI case, we present an explicit weak security scheme by constructing secure polar codes on a one-time pad chaining structure, and prove its weak security, reliability and capability of approaching the secrecy capacity of perfect CSI case with delay CSI assumption. Further for the symmetric no-degraded delay CSI …
We study a symmetric Gaussian wiretap channel with a helper, where a confidential message is sent from a transmitter to a legitimate receiver, in the presence of a helper and an eavesdropper, under a weak notion of secrecy constraint. For this setting, we characterize the optimal secure generalized degrees-of-freedom (GDoF). The result reveals that, adding a helper can significantly increase the secure GDoF of the wiretap channel. The result is supported by a new converse and a new scheme. In the proposed scheme, the helper sends a cooperative jamming signal at a specific power level and direc…
With the growth of wireless networks, security has become a fundamental issue in wireless communications due to the broadcast nature of these networks. In this work, we consider MIMO wiretap channels in a fast fading environment, for which the overall performance is characterized by the ergodic MIMO secrecy rate. Unfortunately, the direct solution to finding ergodic secrecy rates is prohibitive due to the expectations in the rates expressions in this setting. To overcome this difficulty, we invoke the large-system assumption, which allows a deterministic approximation to the ergodic mutual inf…
In this article, the design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied. Recalling the eavesdropper's probability and information bounds, a variant of the latter is given from which it is explicitly seen that both quantities are upper bounded by (increasing functions of) the expected flatness factor of the faded lattice related to the eavesdropper. By making use of a recently developed approximation of the theta series of a lattice, it is further shown how the average flatness factor can be approximated numerically. In particular, based…
The Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel is studied in this paper. The base station broadcasts confidential messages to K intended users while keeping the messages secret from an eavesdropper. The capacity of this channel has already been characterized by applying dirty-paper coding and stochastic encoding. However, K factorial encoding orders may need to be enumerated for that, which makes the problem intractable. We prove that there exists one optimal encoding order and reduced the K factorial times to a one-time encoding. The optimal encoding order i…
In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to b…
In this paper, we consider the transmit design for multi-input multi-output (MIMO) wiretap channel including a malicious jammer. We first transform the system model into the traditional three-node wiretap channel by whitening the interference at the legitimate user. Additionally, the eavesdropper channel state information (ECSI) may be fully or statistically known, even unknown to the transmitter. Hence, some strategies are proposed in terms of different levels of ECSI available to the transmitter in our paper. For the case of unknown ECSI, a target rate for the legitimate user is first specif…
A Gaussian multiple-input multiple-output wiretap channel in which the eavesdropper and legitimate receiver are equipped with arbitrary numbers of antennas and the transmitter has two antennas is studied in this paper. Under an average power constraint, the optimal input covariance to obtain the secrecy capacity of this channel is unknown, in general. In this paper, the input covariance matrix required to achieve the capacity is determined. It is shown that the secrecy capacity of this channel can be achieved by linear precoding. The optimal precoding and power allocation schemes that maximize…
In order to meet the demands of future innovative applications, many efforts have been made to exceed the limits predicted by Shannon's Theory. Besides the investigation of beyond-Shannon metrics such as security, latency, and semantics, another direction is to jointly design the transceiver and the environment by utilizing the intelligent reflecting surface (IRS). In this paper, we consider the analysis and design of IRS-aided multiple-input multiple-output (MIMO) secure communications, which has attracted much research attention but still in its infancy. For example, despite their importance…
We study the secrecy capacity of a helper-assisted Gaussian wiretap channel with a source, a legitimate receiver, an eavesdropper and an external helper, where each terminal is equipped with multiple antennas. Determining the secrecy capacity in this scenario generally requires solving a nonconvex secrecy rate maximization (SRM) problem. To deal with this issue, we first reformulate the original SRM problem into a sequence of convex subproblems. For the special case of single-antenna legitimate receiver, we obtain the secrecy capacity via a combination of convex optimization and one-dimensiona…
To achieve perfect secrecy in a multiple-input multiple-output (MIMO) Gaussian wiretap channel (WTC), we need to find its secrecy capacity and optimal signaling, which involves solving a difference of convex functions program known to be non-convex for the non-degraded case. To deal with this, a class of existing solutions have been developed but only local optimality is guaranteed by standard convergence analysis. Interestingly, our extensive numerical experiments have shown that these local optimization methods indeed achieve global optimality. In this paper, we provide an analytical proof f…
In this paper, we propose a polar coding scheme for secure communication over the multiple-input, single-output, single-antenna eavesdropper (MISOSE) fading channel. We consider the case of block fading channels with known eavesdropper channel state information (CSI) and the case of fading channels with known eavesdropper channel distribution information (CDI). We use the artificial noise assisted secure precoding method to maximize the secrecy capacity in the first case, and to overcome the unawareness of the eavesdropper CSI in the second case. We show that our proposed scheme can provide bo…
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 i…
In this paper, the problem of securely computing a function over the binary modulo-2 adder multiple-access wiretap channel is considered. The problem involves a legitimate receiver that wishes to reliably and efficiently compute a function of distributed binary sources while an eavesdropper has to be kept ignorant of them. In order to characterize the corresponding fundamental limit, the notion of secrecy computation-capacity is introduced. Although determining the secrecy computation-capacity is challenging for arbitrary functions, it surprisingly turns out that if the function perfectly matc…
Full-duplex (FD) jamming transceivers are recently shown to enhance the information security of wireless communication systems by simultaneously transmitting artificial noise (AN) while receiving information. In this work, we investigate if FD jamming can also improve the systems secrecy energy efficiency (SEE) in terms of securely communicated bits-per- Joule, when considering the additional power used for jamming and self-interference (SI) cancellation. Moreover, the degrading effect of the residual SI is also taken into account. In this regard, we formulate a set of SEE maximization problem…
We consider the problem of secure communications over the two-way wiretap channel under a strong secrecy criterion. We improve existing results by developing an achievable region based on strategies that exploit both the interference at the eavesdropper's terminal and cooperation between legitimate users. We leverage the notion of channel resolvability for the multiple-access channel to analyze cooperative jamming and we show that the artificial noise created by cooperative jamming induces a source of common randomness that can be used for secret-key agreement. We illustrate the gain provided …
This paper presents two different low-complexity methods for obtaining the secrecy capacity of multiple-input multiple-output (MIMO) wiretap channel subject to a sum power constraint (SPC). The challenges in deriving computationally efficient solutions to the secrecy capacity problem are due to the fact that the secrecy rate is a difference of convex functions (DC) of the transmit covariance matrix, for which its convexity is only known for \emph{the degraded case}. In the first method, we capitalize on the accelerated DC algorithm, which requires solving a sequence of convex subproblems. In p…
In this paper, interference alignment (IA) is designed for secure multiuser multiple-input multiple-output systems in the presence of an eavesdropper. The proposed IA technique designs the transmit precoding and receiving subspace matrices to minimize both the total inter-main-link interference and the wiretapped signals. With perfect channel state information is known at the transmitters (Txs), the cost function of the optimization problem is alternatively minimized over the precoding matrices at the Txs and the receiving subspace matrices at the receivers (Rxs) and the eavesdropper. The feas…
This paper considers the problem of filter design with secrecy constraints, where two legitimate parties (Alice and Bob) communicate in the presence of an eavesdropper (Eve), over a Gaussian multiple-input-multiple-output (MIMO) wiretap channel. This problem involves designing, subject to a power constraint, the transmit and the receive filters which minimize the mean-squared error (MSE) between the legitimate parties whilst assuring that the eavesdropper MSE remains above a certain threshold. We consider a general MIMO Gaussian wiretap scenario, where the legitimate receiver uses a linear Zer…
In this paper, we consider the secrecy capacity of a wiretap channel in the presence of causal state information and secure rate-limited feedback. In this scenario, the causal state information from the channel is available to both the legitimate transmitter and legitimate receiver. In addition, the legitimate receiver can send secure feedback to the transmitter at a limited rate Rf . We shown that the secrecy capacity is bounded. Moreover, when the channel to the legitimate receiver is less noisy than the channel to the eavesdropper, the bound is shown to be tight. The capacity achieving sche…
Compound MIMO wiretap channel with double sided uncertainty is considered under channel mean information model. In mean information model, channel variations are centered around its mean value which is fed back to the transmitter. We show that the worst case main channel is anti-parallel to the channel mean information resulting in an overall unit rank channel. Further, the worst eavesdropper channel is shown to be isotropic around its mean information. Accordingly, we provide the capacity achieving beamforming direction. We show that the saddle point property holds under mean information mode…
In this paper, we consider the Gaussian multiple-input multiple-output (MIMO) multi-receiver wiretap channel in which a transmitter wants to have confidential communication with an arbitrary number of users in the presence of an external eavesdropper. We derive the secrecy capacity region of this channel for the most general case. We first show that even for the single-input single-output (SISO) case, existing converse techniques for the Gaussian scalar broadcast channel cannot be extended to this secrecy context, to emphasize the need for a new proof technique. Our new proof technique makes u…
Despite several works on secrecy coding for fading and MIMO wiretap channels from an error probability perspective, the construction of information-theoretically secure codes over such channels remains an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. Our channel model includes static channels, i.i.d. block fading channels, and ergodic stationary fading with fast decay of large deviations for the eavesdropper's channel. We extend the flatness factor criterion from the Gaussian wiretap channel…
This paper considers the problem of secure coding design for a type II wiretap channel, where the main channel is noiseless and the eavesdropper channel is a general binary-input symmetric-output memoryless channel. The proposed secure error-correcting code has a nested code structure. Two secure nested coding schemes are studied for a type II Gaussian wiretap channel. The nesting is based on cosets of a good code sequence for the first scheme and on cosets of the dual of a good code sequence for the second scheme. In each case, the corresponding achievable rate-equivocation pair is derived ba…
The adversarial wiretap channel (AWTC) model is a secure communication model in which adversary can directly read and write the transmitted bits in legitimate communication with fixed fractions. In this paper we propose a secure polar coding scheme to provide secure and reliable communication over the AWTC model. For the adversarial reading and writing action, we present a $ρ$ equivalent channel block and study its transformation under the channel polarization operation. We find that the generated channels are polarized in the sense that part of them are full-noise channels with probability al…
In this paper we consider the robust secure beamformer design for MISO wiretap channels. Assume that the eavesdroppers' channels are only partially available at the transmitter, we seek to maximize the secrecy rate under the transmit power and secrecy rate outage probability constraint. The outage probability constraint requires that the secrecy rate exceeds certain threshold with high probability. Therefore including such constraint in the design naturally ensures the desired robustness. Unfortunately, the presence of the probabilistic constraints makes the problem non-convex and hence diffic…
