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 confidential message against any sequence of channel states experienced by the eavesdropper. This yields the conclusion that secure communication is possible regardless of the location or channel states of (potentially infinite number of) eavesdroppers. Additionally, it is observed that, the present setting renders the secrecy capacity problems for multi-terminal wiretap-type channels more tractable as compared the case with full or partial knowledge of eavesdropper channel states. To demonstrate this observation, secure degrees of freedom regions are derived for the Gaussian MIMO multiple access wiretap channel (MIMO MAC-WT) and the Gaussian MIMO broadcast wiretap channel (MIMO BC-WT) where the transmitter(s) and the intended receiver(s) have the same number of antennas.
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…
Information leakage in Wyner's wiretap channel model is usually defined as the mutual information between the secret message and the eavesdropper's received signal. We define a new quantity called "conditional information leakage given the eavesdropper's received signals," which expresses the amount of information that eavesdropper gains from his/her received signal. A benefit of introducing this quantity is that we can develop a fast algorithm for computing the conditional information leakage, which has linear complexity in the code length $n$, while the complexity for computing the usual inf…
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 propose a secure transmission scheme for a relay wiretap channel, where a source communicates with a destination via a decode-and-forward relay in the presence of spatially random-distributed eavesdroppers. We assume that the source is equipped with multiple antennas, whereas the relay, the destination, and the eavesdroppers are equipped with a single antenna each. In the proposed scheme, in addition to information signals, the source transmits artificial noise signals in order to confuse the eavesdroppers. With the target of maximizing the secrecy throughput of the relay wiretap channel, w…
We consider networks of noisy degraded wiretap channels in the presence of an eavesdropper. For the case where the eavesdropper can wiretap at most one channel at a time, we show that the secrecy capacity region, for a broad class of channels and any given network topology and communication demands, is equivalent to that of a corresponding network where each noisy wiretap channel is replaced by a noiseless wiretap channel. Thus in this case there is a separation between wiretap channel coding on each channel and secure network coding on the resulting noiseless network. We show with an example …
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 (…
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 p…
This work investigates the secrecy capacity of the Wiretap Broadcast Channel (WBC) with an external eavesdropper where a source wishes to communicate two private messages over a Broadcast Channel (BC) while keeping them secret from the eavesdropper. We derive a non-trivial outer bound on the secrecy capacity region of this channel which, in absence of security constraints, reduces to the best known outer bound to the capacity of the standard BC. An inner bound is also derived which follows the behavior of both the best known inner bound for the BC and the Wiretap Channel. These bounds are show…
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…
We design a new secure transmission scheme in the relay wiretap channel where a source communicates with a destination through a decode-and-forward relay in the presence of spatially random-distributed eavesdroppers. For the sake of practicality, we consider a general antenna configuration in which the source, relay, destination, and eavesdroppers are equipped with multiple antennas. In order to confuse the eavesdroppers, we assume that both the source and the relay transmit artificial noise signals in addition to information signals. We first derive a closed-form expression for the transmissi…
We consider lattice coset-coded transmissions over a wiretap channel with additive white Gaussian noise (AWGN). Examining a function that can be interpreted as either the legitimate receiver's error probability or the eavesdropper's correct decision probability, we rigorously show that, albeit offering simple bit labeling, orthogonal nested lattices are suboptimal for coset coding in terms of both the legitimate receiver's and the eavesdropper's probabilities.
We propose a location-based beamforming scheme for wiretap channels, where a source communicates with a legitimate receiver in the presence of an eavesdropper. We assume that the source and the eavesdropper are equipped with multiple antennas, while the legitimate receiver is equipped with a single antenna. We also assume that all channels are in a Rician fading environment, the channel state information from the legitimate receiver is perfectly known at the source, and that the only information on the eavesdropper available at the source is her location. We first describe how the beamforming …
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…
The role of multiple antennas for secure communication is investigated within the framework of Wyner's wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacity-achieving. In addition, we show that in the high signal-to-noise (SNR) ratio regime the penalty for not knowing eavesdropper's channel is small--a simple ``secure space-time code'' that can …
In this paper, we study a diamond-relay channel where the source is connected to $M$ relays through orthogonal links and the relays transmit to the destination over a wireless multiple-access channel in the presence of an eavesdropper. The eavesdropper not only observes the relay transmissions through another multiple-access channel, but also observes a certain number of source-relay links. The legitimate terminals know neither the eavesdropper's channel state information nor the location of source-relay links revealed to the eavesdropper except the total number of such links. For this wiretap…
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…
An analogy framework between wiretap channels (WTCs) and state-dependent point-to-point channels with non-causal encoder channel state information (referred to as Gelfand-Pinker channels (GPCs)) is proposed. A good sequence of stealth-wiretap codes is shown to induce a good sequence of codes for a corresponding GPC. Consequently, the framework enables exploiting existing results for GPCs to produce converse proofs for their wiretap analogs. The analogy readily extends to multiuser broadcasting scenarios, encompassing broadcast channels (BCs) with deterministic components, degradation ordering …
A multiple-input single-output (MISO) wiretap channel model is considered, that includes a multi-antenna transmitter, a single-antenna legitimate receiver and a single-antenna eavesdropper. For the scenario in which spherical uncertainty for both the legitimate and the eavesdropper channels is included, the problem of finding the optimal input covariance that maximizes the worst-case secrecy rate subject to a power constraint, is considered, and an explicit expression for the maximum worst-case secrecy rate is provided.
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.
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 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…
The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. It is concluded that the minimization of the (average) flatness factor of the eavesdropper's lattice leads to the study of well-rounded lattices, which are shown to be among the optimal in order to achieve these minima…
We propose a new framework for determining the wiretap code rates of single-input single-output multi-antenna eavesdropper (SISOME) wiretap channels when the capacity of the eavesdropper's channel is not available at the transmitter. In our framework we introduce the effective secrecy throughput (EST) as a new performance metric that explicitly captures the two key features of wiretap channels, namely, reliability and secrecy. Notably, the EST measures the average rate of the confidential information transmitted from the transmitter to the intended receiver without being eavesdropped on. We pr…
In this work we study encoding/decoding schemes for the transmission of a discrete time analog Gaussian source over a Gaussian wiretap channel. The intended receiver is assumed to have a certain minimum signal to noise ratio (SNR) and the eavesdropper is assumed to have a strictly lower SNR compared to the intended receiver. For a fixed information leakage to the eavesdropper, we are interested in minimizing the distortion in source reconstruction at the intended receiver, and we propose joint source channel coding (JSCC) schemes for this setup. For a fixed information leakage to the eavesdrop…
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…
In this paper, we study the degraded compound multi-receiver wiretap channel. The degraded compound multi-receiver wiretap channel consists of two groups of users and a group of eavesdroppers, where, if we pick an arbitrary user from each group of users and an arbitrary eavesdropper, they satisfy a certain Markov chain. We study two different communication scenarios for this channel. In the first scenario, the transmitter wants to send a confidential message to users in the first (stronger) group and a different confidential message to users in the second (weaker) group, where both messages ne…
We consider a complex Gaussian wiretap channel with finite-resolution analog-to-digital converters (ADCs) at both the legitimate receiver and the eavesdropper. For this channel, we show that a positive secrecy rate is always achievable as long as the channel gains at the legitimate receiver and at the eavesdropper are different, regardless of the quantization levels of the ADCs. For the achievability, we first consider the case of one-bit ADCs at the legitimate receiver and apply a binary input distribution where the two input points have the same phase when the channel gain at the legitimate …
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 study the secrecy rate and outage probability in Multiple-Input-Single-Output (MISO) Gaussian wiretap channels at the limit of a large number of legitimate users and eavesdroppers. In particular, we analyze the asymptotic achievable secrecy rates and outage, when only statistical knowledge on the wiretap channels is available to the transmitter. The analysis provides exact expressions for the reduction in the secrecy rate as the number of eavesdroppers grows, compared to the boost in the secrecy rate as the number of legitimate users grows.
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…
In this paper, we consider the transmitter optimization problem in slow fading multiple-input-single-output (MISO) wiretap channel. The source transmits a secret message intended for $K$ users in the presence of $J$ non-colluding eavesdroppers, and operates under a total power constraint. The channels between the source and all users and eavesdroppers are assumed to be slow fading, and only statistical channel state information (CSI) is known at the source. For a given code rate and secrecy rate pair of the wiretap code, denoted by $(R_{D}, R_{s})$, we define the non-outage event as the joint …
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…
We consider three channel models: the wiretap channel with $M$ helpers, the $K$-user multiple access wiretap channel, and the $K$-user interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access…
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…
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…
The secrecy rate region of wiretap interference channels with a multi-antenna passive eavesdropper is studied under receiver energy harvesting constraints. To stay operational in the network, the legitimate receivers demand energy alongside information, which is fulfilled by power transmission and exploiting a power splitting (PS) receiver. By simultaneous wireless information and power transfer (SWIPT), the amount of leakage to the eavesdropper increases, which in turn reduces the secrecy rates. For this setup, lower-bounds for secure communication rate are derived without imposing any limita…
In this paper, we consider the achievable sum secrecy rate in full-duplex wiretap channel in the presence of an eavesdropper and imperfect channel state information (CSI). We assume that the users participating in full-duplex communication and the eavesdropper have single antenna each. The users have individual transmit power constraints. They also transmit jamming signals to improve the secrecy rates. We obtain the achievable perfect secrecy rate region by maximizing the sum secrecy rate. We also obtain the corresponding optimum powers of the message signals and the jamming signals. Numerical…
This paper investigates the capacity region of a discrete memoryless (DM) multiple access wiretap (MAC-WT) channel where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver but only the confidential messages need to be protected from the eavesdropper. By using random coding, we find an achievable secrecy rate region, within which perfect secrecy can be realized, i.e., all users can communicate with the legitimate receiver with arbitrarily small probability of error, while the confidential information leaked …
A Gaussian multiple-input single-output (MISO) wiretap channel model is considered, where there exists a transmitter equipped with multiple antennas, a legitimate receiver and an eavesdropper each equipped with a single antenna. We study the problem of finding the optimal input covariance that achieves ergodic secrecy capacity subject to a power constraint where only statistical information about the eavesdropper channel is available at the transmitter. This is a non-convex optimization problem that is in general difficult to solve. Existing results address the case in which the eavesdropper o…
We consider the problem of polar coding for secure communications over the two-way wiretap channel, where two legitimate users communicate with each other simultaneously while a passive eavesdropper overhears a combination of their exchanged signals. The legitimate users wish to design a cooperative jamming code such that the interference between their codewords can jam the eavesdropper. In this paper, we design a polar coded cooperative jamming scheme that achieves the whole secrecy rate region of the general two-way wiretap channel under the strong secrecy criterion. The chaining method is u…
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…
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…
The finite state Markov channel (FSMC), where the channel transition probability is controlled by a state undergoing a Markov process, is a useful model for the mobile wireless communication channel. In this paper, we investigate the security issue in the mobile wireless communication systems by considering the FSMC with an eavesdropper, which we call the finite state Markov wiretap channel (FSM-WC). We assume that the state is perfectly known by the legitimate receiver and the eavesdropper, and through a noiseless feedback channel, the legitimate receiver sends his received channel output and…
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.
A polar coding scheme is proposed for the Wiretap Broadcast Channel with two legitimate receivers and one eavesdropper. We consider a model in which the transmitter wishes to send a private and a confidential message that must be reliably decoded by the receivers, and the confidential message must also be (strongly) secured from the eavesdropper. The coding scheme aims to use the optimal rate of randomness and does not make any assumption regarding the symmetry or degradedness of the channel. This paper extends previous work on polar codes for the wiretap channel by proposing a new chaining co…
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 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 consider the achievable sum secrecy rate in MISO (multiple-input-single-output) {\em full-duplex} wiretap channel in the presence of a passive eavesdropper and imperfect channel state information (CSI). We assume that the users participating in full-duplex communication have multiple transmit antennas, and that the users and the eavesdropper have single receive antenna each. The users have individual transmit power constraints. They also transmit jamming signals to improve the secrecy rates. We obtain the achievable perfect secrecy rate region by maximizing the worst case sum…
We propose a new location-based beamforming (LBB) scheme for wiretap channels, where a multi-antenna source communicates with a single-antenna legitimate receiver in the presence of a multi-antenna eavesdropper. We assume that all channels are in a Rician fading environment, the channel state information from the legitimate receiver is perfectly known at the source, and that the only information on the eavesdropper available at the source is her location. We first describe how the optimal beamforming vector that minimizes the secrecy outage probability of the system is obtained, illustrating i…
It has been shown recently that coding for the Gaussian Wiretap Channel can be done with nested lattices. A fine lattice intended to the legitimate user must be designed as a usual lattice code for the Gaussian Channel, while a coarse lattice is added to introduce confusion at the eavesdropper, whose theta series must be minimized. We present a design criterion for both the fine and coarse lattice to obtain wiretap lattice codes for the Rayleigh fading Wiretap Channel.
In this paper, we consider the Gaussian diamond-wiretap channel that consists of an orthogonal broadcast channel from a source to two relays and a Gaussian fast-fading multiple access-wiretap channel from the two relays to a legitimate destination and an eavesdropper. For the multiple access part, we consider both the case with full channel state information (CSI) and the case with no eavesdropper's CSI, at the relays and the legitimate destination. For both the cases, we establish the exact secure degrees of freedom and generalize the results for multiple relays. For the converse part, we int…
We consider lattice coding for the Gaussian wiretap channel, where the challenge is to ensure reliable communication between two authorized parties while preventing an eavesdropper from learning the transmitted messages. Recently, a measure called the secrecy function of a lattice coding scheme was proposed as a design criterion to characterize the eavesdropper's probability of correct decision. In this paper, the family of formally unimodular lattices is presented and shown to possess the same secrecy function behavior as unimodular and isodual lattices. Based on Construction A, we provide a …
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 …
We furnish a procedure based on universal hash families (UHFs) that can convert an error correcting coding scheme (ECC) of rate $R$ into a semantically secure wiretap coding scheme of rate $R - ξ$ where $ξ$ is a parameter derived from the eavesdropper's point-to-point channel. This conversion is shown to be polynomial time efficient with block length and is applicable to any channel. When an ECC is chosen, our procedure induces a wiretap coding scheme that is concrete and efficient as long as the ECC is also such. To prove this induced wiretap coding scheme is semantically secure, we have cons…
In this paper, we investigate methods for reducing the likelihood that a message transmitted between two multiantenna nodes is intercepted by an undetected eavesdropper. In particular, we focus on the judicious transmission of artificial interference to mask the desired signal at the time it is broadcast. Unlike previous work that assumes some prior knowledge of the eavesdropper's channel and focuses on maximizing secrecy capacity, we consider the case where no information regarding the eavesdropper is available, and we use signal-to-interference-plus-noise-ratio (SINR) as our performance metr…
