We study a lossy source coding problem with secrecy constraints in which a remote information source should be transmitted to a single destination via multiple agents in the presence of a passive eavesdropper. The agents observe noisy versions of the source and independently encode and transmit their observations to the destination via noiseless rate-limited links. The destination should estimate the remote source based on the information received from the agents within a certain mean distortion threshold. The eavesdropper, with access to side information correlated to the source, is able to listen in on one of the links from the agents to the destination in order to obtain as much information as possible about the source. This problem can be viewed as the so-called CEO problem with additional secrecy constraints. We establish inner and outer bounds on the rate-distortion-equivocation region of this problem. We also obtain the region in special cases where the bounds are tight. Furthermore, we study the quadratic Gaussian case and provide the optimal rate-distortion-equivocation region when the eavesdropper has no side information and an achievable region for a more general setup with side information at the eavesdropper.
We establish a new extremal inequality, which is further leveraged to give a complete characterization of the rate region of the vector Gaussian CEO problem with the trace distortion constraint. The proof of this extremal inequality hinges on a careful analysis of the Karush-Kuhn-Tucker necessary conditions for the non-convex optimization problem associated with the Berger-Tung scheme, which enables us to integrate the perturbation argument by Wang and Chen with the distortion projection method by Rahman and Wagner.
This paper studies a class of source coding problems that combines elements of the CEO problem with the multiple description problem. In this setting, noisy versions of one remote source are observed by two nodes with encoders (which is similar to the CEO problem). However, it differs from the CEO problem in that each node must generate multiple descriptions of the source. This problem is of interest in multiple scenarios in efficient communication over networks. In this paper, an achievable region and an outer bound are presented for this problem, which is shown to be sum rate optimal for a c…
In this paper we investigate the problem of optimal cache placement under secrecy constraints in heterogeneous networks, where small-cell base stations are equipped with caches to reduce the overall backhaul load. For two models for eavesdropping attacks, we formally derive the necessary conditions for secrecy and we derive the corresponding achievable backhaul rate. In particular we formulate the optimal caching schemes with secrecy constraints as a convex optimization problem. We then thoroughly investigate the backhaul rate performance of the heterogeneous network with secrecy constraints u…
In this paper, we study the secrecy rates over weak Gaussian interference channels for different transmission schemes. We focus on the low-SNR regime and obtain the minimum bit energy E_b/N_0_min values, and the wideband slope regions for both TDMA and multiplexed transmission schemes. We show that secrecy constraints introduce a penalty in both the minimum bit energy and the slope regions. Additionally, we identify under what conditions TDMA or multiplexed transmission is optimal. Finally, we show that TDMA is more likely to be optimal in the presence of secrecy constraints.
We study the outage probability of opportunistic relay selection in decode-and-forward relaying with secrecy constraints. We derive the closed-form expression for the outage probability. Based on the analytical result, the asymptotic performance is then investigated. The accuracy of our performance analysis is verified by the simulation results.
In this paper, we study the vector Gaussian Chief Executive Officer (CEO) problem under logarithmic loss distortion measure. Specifically, $K \geq 2$ agents observe independently corrupted Gaussian noisy versions of a remote vector Gaussian source, and communicate independently with a decoder or CEO over rate-constrained noise-free links. The CEO wants to reconstruct the remote source to within some prescribed distortion level where the incurred distortion is measured under the logarithmic loss penalty criterion. We find an explicit characterization of the rate-distortion region of this model.…
An opportunistic relay selection based on instantaneous knowledge of channels is considered to increase security against eavesdroppers. The closed-form expressions are derived for the average secrecy rates and the outage probability when the cooperative networks use Decode-and-Forward (DF) or Amplify-and-Forward (AF) strategy. These techniques are demonstrated analytically and with simulation results.
This paper simplifies an existing coding scheme for the two-receiver discrete memoryless broadcast channel with complementary receiver side information where there is a passive eavesdropper and individual secrecy is required. The existing coding scheme is simplified in two steps by replacing Wyner secrecy coding with Carleial-Hellman secrecy coding. The resulting simplified scheme is free from redundant message splits and random components. Not least, the simplified scheme retains the existing achievable individual secrecy rate region. Finally, its construction simplicity helps us gain additio…
In communication networks secrecy constraints usually incur an extra limit in capacity or generalized degrees-of-freedom (GDoF), in the sense that a penalty in capacity or GDoF is incurred due to the secrecy constraints. Over the past decades a significant amount of effort has been made by the researchers to understand the limits of secrecy constraints in communication networks. In this work, we focus on how to remove the secrecy constraints in communication networks, i.e., how to remove the GDoF penalty due to secrecy constraints. We begin with three basic settings: a two-user symmetric Gauss…
In many communication channels, secrecy constraints usually incur a penalty in capacity, as well as generalized degrees-of-freedom (GDoF). In this work we show an interesting observation that, adding a helper can totally remove the penalty in sum GDoF, for a two-user symmetric Gaussian interference channel. For the interference channel where each transmitter sends a message to an intended receiver without secrecy constraints, the sum GDoF is a well-known "W" curve, characterized by Etkin-Tse-Wang in 2008. If the secrecy constraints are imposed on this interference channel, where the message of…
In this paper, we study the secure transmission in multihop wireless networks with randomize-and-forward (RaF) relaying, in the presence of randomly distributed eavesdroppers. By considering adaptive encoder with on-off transmission (OFT) scheme, we investigate the optimal design of the wiretap code and routing strategies to maximize the secrecy rate while satisfying the secrecy outage probability (SOP) constraint. We derive the exact expressions for the optimal rate parameters of the wiretap code. Then the secure routing problem is solved by revising the classical Bellman-Ford algorithm. Simu…
This paper studies a scalar Gaussian wiretap channel where instead of an average input power constraint, we consider a peak amplitude constraint on the input. The goal is to obtain insights into the secrecy-capacity and the structure of the secrecy-capacity-achieving distribution. Capitalizing on the recent theoretical progress on the structure of the secrecy-capacity-achieving distribution, this paper develops a numerical procedure, based on the gradient ascent algorithm and a version of the Blahut-Arimoto algorithm, for computing the secrecy-capacity and the secrecy-capacity-achieving input …
This paper studies the problem of secure communication over broadcast channels under the individual secrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant of each message (i.e., the information leakage from each message to the eavesdropper is made vanishing). Building upon Carleial-Hellman's secrecy coding, Wyner's secrecy coding, the frameworks of superposition coding and Marton's coding together with techniques such as rate splitting and indirect decoding, ach…
We investigate the delay limited secrecy capacity of the flat fading channel under two different assumptions on the available transmitter channel state information (CSI). The first scenario assumes perfect prior knowledge of both the main and eavesdropper channel gains. Here, upper and lower bounds on the delay limited secrecy capacity are derived, and shown to be tight in the high signal-to-noise ratio (SNR) regime. In the second scenario, only the main channel CSI is assumed to be available at the transmitter where, remarkably, we establish the achievability of a non-zero delay-limited secur…
In this work, we consider a scenario where two multiple-aperture legitimate nodes (Alice and Bob) communicate by means of Free-Space Optical (FSO) communication in the presence of a multiple-aperture eavesdropper (Eve), which is subject to pointing errors. Two different schemes are considered depending on the availability of channel state information (CSI) at Alice: i) the adaptive scheme, where Alice possesses the instantaneous CSI with respect to Bob; ii) the fixed-rate scheme, where such information is not available at Alice. The performance of the aforementioned schemes is evaluated in ter…
We study the optimality of linear precoding for the two-receiver multiple-input multiple-output (MIMO) Gaussian broadcast channel (BC) with confidential messages. Secret dirty-paper coding (SDPC) is optimal under an input covariance constraint, but there is no computable secrecy capacity expression for the general MIMO case under an average power constraint. In principle, for this case, the secrecy capacity region could be found through an exhaustive search over the set of all possible matrix power constraints. Clearly, this search, coupled with the complexity of dirty-paper encoding and decod…
We study the vector Gaussian Chief Executive Officer (CEO) problem under logarithmic loss distortion measure. Specifically, $K \geq 2$ agents observe independently corrupted Gaussian noisy versions of a remote vector Gaussian source, and communicate independently with a decoder or CEO over rate-constrained noise-free links. The CEO also has its own Gaussian noisy observation of the source and wants to reconstruct the remote source to within some prescribed distortion level where the incurred distortion is measured under the logarithmic loss penalty criterion. We find an explicit characterizati…
In this paper, the individual secrecy of two-way wiretap channel is investigated, where two legitimate users' messages are separately guaranteed secure against an external eavesdropper. For one thing, in some communication scenarios, the joint secrecy is impossible to achieve both positive secrecy rates of two users. For another, the individual secrecy satisfies the secrecy demand of many practical communication systems. Thus, firstly, an achievable secrecy rate region is derived for the general two-way wiretap channel with individual secrecy. In a deterministic channel, the region with indivi…
This paper considers a three-receiver broadcast channel with degraded message sets and message cognition. The model consists of a common message for all three receivers, a private common message for only two receivers and two additional private messages for these two receivers, such that each receiver is only interested in one message, while being fully cognizant of the other one. First, this model is investigated without any secrecy constraints, where the capacity region is established, showing that the straightforward extension of the Körner and Marton inner bound to the investigated scenari…
Two-Way Wiretap Channel under Mixed Secrecy Constraint
Volkswagen Infotainment GmbH（大众车载娱乐有限公司）；School of Data Science, The Chinese University of Hong Kong Shenzhen（香港中文大学深圳校区数据科学学院）；International Quantum Academy, Shenzhen（深圳国际量子研究院）；Graduate School of Mathematics, Nagoya University（名古屋大学大学院数学研究科）
In this paper, collaborative use of relays to form a beamforming system with the aid of perfect channel state information (CSI) and to provide physical-layer security is investigated. In particular, a decode-and-forward-based relay beamforming design subject to total and individual relay power constraints is studied with the goal of maximizing the secrecy rate. It is shown that the total power constraint leads to a closed-form solution. The design under individual relay power constraints is formulated as an optimization problem which is shown to be easily solved using two different approaches,…
In the spectrum-sharing technology, a secondary user may utilize the primary user's licensed band as long as its interference to the primary user is below a tolerable value. In this paper, we consider a scenario in which a secondary user is operating in the presence of both a primary user and an eavesdropper. Hence, the secondary user has both interference limitations and security considerations. In such a scenario, we study the secrecy capacity limits of opportunistic spectrum-sharing channels in fading environments and investigate the optimal power allocation for the secondary user under ave…
This paper analyzes the throughput of industrial communication networks under a secrecy constraint. The proposed scenario is composed by sensors that measure some relevant information of the plant that is first processed by aggregator node and then sent to the control unit. The sensor measurements, their communication with the aggregetor and the information processing are all assumed perfect. To reach the control unit, the message may travel through relay nodes, forming a multi-hop, wireless link. At every hop, eavesdropper nodes attempt to acquire the messages transmitted through the legitima…
This work studies the secrecy-capacity of a scalar-Gaussian wiretap channel with an amplitude constraint on the input. It is known that for this channel, the secrecy-capacity-achieving distribution is discrete with finitely many points. This work improves such result by showing an upper bound of the order $\frac{\mathsf{A}}{σ_1^2}$ where $\mathsf{A}$ is the amplitude constraint and $σ_1^2$ is the variance of the Gaussian noise over the legitimate channel.
Recently, physical layer security based approaches have drawn considerable attentions and are envisaged to provide secure communications in the wireless networks. However, most existing literatures only focus on the physical layer. Thus, how to design an effective transmission scheme which also considers the requirements from the upper layers is still an unsolved problem. We consider such cross-layer resource allocation problem in the multi-user downlink environment for both having instantaneous and partial eavesdropping channel information scenarios. The problem is first formulated in a new s…
This paper studies the value of limited rate cooperation between the transmitters for managing interference and simultaneously ensuring secrecy, in the 2-user Gaussian symmetric interference channel (GSIC). First, the problem is studied in the symmetric linear deterministic IC (SLDIC) setting, and achievable schemes are proposed, based on interference cancelation, relaying of the other user's data bits, and transmission of random bits. In the proposed achievable scheme, the limited rate cooperative link is used to share a combination of data bits and random bits depending on the model paramete…
This paper studies the capacity of the multi-antenna or multiple-input multiple-output (MIMO) secrecy channels with multiple eavesdroppers having single/multiple antennas. It is known that the MIMO secrecy capacity is achievable with the optimal transmit covariance matrix that maximizes the minimum difference between the channel mutual information of the secrecy user and those of the eavesdroppers. The MIMO secrecy capacity computation can thus be formulated as a non-convex max-min problem, which cannot be solved efficiently by standard convex optimization techniques. To handle this difficulty…
In this paper, we study the problem of secret communication over a multiple-access channel with a common message. Here, we assume that two transmitters have confidential messages, which must be kept secret from the wiretapper (the second receiver), and both of them have access to a common message which can be decoded by the two receivers. We call this setting as Multiple-Access Wiretap Channel with Common message (MAWC-CM). For this setting, we derive general inner and outer bounds on the secrecy capacity region for the discrete memoryless case and show that these bounds meet each other for a …
The optimal power allocation that maximizes the secrecy capacity of block fading Gaussian (BF-Gaussian) networks with causal channel state information (CSI), M-block delay tolerance and a frame based power constraint is examined. In particular, we formulate the secrecy capacity maximization as a dynamic program. We propose suitable linear approximations of the secrecy capacity density in the low SNR, the high SNR and the intermediate SNR regimes, according to the overall available power budget. Our findings indicate that when the available power resources are very low (low SNR case) the optima…
This paper investigates the physical-layer security for an indoor visible light communication (VLC) network consisting of a transmitter, a legitimate receiver and an eavesdropper. Both the main channel and the wiretapping channel have nonnegative inputs, which are corrupted by additive white Gaussian noises. Considering the illumination requirement and the physical characteristics of lighting source, the input is also constrained in both its average and peak optical intensities. Two scenarios are investigated: one is only with an average optical intensity constraint, and the other is with both…
In many information-theoretic channel coding problems, adding an input cost constraint to the operational setup amounts to restricting the optimization domain in the capacity formula. This paper shows that, in contrast to common belief, such a simple modification does not hold for the cost-constrained (CC) wiretap channel (WTC). The secrecy-capacity of the discrete memoryless (DM) WTC without cost constraints is described by a single auxiliary random variable. For the CC DM-WTC, however, we show that two auxiliaries are necessary to achieve capacity. Specifically, we first derive the secrecy-c…
This paper studies the problem of secure communication over the broadcast channel with receiver side information under the lens of individual secrecy constraints. That is, the transmitter wants to send two independent messages to two receivers which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the ca…
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…
This paper proposes a new design of non-orthogonal multiple access (NOMA) under secrecy considerations. We focus on a NOMA system where a transmitter sends confidential messages to multiple users in the presence of an external eavesdropper. The optimal designs of decoding order, transmission rates, and power allocated to each user are investigated. Considering the practical passive eavesdropping scenario where the instantaneous channel state of the eavesdropper is unknown, we adopt the secrecy outage probability as the secrecy metric. We first consider the problem of minimizing the transmit po…
In this paper, collaborative use of relays to form a beamforming system and provide physical-layer security is investigated. In particular, decode-and-forward (DF) and amplify-and-forward (AF) relay beamforming designs under total and individual relay power constraints are studied with the goal of maximizing the secrecy rates when perfect channel state information (CSI) is available. In the DF scheme, the total power constraint leads to a closed-form solution, and in this case, the optimal beamforming structure is identified in the low and high signal-to-noise ratio (SNR) regimes. The beamform…
In this paper, we show the equivalency of weak and strong secrecy conditions for a large class of secure network coding problems. When we restrict to linear operations, we show the equivalency of "perfect secrecy and zero-error constraints" with "weak secrecy and $ε$-error constraints".
In this paper, we propose a device to device (D2D) communication scenario underlaying a cellular network where both D2D and cellular users (CUs) are discrete power-rate systems with limited feedback from the receivers. It is assumed that there exists an adversary which wants to eavesdrop on the information transmission from the base station (BS) to CUs. Since D2D communication shares the same spectrum with cellular network, cross interference must be considered. However, when secrecy capacity is considered, the interference caused by D2D communication can help to improve the secrecy communicat…
We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed wire-tapper who receives a degraded version of the signal at the receiver. We define a suitable security measure for this multi-access environment. We derive an outer bound for the rate region such that secrecy to some pre-determined degree can be maintained. We also find, using Gaussian codebooks, an achievable such secrecy region. Gaussian codewords are shown to achieve the sum capacity outer bound, and the …
This work presents novel achievable schemes for the 2-user symmetric linear deterministic interference channel with limited-rate transmitter cooperation and perfect secrecy constraints at the receivers. The proposed achievable scheme consists of a combination of interference cancelation, relaying of the other user's data bits, time sharing, and transmission of random bits, depending on the rate of the cooperative link and the relative strengths of the signal and the interference. The results show, for example, that the proposed scheme achieves the same rate as the capacity without the secrecy …
The wiretap channel model of Wyner is one of the first communication models with both reliability and security constraints. Capacity-achieving schemes for various models of the wiretap channel have received considerable attention in recent literature. In this paper, we show that capacity of the general (not necessarily degraded or symmetric) wiretap channel under a "strong secrecy constraint" can be achieved using a transmission scheme based on polar codes. We also extend our construction to the case of broadcast channels with confidential messages defined by Csisz{á}r and K{örner}, achieving …
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…
In this paper, we consider the secure transmission design for a multiple-input single-output Femtocell overlaid with a Macrocell in co-channel deployment. The Femtocell base station sends confidential messages to information receiving Femtocell users (FUs) and energy signals to energy receiving (ER) FUs while limiting the interference to Macrocell users (MUs). The ER FUs have the potential to wiretap the confidential messages. By taking fairness into account, we propose a sum logarithmic secrecy rate maximization beamforming design problem under the interference constraints for MUs and energy …
The existing research on physical layer security commonly assumes the number of eavesdropper antennas to be known. Although this assumption allows one to easily compute the achievable secrecy rate, it can hardly be realized in practice. In this paper, we provide an innovative approach to study secure communication systems without knowing the number of eavesdropper antennas by introducing the concept of spatial constraint into physical layer security. Specifically, the eavesdropper is assumed to have a limited spatial region to place (possibly an infinite number of) antennas. From a practical p…
This paper derives outer bounds on the secrecy capacity region of the 2-user Z interference channel (Z-IC) with rate-limited unidirectional cooperation between the transmitters. First, the model is studied under the linear deterministic setting. The derivation of the outer bounds on the secrecy capacity region involves careful selection of the side information to be provided to the receivers and using the secrecy constraints at the receivers in a judicious manner. To this end, a novel partitioning of the encoded messages and outputs is proposed for the deterministic model based on the strength…
In this work, we consider achievable secrecy rates for symmetric $K$-user ($K \ge 3$) interference channels with confidential messages. We find that nested lattice codes and layered coding are useful in providing secrecy for these channels. Achievable secrecy rates are derived for very strong interference. In addition, we derive the secure degrees of freedom for a range of channel parameters. As a by-product of our approach, we also demonstrate that nested lattice codes are useful for K-user symmetric interference channels without secrecy constraints in that they yield higher degrees of freedo…
We study channel resolvability for the discrete memoryless multiple-access channel with cribbing, i.e., the characterization of the amount of randomness required at the inputs to approximately produce a chosen i.i.d. output distribution according to KL divergence. We analyze resolvability rates when one encoder cribs (i) the input of the other encoder; or the output of the other encoder, (ii) non-causally, (iii) causally, or (iv) strictly-causally. For scenarios (i)-(iii), we exactly characterize the channel resolvability region. For (iv), we provide inner and outer bounds for the channel reso…
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.
The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage rate to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived when the eavesdropper knows the codebook. The inner bound relies o…
Reconfigurable intelligent surface (RIS) assisted radio is considered as an enabling technology with great potential for the sixth-generation (6G) wireless communications standard. The achievable secrecy rate (ASR) is one of the most fundamental metrics to evaluate the capability of facilitating secure communication for RIS-assisted systems. However, the definition of ASR is based on Shannon's information theory, which generally requires long codewords and thus fails to quantify the secrecy of emerging delay-critical services. Motivated by this, in this paper we investigate the problem of maxi…
We investigate transmission optimization for intelligent reflecting surface (IRS) assisted multi-antenna systems from the physical-layer security perspective. The design goal is to maximize the system secrecy rate subject to the source transmit power constraint and the unit modulus constraints imposed on phase shifts at the IRS. To solve this complicated non-convex problem, we develop an efficient alternating algorithm where the solutions to the transmit covariance of the source and the phase shift matrix of the IRS are achieved in closed form and semi-closed forms, respectively. The convergen…
This paper considers multiple-input multiple-output (MIMO) full-duplex (FD) two-way secrecy systems. Specifically, both multi-antenna FD legitimate nodes exchange their own confidential message in the presence of an eavesdropper. Taking into account the imperfect channel state information (CSI) of the eavesdropper, we formulate a robust sum secrecy rate maximization (RSSRM) problem subject to the outage probability constraint of the achievable sum secrecy rate and the transmit power constraint. Unlike other existing channel uncertainty models, e.g., norm-bounded and Gaussian-distribution, we e…
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…
