Broadcast Channel With Confidential Messages Research Articles

Secure Degrees of Freedom of the Three-User MIMO Broadcast Channel With Delayed CSIT

This paper investigates the sum-secure degrees-of-freedom (SDoF) of three-user multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). Specifically, we obtain non-trivial sum-SDoF upper and lower bounds. Firstly, we derive the sum-SDoF upper bound by means of statistical equivalence property, security constraints, and permutations. Then, for the sum-SDoF lower bound, we leverage the artificial noise transmission and interference re-transmission to design two transmission schemes, which have holistic and sequential higher-order symbol generation, respectively. For these two schemes, we propose the redundancy reduction approach for security analysis, by which the minimal duration of artificial noise transmission phase of the scheme is obtained. To eliminate the redundant equations in security analysis, this approach first identifies the constituent equations, and then analyzes the rank of assemble of them. As a result, both the proposed sum-SDoF upper and lower bounds are tighter than the existing sum-SDoF upper and lower bounds, respectively. Furthermore, the proposed lower bound showcases a three-user coding gain.

Full-Duplex Relay with Delayed CSI Elevates the SDoF of the MIMO X Channel

In this article, the sum secure degrees-of-freedom (SDoF) of the multiple-input multiple-output (MIMO) X channel with confidential messages (XCCM) and arbitrary antenna configurations is studied, where there is no channel state information (CSI) at two transmitters and only delayed CSI at a multiple-antenna, full-duplex, and decode-and-forward relay. We aim at establishing the sum-SDoF lower and upper bounds. For the sum-SDoF lower bound, we design three relay-aided transmission schemes, namely, the relay-aided jamming scheme, the relay-aided jamming and one-receiver interference alignment scheme, and the relay-aided jamming and two-receiver interference alignment scheme, each corresponding to one case of antenna configurations. Moreover, the security and decoding of each scheme are analyzed. The sum-SDoF upper bound is proposed by means of the existing SDoF region of two-user MIMO broadcast channel with confidential messages (BCCM) and delayed channel state information at the transmitter (CSIT). As a result, the sum-SDoF lower and upper bounds are derived, and the sum-SDoF is characterized when the relay has sufficiently large antennas. Furthermore, even assuming no CSI at two transmitters, our results show that a multiple-antenna full-duplex relay with delayed CSI can elevate the sum-SDoF of the MIMO XCCM. This is corroborated by the fact that the derived sum-SDoF lower bound can be greater than the sum-SDoF of the MIMO XCCM with output feedback and delayed CSIT.

Sparse Non-Orthogonal Frequency Division Multiplexing for Secure Transmission Over Broadcast Channels

We propose a novel transmission scheme for the parallel Gaussian broadcast channel with confidential messages (BCCM). In this model, The source node wishes to transmit a confidential message to each user over N independent sub-channels, where each sub-channel is degraded for one user than others. Our objective is to design a secure transmission technique that maximizes the sum secrecy rate under an average power constraint. The most common technique to tackle this problem in practice is orthogonal frequency division multiplexing (OFDM). Nevertheless, the OFDM-based BCCM suffers from excessive bandwidth utilization due to the sub-carrier orthogonality requirement. We propose a sparse non-orthogonal frequency-division Multiplexing (SNOFDM) transmission scheme. In SNOFDM, sub-carriers are generated by first selecting a subset of orthogonal sub-channels to reduce spectral resources. Then, the selected sub-channels are multiplexed in time to generate non-orthogonal sub-carriers. This, in effect increases, the spectral efficiency compared to OFDM. To overcome the interference introduced due to the non-orthogonality of sub-carriers, the transmitter sends the sparsest representation of the transmitted codeword. Furthermore, we provide a sub-carrier selection and power control procedures to maximize the sum rate of SNOFDM according to CSI fed back from receivers to source node. Our numerical results show that SNOFDM offers better spectral efficiency and a higher secrecy rate compared to OFDM. We provide extensive simulation results to study the effects of transmission parameters of SNOFDM on the achievable secrecy rate.

Securing Multi-User Broadcast Wiretap Channels With Finite CSI Feedback

In this work, we investigate the problem of secure broadcasting over block-fading wiretap channels with limited channel knowledge at the transmitter. More particularly, we analyze the effect of having a finite rate feedback on the throughput of multi-user broadcast wiretap channels. We consider that the transmitter is only provided by a $b$-bits feedback of the main channel state information (CSI) sent by each legitimate receiver, at the beginning of each fading block, over error-free public links with limited capacity. Also, we assume that the transmitter is aware of the statistics of the eavesdropper's CSI but not of its channel's realizations. Under these assumptions of CSI uncertainty, we characterize the ergodic secrecy capacity of the system when a common message is broadcasted to all legitimate receivers, the ergodic secrecy sum-capacity when multiple independent messages are transmitted, and the ergodic secrecy capacity region for the broadcast channel with confidential messages (BCCM). In all three scenarios, we show that as long as the transmitter has some knowledge of the main CSI, obtained even through a 1-bit CSI feedback, a non-zero secrecy rate can still be achieved. The impact of having the feedback sent over a binary erasure channel (BEC) is also investigated for the BCCM case. Here again, and even with the possibility of having the feedback bits erased, a positive secrecy rate can still be achieved as long as the erasure event is not a probability-one event. An asymptotic analysis of the obtained results is provided for the high SNR regime, and the scaling law of the system, when the number of legitimate receivers is large, is also presented.

Secure Degrees of Freedom of Rank-Deficient BCCM and Rank-Deficient ICCM

The secure degrees of freedom (SDoF) of two-user rank-deficient multiple-input multiple-output (MIMO) broadcast channel with confidential messages (BCCM) and two-user rank- deficient MIMO interference channel with confidential messages (ICCM) are studied respectively in this paper. In the systems, each transmitter has $M$ antennas, and each receiver has $N$ antennas. We consider that each transmitter intends to send secure messages to the corresponding receiver, and another receiver can receive the messages but cannot decode them, which ensures that the messages are confidential. Comparing with previous studies on two-user broadcast channel and interference channel, we explore the case that channel matrices are rank-deficient, and the rank of channel matrices can take arbitrary value, $D \leq \text{min} (M,N)$ . For the two rank-deficient channels, BCCM and ICCM, we divide the problem into several regimes according to the different configurations of the rank of channel matrices and the number of antennas at each node. The outer bound of rank-deficient BCCM is inferred from information theoretic methods and the achievable schemes are given by zero forcing techniques. We derive the outer bound of rank-deficient ICCM by taking the minimum region of the three outer bounds, where the first outer bound is the result of rank-deficient interference channel model without secrecy constraints, the second outer bound is obtained by considering secrecy constraints, and the third outer bound is achieved by transmitters cooperation. Then we present the achievable schemes by combining zero-forcing, real interference alignment, and spatial alignment. Finally, we determine the exact SDoF of the rank-deficient BCCM and the rank-deficient ICCM.

Secure Degrees of Freedom in Networks with User Misbehavior

We investigate the secure degrees of freedom (s.d.o.f.) of three new channel models: broadcast channel with combating helpers, interference channel with selfish users, and multiple access wiretap channel with deviating users. The goal of introducing these channel models is to investigate various malicious interactions that arise in networks, including active adversaries. That is in contrast with the common assumption in the literature that the users follow a certain protocol altruistically and transmit both message-carrying and cooperative jamming signals in an optimum manner. In the first model, over a classical broadcast channel with confidential messages (BCCM), there are two helpers, each associated with one of the receivers. In the second model, over a classical interference channel with confidential messages (ICCM), there is a helper and users are selfish. By casting each problem as an extensive-form game and applying recursive real interference alignment, we show that, for the first model, the combating intentions of the helpers are neutralized and the full s.d.o.f. is retained; for the second model, selfishness precludes secure communication and no s.d.o.f. is achieved. In the third model, we consider the multiple access wiretap channel (MAC-WTC), where multiple legitimate users wish to have secure communication with a legitimate receiver in the presence of an eavesdropper. We consider the case when a subset of users deviate from the optimum protocol that attains the exact s.d.o.f. of this channel. We consider two kinds of deviation: when some of the users stop transmitting cooperative jamming signals, and when a user starts sending intentional jamming signals. For the first scenario, we investigate possible responses of the remaining users to counteract such deviation. For the second scenario, we use an extensive-form game formulation for the interactions of the deviating and well-behaving users. We prove that a deviating user can drive the s.d.o.f. to zero; however, the remaining users can exploit its intentional jamming signals as cooperative jamming signals against the eavesdropper and achieve an optimum s.d.o.f.

Secure Degrees of Freedom Region of Static and Time-Varying Gaussian MIMO Interference Channel

We consider the two-user multiple-input multiple-output (MIMO) interference channel with confidential messages (ICCM). We determine the exact secure degrees of freedom (s.d.o.f.) region for the symmetric case of $M$ antennas at both transmitters and $N$ antennas at both receivers. We develop the converse by combining the broadcast channel with confidential messages (BCCM) cooperative upper bound, decodability upper bound for the interference channel with no secrecy constraints, and vector extensions of the secrecy penalty and role of a helper lemmas. For the achievability, we first show that the s.d.o.f. region is a four-vertex polytope. For the sum s.d.o.f. point, we propose a novel achievable scheme for the $2 \times 2$ ICCM, which combines asymptotic real interference alignment with spatial interference alignment. Using this scheme, we provide achievable schemes for any $M$ and $N$ by proper vector space operations. We achieve the other non-trivial extreme polytope points by employing one of the transmitters as a deaf helper for assisting the secure transmission of the other user. We present simplified achievable schemes for the special case of time-varying MIMO ICCM. The achievable schemes, in this case, make use of the time-varying nature of the channel to construct vector-space alignment counterpart of the real interference alignment used in the static channel case.

On Linear Precoding for the Two-User MISO Broadcast Channel With Confidential Messages and Per-Antenna Constraints

We study the design of linear precoders for secure transmission in the two-user multiple-input single-output (MISO) broadcast channel with confidential messages (BC-CM). The transmitter has multiple antennas, and each user has a single receive antenna. Two independent messages are simultaneously transmitted, one intended for each user, and each message should be kept confidential from the other user. Assuming real-valued transmitted signals, we design the linear precoders subject to total and per-antenna average power constraints, and also subject to amplitude constraints. In both cases, we tackle the design problem via weighted secrecy sum rate maximization. The resulting problem, however, involves a fractional objective, making it nonconvex and difficult to solve. Nevertheless, we show that this difficult problem can be transformed into a more tractable problem, for which a solution can be obtained by an iterative search algorithm. In addition, we characterize a condition under which the obtained solution is guaranteed to be optimal. Furthermore, we show that the problem formulation and solution approach can be easily extended to handle the robust version of the design problem with uncertain channel information. We provide numerical examples to demonstrate the performance of the proposed precoder in terms of the achievable secrecy rate regions subject to the aforementioned constraints. We also demonstrate the performance of the robust precoder under different channel uncertainty levels.

How Can We Fully Use Noiseless Feedback to Enhance the Security of the Broadcast Channel with Confidential Messages

The model for a broadcast channel with confidential messages (BC-CM) plays an important role in the physical layer security of modern communication systems. In recent years, it has been shown that a noiseless feedback channel from the legitimate receiver to the transmitter increases the secrecy capacity region of the BC-CM. However, at present, the feedback coding scheme for the BC-CM only focuses on producing secret keys via noiseless feedback, and other usages of the feedback need to be further explored. In this paper, we propose a new feedback coding scheme for the BC-CM. The noiseless feedback in this new scheme is not only used to produce secret keys for the legitimate receiver and the transmitter but is also used to generate update information that allows both receivers (the legitimate receiver and the wiretapper) to improve their channel outputs. From a binary example, we show that this full utilization of noiseless feedback helps to increase the secrecy level of the previous feedback scheme for the BC-CM.

Secure Degrees of Freedom Region of the Two-User MISO Broadcast Channel With Alternating CSIT

The two user multiple-input single-output (MISO) broadcast channel with confidential messages (BCCM) is studied, in which the nature of channel state information at the transmitter (CSIT) from each user can be of the form $I_{i}$ , $i=1,2$ where $I_{1}, I_{2}\in \{\mathsf {P}, \mathsf {D}, \mathsf {N}\}$ , and the forms $\mathsf {P}$ , $\mathsf {D}$ , and $\mathsf {N}$ correspond to perfect and instantaneous, completely delayed, and no CSIT, respectively. Thus, the overall CSIT can alternate between nine possible states corresponding to all possible values of $I_{1}I_{2}$ , with each state occurring for $\lambda _{I_{1}I_{2}}$ fraction of the total duration. We assume that perfect and instantaneous CSI is available at the all receivers. The main contribution of this paper is to establish the secure degrees of freedom (s.d.o.f.) region of the MISO BCCM with alternating CSIT with the symmetry assumption, where $\lambda _{I_{1} I_{2}}=\lambda _{I_{2}I_{1}}$ . The main technical contributions include developing 1) novel achievable schemes for MISO BCCM with alternating CSIT with security constraints, which also highlight the synergistic benefits of inter-state coding for secrecy; 2) new converse proofs via local statistical equivalence and channel enhancement; and 3) showing the interplay between various aspects of channel knowledge and their impact on s.d.o.f.