Multiple Access Wiretap Channel Research Articles

10 Gb/s two-dimensional free-space optical code division multiple access wiretap channel with spatial diversity

We experimentally demonstrate a 10 Gb/s free-space optical wiretap channel based on a spatial-diversity scheme and optical code division multiple access. In weak and middle turbulence cases, the bit error rate of a legitimate user can be decreased, and physical layer security can be simultaneously enhanced.

Polar Coding for the Multiple Access Wiretap Channel via Rate-Splitting and Cooperative Jamming

We consider strongly secure communication over a discrete memoryless multiple access wiretap channel with two transmitters. No degradation or symmetry assumptions are made on the channel. Our main result is that any rate pair known to be achievable with a random coding like proof, is also achievable with an explicit and low-complexity polar coding scheme. Moreover, if the rate pair is known to be achievable without time-sharing, then time-sharing is not needed in our polar coding scheme as well. Our proof technique relies on rate-splitting, which introduces two virtual transmitters, and cooperative jamming strategies implemented by these virtual transmitters. Specifically, our coding scheme combines point-to-point codes that either aim at secretly conveying a message to the legitimate receiver or at performing cooperative jamming. Each point-to-point code relies on block Markov encoding to be able to deal with an arbitrary channel and strong secrecy. Consequently, our coding scheme is the combination of inter-dependent block Markov constructions. We assess reliability and strong secrecy through a detailed analysis of the dependencies between the random variables involved in the scheme.

LDPC codes over Gaussian multiple access wiretap channel

The authors study the problem of two-user Gaussian multiple access channel (GMAC) in the presence of an external eavesdropper, where all transmitted messages should be kept confidential against the eavesdropper. For this purpose, they propose a secure coding scheme on this channel which utilises low-density parity-check (LDPC) codes by employing random bit insertion and puncturing techniques. At each encoder, the confidential message with some random bits as a random message are systematically encoded, and then the associated bits to the confidential message are punctured. Next, the encoders send their unpunctured bits over a Gaussian multiple access wiretap channel (GMAC-WT). The puncturing distribution applied to the LDPC code is considered in random and optimised cases. They utilise a modified extrinsic information transfer chart analysis to optimise the puncturing distributions. The security gap is used as a measure of secrecy. They compared the achieved secure rate pair with an achievable secrecy rate region of GMAC-WT to show the effective performance of the proposed scheme. In this study, equal and unequal power conditions at the transmitters are investigated. For both cases, they attain a fairly small security gap which is equivalent to achieve the points near the secrecy rate region of GMAC-WT.

Secure Degrees of Freedom of the Multiple Access Wiretap Channel With Multiple Antennas

We consider a two-user multiple-input multiple-output multiple access wiretap channel with $N$ antennas at each transmitter, $N$ antennas at the legitimate receiver, and $K$ antennas at the eavesdropper. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for this model for all values of $N$ and $K$ . We subdivide our problem into several regimes based on the values of $N$ and $K$ , and provide achievable schemes based on vector space alignment and real alignment techniques for fixed and fading channel gains. To prove the optimality of the achievable schemes, we provide matching converses for each regime. Our results show how the number of eavesdropper antennas affects the optimal sum s.d.o.f. of the multiple access wiretap channel.

Secure Communication Over Finite State Multiple-Access Wiretap Channel With Delayed Feedback

Recently, it has been shown that the time-varying multiple-access channel (MAC) with perfect channel state information (CSI) at the receiver and delayed feedback CSI at the transmitters can be modeled as the finite state MAC (FS-MAC) with delayed state feedback, where the time variation of the channel is characterized by the statistics of the underlying state process. To study the fundamental limit of the secure transmission over multi-user wireless communication systems, we re-visit the FS-MAC with delayed state feedback by considering an external eavesdropper, which we call the finite state multiple-access wiretap channel (FS-MAC-WT) with delayed feedback. The main contribution of this paper is to show that taking full advantage of the delayed channel output feedback helps to increase the secrecy rate region of the FS-MAC-WT with delayed state feedback. Moreover, by a degraded Gaussian fading example, we show the effects of feedback delay and channel memory on the secrecy sum rate of the FS-MAC-WT with delayed feedback.

Individual secrecy of fading homogeneous multiple access wiretap channel with successive interference cancellation

We investigate individual secrecy performance in a K-user quasi-static Rayleigh fading homogeneous multiple access wiretap channel (MAC-WT), where a legitimate receiver employs successive interference cancellation (SIC) decoding. We first evaluate individual secrecy performance under an arbitrary SIC order by deriving closed-form expressions with respect to secrecy outage probability and effective secrecy throughput (EST) as main metrics. The resulting closed-form expressions disclose a significant impact on the secrecy performance from the order of SIC decoding. Therefore, we propose three SIC decoding order scheduling schemes: (1) round-robin scheme, absolutely fair and served as a benchmark; (2) suboptimal scheme, based on each user’s main channel condition; and (3) optimal scheme, based on each user’s achievable secrecy rate. Comparison results show that the last two schemes outperform the first one with regard to both the EST and the multi-user diversity gain, whereas the performance of the suboptimal scheme is highly close to that of the optimal scheme which is usually impractical due to a requirement for the eavesdropper’s channel state information (CSI).

Multiple access wiretap channel with noiseless feedback

The physical layer security in the up-link of the wireless communication systems is often modeled as the multiple access wiretap channel (MAC-WT), and recently it has received a lot attention. In this paper, the MAC-WT has been re-visited by considering the situation that the legitimate receiver feeds his received channel output back to the transmitters via two noiseless channels, respectively. This model is called the MAC-WT with noiseless feedback. Inner and outer bounds on the secrecy capacity region of this feedback model are provided. To be specific, we first present a decode-and-forward (DF) inner bound on the secrecy capacity region of this feedback model, and this bound is constructed by allowing each transmitter to decode the other one's transmitted message from the feedback, and then each transmitter uses the decoded message to re-encode his own messages, i.e., this DF inner bound allows the independent transmitters to co-operate with each other. Then, we provide a hybrid inner bound which is strictly larger than the DF inner bound, and it is constructed by using the feedback as a tool not only to allow the independent transmitters to co-operate with each other, but also to generate two secret keys respectively shared between the legitimate receiver and the two transmitters. Finally, we give a sato-type outer bound on the secrecy capacity region of this feedback model. The results of this paper are further explained via a Gaussian example.

Precoder Designs for MIMO Gaussian Multiple Access Wiretap Channels

This paper studies multiple-input multiple-output multiple access wiretap channels (MAC-WT) where an eavesdropper tries to tap the communication between multiple legitimate transmitters and a legitimate receiver. In this system, we propose precoder optimization methods at the transmitters in order to maximize the sum secrecy rate performance. Although this problem can be solved by the well-known difference of convex (DC) programming, we present a more efficient algorithm whose computational complexity is much lower than that of the conventional DC approach. By investigating the Karush-Kuhn-Tucker conditions, it is confirmed that the proposed low-complexity algorithm achieves the same performance as the conventional DC method. Our analysis also reveals that the proposed algorithm ensures global optimality for multiple-input single-output MAC-WT cases, while binary power control is optimal for single-input multiple-output scenarios. Simulation results demonstrate the efficacy of the proposed precoding methods.

Linear Precoding for Fading Cognitive Multiple-Access Wiretap Channel With Finite-Alphabet Inputs

We investigate the fading cognitive multiple-access wiretap channel (CMAC-WT), in which two secondary-user transmitters (STs) send secure messages to a secondary-user receiver (SR) in the presence of an eavesdropper and subject to interference threshold constraints at multiple primary-user receivers (PRs). We design linear precoders to maximize the average secrecy sum rate for a multiple-input–multiple-output (MIMO) fading CMAC-WT under finite-alphabet inputs and statistical channel state information at STs. For this nondeterministic polynomial-time NP-hard problem, we utilize an accurate approximation of the average secrecy sum rate to reduce the computational complexity and then present a two-layer algorithm by embedding the convex–concave procedure into an outer-approximation framework. The idea behind this algorithm is to reformulate the approximated average secrecy sum rate as a difference of convex functions and then generate a sequence of simpler relaxed sets to approach the nonconvex feasible set. Subsequently, we maximize the approximated average secrecy sum rate over the sequence of relaxed sets by using the convex–concave procedure. Numerical results indicate that our proposed precoding algorithm is superior to the conventional Gaussian precoding method in the medium and high signal-to-noise ratio (SNR) regimes.

Secure Degrees of Freedom of One-Hop Wireless Networks With No Eavesdropper CSIT

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 wiretap channel and the interference channel with an external eavesdropper. In particular, we show that in the absence of eavesdropper's CSIT, the $K$-user multiple access wiretap channel reduces to a wiretap channel with $(K-1)$ helpers from a sum s.d.o.f. perspective, and the optimal sum s.d.o.f. reduces from $\frac{K(K-1)}{K(K-1)+1}$ to $\frac{K-1}{K}$. For the interference channel with an external eavesdropper, the optimal sum s.d.o.f. decreases from $\frac{K(K-1)}{2K-1}$ to $\frac{K-1}{2}$ in the absence of the eavesdropper's CSIT. Our results show that the lack of eavesdropper's CSIT does not have a significant impact on the optimal s.d.o.f. for any of the three channel models, especially when the number of users is large. This implies that physical layer security can be made robust to the unavailability of eavesdropper CSIT at high signal to noise ratio (SNR) regimes by careful modification of the achievable schemes as demonstrated in this paper.

Secrecy in MIMO Networks with No Eavesdropper CSIT

We consider two fundamental multi-user channel models: the multiple-input multiple-output (MIMO) wiretap channel with one helper (WTH) and the MIMO multiple access wiretap (MAC-WT) channel. In each case, the eavesdropper has $K$ antennas while the remaining terminals have $N$ antennas each. We consider a fast fading channel where the channel state information (CSI) of the legitimate receiver is available at the transmitters but no CSI at the transmitters (CSIT) is available for the eavesdropper’s channel. We determine the optimal sum secure degrees of freedom (s.d.o.f.) for each channel model for the regime $K\leq N$ , and show that in this regime, the MAC-WT channel reduces to the WTH in the absence of eavesdropper CSIT. For the regime $N\leq K\leq 2N$ , we obtain the optimal linear s.d.o.f., and show that the MAC-WT channel and the WTH have the same optimal s.d.o.f. when restricted to linear encoding strategies. In the absence of any such restrictions, we provide an upper bound for the sum s.d.o.f. of the MAC-WT channel in the regime $N\leq K\leq 2N$ . Our results show that unlike in the single-input single-output case, there is loss of s.d.o.f. for even the WTH due to lack of eavesdropper CSIT when $K\geq N$ .

ZF-SIC Based Individual Secrecy in SIMO Multiple Access Wiretap Channel

In this paper, a decoding method of joint zero-forcing and successive interference cancellation (ZF-SIC) is put forward to assist the study of the individual secrecy in the quasi-static Rayleigh fading single-input multiple-output multiple access wiretap channel. We first evaluate the individual secrecy performance by deriving the closed-form expressions in terms of positive secrecy capacity probability, secrecy outage probability, and effective secrecy throughput (EST). Besides the expected impact of the SIC order, we find, in high signal-to-noise ratio (SNR) regime, the secrecy performance is only determined by the transmitter’s relative distance to eavesdropper over legitimate receiver rather than the SNR. Such a result prompts us to propose an SIC order scheduling scheme (alternative scheme) on basis of the transmitters’ relative distances from the shortest to the longest. It is proved optimal in achieving total maximum EST in high SNR regime. Finally, we also investigate the problem of optimal power allocation to each transmitter under the constraint of the limited total power. An interesting solution to this problem is disclosed with the aid of numerical analysis.

Secure Degrees of Freedom of the Gaussian Diamond-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. Our results show: 1) how to strike a balance between sending message symbols and common noise symbols from the source to the relays in the broadcast component and 2) how to combine artificial noise-beamforming and noise-alignment techniques at the relays in the multiple access component. In the case with full CSI, we propose a scheme where the relays simultaneously beamform common noise signals in the null space of the legitimate destination’s channel, and align them with the message signals at the eavesdropper. In the case with no eavesdropper’s CSI, we present a scheme that efficiently utilizes the broadcast links by incorporating computation between the message and common noise symbols at the source. Finally, most of our achievability and converse techniques can also be adapted to the Gaussian (non-fading) channel model.

Secure Degrees of Freedom Regions of Multiple Access and Interference Channels: The Polytope Structure

The sum secure degrees of freedom (s.d.o.f.) of two fundamental multi-user network structures, the K-user Gaussian multiple access (MAC) wiretap channel and the K-user interference channel (IC) with secrecy constraints, have been determined recently as K(K-1)/(K(K-1)+1) [1,2] and K(K-1)/(2K-1) [3,4], respectively. In this paper, we determine the entire s.d.o.f. regions of these two channel models. The converse for the MAC follows from a middle step in the converse of [1,2]. The converse for the IC includes constraints both due to secrecy as well as due to interference. Although the portion of the region close to the optimum sum s.d.o.f. point is governed by the upper bounds due to secrecy constraints, the other portions of the region are governed by the upper bounds due to interference constraints. Different from the existing literature, in order to fully understand the characterization of the s.d.o.f. region of the IC, one has to study the 4-user case, i.e., the 2 or 3-user cases do not illustrate the generality of the problem. In order to prove the achievability, we use the polytope structure of the converse region. In both MAC and IC cases, we develop explicit schemes that achieve the extreme points of the polytope region given by the converse. Specifically, the extreme points of the MAC region are achieved by an m-user MAC wiretap channel with (K-m) helpers, i.e., by setting (K-m) users' secure rates to zero and utilizing them as pure (structured) cooperative jammers. The extreme points of the IC region are achieved by a (K-m)-user IC with confidential messages, m helpers, and N external eavesdroppers, for m>=1 and a finite N. A byproduct of our results in this paper is that the sum s.d.o.f. is achieved only at one extreme point of the s.d.o.f. region, which is the symmetric-rate extreme point, for both MAC and IC channel models.

Polar Coding for the General Wiretap Channel With Extensions to Multiuser Scenarios

Information-theoretic work for wiretap channels is mostly based on random coding schemes. Designing practical coding schemes to achieve information-theoretic secrecy is an important problem. By applying two recently developed techniques for polar codes, namely, universal polar coding and polar coding for asymmetric channels, we propose a polar coding scheme to achieve the secrecy capacity of the general wiretap channel. We then apply this coding scheme to achieve the best-known inner bounds for the multiple access wiretap channel (MAC-WTC), and the broadcast and interference channels with confidential messages (BC-CM and IC-CM).

Multiple access channel with common message and secrecy constraint

The authors study the problem of secret communication over a multiple-access channel with a common message. Here, the authors 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. The authors call this setting as multiple-access wiretap channel with common message (MAWC-CM). For this setting, the authors 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 special case called the switch channel. As well, for a Gaussian version of MAWC-CM, the authors derive inner and outer bounds on the secrecy capacity region. Providing numerical results for the Gaussian case, the authors illustrate the comparison between the derived achievable rate region and the outer bound for the considered model and the capacity region of compound multiple access channel.

Secure Degrees of Freedom of Multiuser Networks: One-Time-Pads in the Air via Alignment

We revisit the recent secure degrees of freedom (s.d.o.f.) results for one-hop multiuser wireless networks by considering three fundamental wireless network structures: Gaussian wiretap channel with helpers, Gaussian multiple access wiretap channel, and Gaussian interference channel with secrecy constraints. We present main enabling tools and resulting communication schemes in an expository manner, along with key insights and design principles emerging from them. The main achievable schemes are based on real interference alignment, channel prefixing via cooperative jamming, and structured signalling. Real interference alignment enables aligning the cooperative jamming signals together with the message carrying signals at the eavesdroppers to protect them akin to one-time-pad protecting messages in wired systems. Real interference alignment also enables decodability at the legitimate receivers by rendering message carrying and cooperative jamming signals separable, and simultaneously aligning the cooperative jamming signals in the smallest possible subspace. The main converse techniques are based on two key lemmas which quantify the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs; and the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. These two lemmas when applied according to the unique structure of individual networks provide tight converses. Finally, we present a blind cooperative jamming scheme for the helper network with no eavesdropper channel state information at the transmitters that achieves the same optimal s.d.o.f. as in the case of full eavesdropper channel state information.

Multiple-Access Relay Wiretap Channel

In this paper, we investigate the effects of an additional trusted relay node on the secrecy of multiple-access wiretap channel (MAC-WT) by considering the model of multiple-access relay wiretap channel (MARC-WT). More specifically, first, we investigate the discrete memoryless MARC-WT. Three inner bounds (with respect to decode-forward (DF), noise-forward (NF) and compress-forward (CF) strategies) on the secrecy capacity region are provided. Second, we investigate the degraded discrete memoryless MARC-WT, and present an outer bound on the secrecy capacity region of this degraded model. Finally, we investigate the Gaussian MARC-WT, and find that the NF and CF strategies help to enhance Tekin-Yener's achievable secrecy rate region of Gaussian MAC-WT. Moreover, we find that if the noise variance of the transmitters-relay channel is smaller than that of the transmitters-receiver channel, the DF strategy may also enhance Tekin-Yener's achievable secrecy rate region of Gaussian MAC-WT, and it may perform even better than the NF and CF strategies.

Lossy transmission of correlated sources over multiple‐access wiretap channels

In this study, the authors study lossy communication of correlated sources over a multiple-access wiretap channel (MAC-WT). Consider a system with two transmitters, a receiver and an eavesdropper. There are two correlated sources where each of them is observed by the corresponding transmitter, separately. Each transmitter wishes to describe its source sequence to the receiver with a desired distortion. The sources need to be kept secret from the eavesdropper. They find an achievable region for the MAC-WT with correlated sources by separation. A joint source-channel coding scheme for the MAC-WT is also proposed. They consider lossy communication of a bivariate Gaussian source over Gaussian MAC-WT (GMAC-WT). They propose a separation-based achievable scheme for the GMAC-WT. An achievable region for the GMAC-WT based on uncoded transmission is also found. They compare the separate and the uncoded schemes for the symmetric GMAC-WT, where the same constraint on the power of each transmitter is imposed and the same distortion on each source is achieved. For another case of source correlation coefficient, they compare the separate, uncoded and hybrid schemes. They obtain outer bounds to the rate-distortion-equivocation region of: (i) the degraded MAC-WT where the output at the eavesdropper is a degraded version of the output at the receiver, (ii) the GMAC-WT with independent sources and (iii) the symmetric GMAC-WT when the correlation of the sources is maximum. Optimal regions for some cases are established.

MIMO Wiretap Channels With Unknown and Varying Eavesdropper Channel States

In this paper, a class of information theoretic secrecy problems is addressed where the eavesdropper channel state is completely unknown to the legitimate parties. In particular, a Gaussian MIMO wiretap channel is considered, where the eavesdropper channel state can vary from one channel use to the next, and the overall channel state sequence is known only to the eavesdropper. When the eavesdropper has fewer antennas than the transmitter and its intended receiver, a positive secrecy rate in the sense of strong secrecy is proved to be achievable and shown to match with the converse in secure degrees of freedom. This yields the conclusion that secure communication is possible regardless of the location or channel states of the eavesdropper. Additionally, it is observed that, the present setting renders the secrecy capacity problems for some multiterminal wiretap-type channels more tractable as compared to 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 (MAC) wiretap channel and the two-user Gaussian MIMO broadcast (BC) wiretap channel, where the transmitter(s) and intended receiver(s) have the same number of antennas.