Multiple Access Wiretap Channel Research Articles

Some New Results on the Multiple-AccessWiretap Channel

In this paper, some new results on the multiple-access wiretap channel (MAC-WT) are provided. Specifically, first, we investigate the degraded MAC-WT, where two users transmit their corresponding confidential messages (no common message) to a legitimate receiver via a multiple-access channel (MAC), while a wiretapper wishes to obtain the messages via a physically degraded wiretap channel. The secrecy capacity region of this model is determined for both the discrete memoryless and Gaussian cases. For the Gaussian case, we find that this secrecy capacity region is exactly the same as the achievable secrecy rate region provided by Tekin and Yener, i.e., Tekin–Yener’s achievable region is exactly the secrecy capacity region of the degraded Gaussian MAC-WT. Second, we study a special Gaussian MAC-WT, and find the power control for two kinds of optimal points (max-min point and single user point) on the secrecy rate region of this special Gaussian model.

Multiple‐access wiretap channel with common channel state information at the encoders

The multiple-access wiretap channel (MAC-WTC) with common channel state information (CSI) at the encoders is studied, where two transmitters wish to send their confidential messages (no common message) to a legitimate receiver, while keeping a wiretapper as ignorant of the confidential messages as possible. Meanwhile, the channel is controlled by CSI, and it is available at the transmitters in a non-causal manner or causal manner. This model can be viewed as a MAC extension of the WTC with CSI. Both the situation that the encoders can cooperate with each other and the situation that cooperation is not allowed between the encoders are investigated. More specifically, first, the cooperative MAC-WTC with common CSI at the encoders is investigated, inner bounds on the secrecy capacity regions are provided for both non-causal and causal manners. Secondly, the non-cooperative MAC-WTC with common CSI at the encoders is investigated, and also provide inner bounds on the secrecy capacity regions for both non-causal and causal manners. Finally, by calculating the binary examples, the authors find that the cooperation between the encoders helps to obtain a larger secrecy rate region, that is, cooperation enhances the security of the MAC-WTC with common CSI at the encoders.

Discrete Memoryless Multiple-Access Wiretap Channel with Non-Cooperative Encoders

In this paper, the discrete memoryless multiple-access wiretap channel (MAC-WT) with non-cooperative encoders is studied, where two users (cooperation between the users is not allowed) transmit their corresponding confidential messages (no common message) to a legitimate receiver, while an additional wiretapper wishes to obtain the messages via a wiretap channel. The inner and outer bounds on the capacity-equivocation region are provided forthis new model, and the result is further explained via a binary example.

MIMO Multiple Access Channel With an Arbitrarily Varying Eavesdropper: Secrecy Degrees of Freedom

A two-transmitter Gaussian multiple access wiretap channel with multiple antennas at each of the nodes is investigated. The channel matrices of the legitimate users are fixed and revealed to all the terminals, whereas the channel matrices of the eavesdropper are arbitrarily varying and only known to the eavesdropper. The secrecy degrees of freedom (s.d.o.f.) region under a strong secrecy constraint is characterized. A transmission scheme that orthogonalizes the transmit signals of the two users at the intended receiver, and uses a single-user wiretap code for each user, is shown to achieve the s.d.o.f. region. The converse involves establishing an upper bound on a weighted-sum-rate expression. This is accomplished by using induction, where at each step one combines the secrecy and multiple-access constraints associated with an adversary eavesdropping a carefully selected group of sub-channels.

Secure Degrees of Freedom of One-Hop Wireless Networks

We study the secure degrees of freedom (d.o.f.) of one-hop wireless networks by considering four fundamental wireless network structures: 1) Gaussian wiretap channel; 2) Gaussian broadcast channel with confidential messages; 3) Gaussian interference channel with confidential messages; and 4) Gaussian multiple access wiretap channel. The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper, which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies 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. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M/M+1.We then generalize this approach to more general network structures with multiple messages. We show that the sum secure d.o.f. of the Gaussian broadcast channel with confidential messages and M helpers is 1, the sum secure d.o.f. of the twouser interference channel with confidential messages is 2/3, the sum secure d.o.f. of the two-user interference channel with confidential messages and M helpers is 1, and the sum secure d.o.f. of the K-user multiple access wiretap channel is K(K-1)/K(K-1)+1.

Ergodic Secret Alignment

In this paper, we introduce two new achievable schemes for the fading multiple access wiretap channel (MAC-WT). In the model that we consider, we assume that perfect knowledge of the state of all channels is available at all the nodes in a causal fashion. Our schemes use this knowledge together with the time-varying nature of the channel model to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher dimensionality space for the interfering signals at the legitimate receiver, hence allowing for better chance of recovery. While we achieve this alignment through signal scaling at the transmitters in our first scheme (scaling-based alignment), we let nature provide this alignment through the ergodicity of the channel coefficients in the second scheme [ergodic secret alignment (ESA)],. For each scheme, we obtain the resulting achievable secrecy rate region. We show that the secrecy rates achieved by both schemes in the two-user fading MAC-WT scale with signal-to-noise ratio (SNR) as. Hence, we show the suboptimality of the independent identically distributed (i.i.d.) Gaussian signaling-based schemes with and without cooperative jamming by showing that the secrecy rates achieved using i.i.d. Gaussian signaling with cooperative jamming do not scale with SNR. In addition, we introduce an improved version of our ESA scheme where we incorporate cooperative jamming to achieve higher secrecy rates. Moreover, we derive the necessary optimality conditions for the power control policy that maximizes the secrecy sum rate achievable by our ESA scheme when used solely and with cooperative jamming. Finally, we discuss the extension of the proposed schemes to the case where there are more than two users and show that, for the -user fading MAC-WT, each of the two schemes achieves secrecy sum rate that scales with SNR as.

Correction to: “The Gaussian Multiple Access Wire-Tap Channel” and “The General Gaussian Multiple Access and Two-Way Wire-Tap Channels: Achievable Rates and Cooperative Jamming” [Dec 08 5747-5755 and Jun 08 2735-2751

The authors used superposition coding as opposed to the more standard random binning approach to wire-tap channels.

Erratum to "The Gaussian Multiple Access Wire-Tap Channel"

Erratum to "The Gaussian Multiple Access Wire-Tap Channel"

The Gaussian Multiple Access Wire-Tap Channel

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 suitable security measures for this multiaccess environment. Using codebooks generated randomly according to a Gaussian distribution, achievable secrecy rate regions are identified using superposition coding and time-division multiple access (TDMA) coding schemes. An upper bound for the secrecy sum-rate is derived, and our coding schemes are shown to achieve the sum capacity. Numerical results are presented showing the new rate region and comparing it with the capacity region of the Gaussian multiple-access channel (GMAC) with no secrecy constraints, which quantifies the price paid for secrecy.

The General Gaussian Multiple-Access and Two-Way Wiretap Channels: Achievable Rates and Cooperative Jamming

The general Gaussian multiple-access wiretap channel (GGMAC-WT) and the Gaussian two-way wiretap channel (GTW-WT) are considered. In the GGMAC-WT, multiple users communicate with an intended receiver in the presence of an eavesdropper who receives their signals through another GMAC. In the GTW-WT, two users communicate with each other over a common Gaussian channel, with an eavesdropper listening through a GMAC. A secrecy measure that is suitable for this multiterminal environment is defined, and achievable secrecy rate regions are found for both channels. For both cases, the power allocations maximizing the achievable secrecy sum rate are determined. It is seen that the optimum policy may prevent some terminals from transmission in order to preserve the secrecy of the system. Inspired by this construct, a new scheme cooperative jamming is proposed, where users who are prevented from transmitting according to the secrecy sum rate maximizing power allocation policy ldquojamrdquo the eavesdropper, thereby helping the remaining users. This scheme is shown to increase the achievable secrecy sum rate. Overall, our results show that in multiple-access scenarios, users can help each other to collectively achieve positive secrecy rates. In other words, cooperation among users can be invaluable for achieving secrecy for the system.