We study deterministic approximations of the Gaussian two-user multiple access wiretap channel (G-MAC-WT) and the Gaussian wiretap channel with a helper (G-WT-H). These approximations enable results beyond the recently shown 2/3 and 1/2 secure degrees of freedom (s.d.o.f.) for the G-MAC-WT and the G-WT-H, respectively. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show achievable schemes which are independent of the rationality of the channel gains. Moreover, our results can differentiate between channel strengths, in particular, between both users, and will establish secrecy rates dependent on this difference. We can show that the resulting achievable secrecy rates tend to the s.d.o.f. for vanishing channel gain differences. Moreover, we extend previous and develop new techniques to prove generalized s.d.o.f. bounds for varying channel strengths and show that our achievable schemes reach the bounds for certain channel gain parameters. We believe that our analysis is the next step toward a constant-gap analysis of the G-MAC-WT and the G-WT-H.
We study deterministic approximations of the Gaussian two-user multiple access wiretap channel (G-MAC-WT) and the Gaussian wiretap channel with a helper (G-WT-H). These approximations enable results beyond the recently shown 2/3 and 1/2 secure degrees of freedom (s.d.o.f.) for the G-MAC-WT and the G-WT-H, respectively. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show achievable schemes which are independent of the rationality of the channel gains. Moreover, our results can differentiate between channel strengths, in particular, between both users, and will establish secrecy rates dependent on this difference. We can show that the resulting achievable secrecy rates tend to the s.d.o.f. for vanishing channel gain differences. Moreover, we extend previous and develop new techniques to prove generalized s.d.o.f. bounds for varying channel strengths and show that our achievable schemes reach the bounds for certain channel gain parameters. We believe that our analysis is the next step toward a constant-gap analysis of the G-MAC-WT and the G-WT-H.
We study a deterministic approximation of the two-user multiple access wiretap channel. This approximation enables results beyond the recently shown 32 secure degrees of freedom (s.d.o.f.) for the Gaussian multiple access channel. While the s.d.o.f. were obtained by real interference alignment, our approach uses signal-scale alignment. We show an achievable scheme which is independent of the rationality of the channel gains. Moreover, our result can differentiate between channel strengths, in particular between both users, and establishes a secrecy rate dependent on this difference. We can show that the resulting achievable secrecy rate tends to the s.d.o.f. for vanishing channel gain differences. Moreover, we extend the s.d.o.f. bound towards a general bound for varying channel strengths and show that our achievable scheme reaches the bound for certain channel gain parameters. We believe that our analysis is the first step towards a constant-gap analysis of the Gaussian multiple access wiretap channel.
Recent investigations have shown that the sum secure degrees of freedom of the Gaussian wiretap channel with a helper is 1/2. The achievable scheme for this result is based on the real interference alignment approach. While providing a good way to show degrees of freedom results, this technique has the disadvantage of relying on the Khintchine-Groshev theorem and is therefore limited to almost all channel gains. This means that there are infinitely many channel gains, where the scheme fails. Furthermore, the real interference alignment approach cannot be used to yield stronger constant-gap results. We approach this topic from a signal-scale alignment perspective and use the linear deterministic model as a first approximation. Here we can show a constant-gap sum capacity for certain channel gain parameters. We transfer these results to the Gaussian model and discuss the results.
We consider a 2-user Gaussian Multiple-Access Wiretap channel (GMAC-WT), with the Eavesdropper (E) having access to signal from only one (say, T2) of the two transmitters. We characterize the capacity region of this channel approximately within. 5 bits, where the approximation is in terms of only T1's rate or the sum-rate depending on the relative strength of the eavesdropper's channel. However, the approximation is. 5 bits independent of channel coefficients or operating Signal-to-Noise Ratios (SNR). To prove this approximate result we propose two different coding schemes, namely, the power adaptation and the time sharing coding schemes and derive their corresponding achievable rate regions. Both of them use Gaussian input distribution. To establish the approximate capacity, we first derive supersets to the capacity region and then show that corresponding to each rate pair at the boundary of these supersets there exists an achievable rate pair in one of the aforementioned achievable rate regions which are within 1/2 bits to the former pair. In comparison to a very recent result (Xie and Ulukus, ISIT 2013) on a GMAC-WT showing the requirement of interference alignment (IA) to achieve even the degrees of freedom performance, the result of this paper is surprising: our channel model is an interesting variation of the GMAC-WT for which IA is not necessary and Gaussian signalling is sufficient to achieve the entire capacity region within. 5 bits.
We develop an outer bound for the secrecy capacity region of a class of multiple access wiretap channels (MAC-WT). In this class, which we call the weak eavesdropper class, each user's link to the legitimate receiver is stronger than its link to the eavesdropper. Our outer bound partially matches the achievable region in an n-letter form. In addition, a looser version of our outer bound provides close approximations to the capacity region of the Gaussian MAC-WT channel. In particular, we prove that our outer bound is within 0.5 bits/channel use of the achievable rates along the individual rates for all weak eavesdropper Gaussian MAC-WT, and within 0.5 bits/channel use in all directions for certain weak eavesdropper Gaussian MAC-WT channels.
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)] [1], [2].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 1 2 log(SNR).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 1 log(SNR).
In this paper, we determine the entire secure degrees of freedom (s.d.o.f.) regions of the K-user Gaussian multiple access (MAC) wiretap channel and the K-user interference channel (IC) with secrecy constraints. For the IC, we consider three secrecy constraints: K-user IC with an external eavesdropper (ICEE), K-user IC with confidential messages (IC-CM), and their combination Kuser IC with confidential messages and external eavesdropper (IC-CM-EE). The converse for the IC includes constraints both due to secrecy as well as due to interference. For the IC, 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 four-user case, i.e., the twoor three-user cases do not illustrate the full 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. In particular, 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.