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International Conference on Wireless Communication, Vehicular Technology, Information Theory and Aerospace & Electronic Systems Technology

On the sum-rate capacity of a 2-user Multiple Access Wiretap Channel with one secret user

Sanjay Karmakar

Published May 1, 2014• 1 citation
Publisher

Abstract

We consider a 2-user Gaussian Multiple-Access Wiretap channel (MA-WC), with the unintended receiver having access to signal from only one of the two transmitters. We have characterized the sum-rate capacity of this channel within .5 bits and proved that Gaussian signalling at the transmitters is approximate sum-rate capacity optimal. For the scenario when the additive noise plus the signal from first transmitter have a combined strength poorer than the additive noise of the evesdropper, the above sum-rate capacity characterization leads to an approximate capacity region characterization for the channel. It is shown that, under this circumstances, a timesharing scheme between the two users can achieve the capacity region of the channel within .25 bits. It has been proved (Xie and Ulukus, ISIT 2013 [1]) recently that on a Multiple-Access Wiretap channel interference alignment (IA) is necessary to achieve optimal performance. Our channel model is an interesting variation of the MA-WC for which IA is not necessary and independent Gaussina signalling is sufficient to achieve the optimal sum-rate within .5 bits.

DOI
10.1109/vitae.2014.6934477

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On the Optimality of Secure Communication Without Using Cooperative Jamming

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arXiv:1706.06220•Jun 19, 2017•2 citations
We consider a 2-user Gaussian Multiple-Access Wiretap channel (MA-WC), with the unintended receiver having access to signal from only one of the two transmitters. We have characterized the sum-rate capacity of this channel within .5 bits and proved that Gaussian signalling at the transmitters is approximate sum-rate capacity optimal. For the scenario when the additive noise plus the signal from first transmitter have a combined strength poorer than the additive noise of the evesdropper, the above sum-rate capacity characterization leads to an approximate capacity region characterization for the channel. It is shown that, under this circumstances, a timesharing scheme between the two users can achieve the capacity region of the channel within .25 bits. It has been proved (Xie and Ulukus, ISIT 2013 [1]) recently that on a Multiple-Access Wiretap channel interference alignment (IA) is necessary to achieve optimal performance. Our channel model is an interesting variation of the MA-WC for which IA is not necessary and independent Gaussina signalling is sufficient to achieve the optimal sum-rate within .5 bits.
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 study a deterministic approximation of the two-user multiple access wiretap channel. This approximation enables results beyond the recently shown 23\tfrac{2}{3}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.
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).
We give a new achievable ergodic secrecy rate region for the two-user fading multiple access wiretap channel. Our scheme creates a vector channel between the two transmitters and the intended receiver that has full-rank and creates another vector channel between the two transmitters and the eavesdropper whose rank is 1. In this sense, our scheme removes interference from the main receiver multiple access channel by introducing an extra dimension in this channel, while sustaining the interference in the eavesdropper multiple access channel by keeping the rank of this channel equal to one. We show that the secrecy sum rate achieved by our scheme scales with SNR. In particular, we show that a total number of 1/2 secure degrees of freedom is achievable for the two users. Moreover, we compare our scheme with the Gaussian signaling scheme with cooperative jamming which improves significantly over the plain Gaussian signaling scheme. Our proposed scheme outperforms Gaussian signaling schemes (with or without cooperative jamming) at high signal-to-noise ratios (SNR). In particular, we show that Gaussian signaling schemes with or without cooperative jamming achieve zero secure degrees of freedom, while our proposed scheme achieves 1/2 total secure degrees of freedom.
We consider secure communication over a two-user Gaussian interference channel, where each transmitter sends a confidential message to its legitimate receiver. For this setting, we identify a regime where the simple scheme of using Gaussian wiretap codebook at each transmitter (without cooperative jamming) and treating interference as noise at each intended receiver (in short, GWC-TIN scheme) achieves the optimal secure sum capacity to within a constant gap. The results are proved by first considering the deterministic interference channel model and identifying a regime in which a simple scheme without using cooperative jamming is optimal in terms of secure sum capacity. For the symmetric case of the deterministic model, this simple scheme is optimal if and only if the interference-to-signal ratio (in channel strengths) is no more than 2/3.