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 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 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 (SBA)), 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 scale with SNR as 1/2log(SNR). Hence, we show the sub-optimality of the 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.
The study of the physical layer has offered a new perspective to the problem of communication security. This led to the development of a vast set of ideas and techniques rooted in information theory which can be employed in practice to provide unbreakable security. The information-theoretic approach relies mainly on the physical nature of the communication medium. In a wireless medium, the unique features of the wireless communication channel, such as its fading and broadcast nature, can be exploited to achieve higher secure information rates. In this dissertation, we study the secure transmission problem in wireless channels from an information-theoretic perspective. We first consider the fading multiple access wiretap channel. We give two new achievable schemes that use the time-varying (fading) nature of the channel to align the interference from different users at the eavesdropper perfectly in a one-dimensional space while creating a higher-dimensional 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). For each scheme, we show that the achievable secrecy rates scale logarithmically with the signal-to-noise ratio (SNR). Next, we study the security gains that can be achieved in a wireless network by employing cooperation among the nodes which is possible due to the broadcast nature of the wireless channel. We investigate the role of passive (also known as deaf) cooperation in improving the achievable secrecy rates in a Gaussian multiple relay network with an external eavesdropper. We distinguish between two modes of deaf cooperation, namely, cooperative jamming (CJ) and noise forwarding (NF). We derive the conditions in which each mode of deaf cooperation achieves secrecy rates that are higher than the secrecy capacity of the original Gaussian wiretap channel. As a result, we show that a deaf helper cannot be a useful cooperative jammer and noise forwarder at the same time. We derive the optimal power control policy for each mode. We consider the deaf helper selection problem where a fixed-size set of deaf helpers (possibly operating in different modes) are to be selected from the set of available relays so that the achievable secrecy rate is maximized. We propose a simple and efficient suboptimal strategy for selection which is shown to be optimal when only one helper is selected. Furthermore, we study the role of a multi-antenna deaf helper. Unlike the single antenna case, we show that, in general, it is useful to split the helper's power between cooperative jamming and noise forwarding. Hence, we propose a deaf cooperation strategy for this model and derive its optimal power control policy. We also show, for specific class of relay-eavesdropper channels, that a simple cooperative jamming strategy yields a secrecy rate that approaches the secrecy capacity as the helper's power is increased. Finally, we consider the role of active cooperation for secrecy in the multiple relay networks. We propose several relaying strategies for secure communication and derive the achievable secrecy rate for each strategy. In our strategies the relays decode the source signal and then forward it to the destination either in a single-hop or a multi-hop fashion. Each relay scales its transmitted signal in a way that ensures that signal components from different relays are canceled out at the eavesdropper.
In this paper, we provide a new achievable ergodic secrecy rate region for the multiple access wiretap channel in fading. Our achievable scheme is based on repeating each symbol at two fading instances, as in the original ergodic interference alignment technique of Nazer et. al. We choose the channel states where the symbols are repeated in such a way that the received signals are aligned favorably at the legitimate receiver, while they are aligned unfavorably at the eavesdropper. We show that our new scheme outperforms plain Gaussian signaling and Gaussian signaling with Gaussian channel prefixing, i.e., cooperative jamming, in high signal-to-noise ratios (SNR). In particular, we show that, while Gaussian signaling with or without channel prefixing yields zero secure degrees of freedom, our new achievable scheme provides a total of 1/2 secure degrees of freedom in a two-user multiple access channel in fading.
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.
It is commonly known that physical layer security is achieved with a trade-off in terms of the achievable rate. Hence, security constraints generate rate losses in wiretap channels. To mitigate such rate losses in multi-user channels, we propose a coding/decoding scheme for multi-user multiple access wiretap channel (MAC-WT), where previously transmitted messages are used as a secret key to enhance the secrecy rates of the transmitting users, until the usual Shannon capacity region of a multiple access channel (MAC) is achieved without the secrecy constraint. With this coding scheme, all messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal, we introduce secret key buffers at both the users and the legitimate receiver. Finally, we consider a fading MAC-WT and show that with this coding/decoding scheme, we can achieve the capacity region of a fading MAC channel (in the ergodic sense).
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.