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.
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.
Abstract — We consider the Gaussian Multiple Access Wire-Tap Channel (GMAC-WT) where multiple users communicate with the intended receiver in the presence of an intelligent and informed wire-tapper (eavesdropper). The wire-tapper receives a degraded version of the signal at the receiver. We assume that the wire-tapper is as capable as the intended receiver, and there is no other shared secret key. We consider two different secure communication scenarios: (i) keeping the wire-tapper totally ignorant of the message of any group of users even if the remaining users are compromised, (ii) using the secrecy of the other users to ensure secrecy for a group of users. We first derive the outer bounds for the secure rate region. Next, using Gaussian codebooks, we show the achievability of a secure rate region for each measure in which the wire-tapper is kept perfectly ignorant of the messages. We also find the power allocations that yield the maximum sum rate, and show that upper bound on the secure sum rate can be achieved by a TDMA scheme. We present numerical results showing the new rate region and compare it with that of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. I.
The physical layer security in the up‐link of the wireless communication systems is often modelled 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, and from this example, we see that the noiseless feedback helps to enhance the achievable secrecy rate region of the Gaussian MAC‐WT without feedback.
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.
We investigate the problem of secure multi-terminal strong coordination aided by a multiple-access wiretap channel (MAC-WT). In this setup, independent and identically distributed (i.i.d.) copies of correlated sources are observed by two transmitters who encode the channel inputs to the MAC-WT. The legitimate receiver on observing the channel output must produce approximately i.i.d. copies of an output random variable jointly distributed with the two sources. Furthermore, we demand that an external eavesdropper learns essentially nothing about the sources and the simulated output sequence by observing its corresponding MAC-WT output. This is aided by the presence of independent pairwise shared randomness between each encoder and the legitimate decoder. The shared randomness rate tuples which permit such channel simulation with strong secrecy are of interest. We derive an achievable rate region based on a combination of coordination coding and wiretap coding, along with an outer bound. The inner bound is shown to be tight and a complete characterization is derived for the special case when the sources are independent and the legitimate receiver's channel is composed of deterministic links.
This paper investigates the secrecy achievable region of multiple access wiretap (MAC-WT) channels where, besides confidential messages, the users have also open messages to transmit. All these messages are intended for the legitimate receiver (or Bob for brevity) but only the confidential messages need to be protected from the eavesdropper (Eve). We first consider a discrete memoryless (DM) MAC-WT channel where both Bob and Eve jointly decode their interested messages. By using random coding, we find an achievable rate region, within which perfect secrecy can be realized, i.e., all users can communicate with Bob with arbitrarily small probability of error, while the confidential information leaked to Eve tends to zero. Due to the high implementation complexity of joint decoding, we also consider the DM MAC-WT channel where Bob simply decodes messages independently while Eve still applies joint decoding. We then extend the results in the DM case to a Gaussian vector (GV) MAC-WT channel. Based on the information theoretic results, we further maximize the sum secrecy rate of the GV MAC-WT system by designing precoders for all users. Since the problems are non-convex, we provide iterative algorithms to obtain suboptimal solutions. Simulation results show that compared with existing schemes, secure communication can be greatly enhanced by the proposed algorithms, and in contrast to the works which only focus on the network secrecy performance, the system spectrum efficiency can be effectively improved since open messages can be simultaneously transmitted.
We consider the General Gaussian Multiple Access Wire-Tap Channel (GGMAC-WT). In this scenario, multiple users communicate with an intended receiver in the presence of an intelligent and informed eavesdropper. We define two suitable secrecy measures, termed individual and collective, to reflect the confidence in the system for this multi-access environment. We determine achievable rates such that secrecy to some pre-determined degree can be maintained, using Gaussian codebooks. We also find outer bounds for the case when the eavesdropper receives a degraded version of the intended receiver's signal. In the degraded case, Gaussian codewords are shown to achieve the sum capacity for collective constraints. In addition, a TDMA scheme is shown to also achieve sum capacity for both sets of constraints. Numerical results showing the new rate region are presented and compared with the capacity region of the Gaussian Multiple-Access Channel (GMAC) with no secrecy constraints. We then find the secrecy sum-rate maximizing power allocations for the transmitters, and show that a cooperative jamming scheme can be used to increase achievable rates in this scenario.