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IEEE Information Theory Workshop (ITW)

The capacity of a broadcast channel with Gaussian jamming and a friendly eavesdropper

Kevin Ai Xin Jue Luo, Ramy H. Gohary, Halim Yanıkömeroğlu

Published Oct 1, 2015• 9 citations
Publisher

Abstract

A friendly eavesdropper assists communication in a broadcast scenario in which one transmitter wishes to send a common message to two receivers in the presence of a malicious jammer. The jammer attempts to disrupt communication by transmitting a high power Gaussian signal, whereas the friendly eavesdropper `hears' the jammer's transmission and sends an assisting signal to the destinations over an orthogonal channel in order to help them alleviate the jammer's impact. We derive an expression for capacity, i.e., the maximum data rate that can be reliably communicated from the transmitter to the receivers and we show that it is optimal for the friendly eavesdropper to send a Gaussian description of the jamming signal with the help of a scheme based on a modified compress-and-forward relaying that uses a list decoding procedure.

DOI
10.1109/itwf.2015.7360789

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A friendly eavesdropper assists communication in a broadcast scenario in which one transmitter wishes to send a common message to two receivers in the presence of a malicious jammer. The jammer attempts to disrupt communication by transmitting a high power Gaussian signal, whereas the friendly eavesdropper `hears' the jammer's transmission and sends an assisting signal to the destinations over an orthogonal channel in order to help them alleviate the jammer's impact. We derive an expression for capacity, i.e., the maximum data rate that can be reliably communicated from the transmitter to the receivers and we show that it is optimal for the friendly eavesdropper to send a Gaussian description of the jamming signal with the help of a scheme based on a modified compress-and-forward relaying that uses a list decoding procedure.
This paper considers the two-user Gaussian arbitrarily-varying broadcast channel, wherein a power-limited transmitter wishes to send a message to each of two receivers. Each receiver sees a superposition of the transmitter's sequence, Gaussian noise, and a signal from a power-limited malicious jammer. The jammer is assumed to know the code, but is oblivious to real-time transmissions. The exact capacity region of this setting is determined to be the capacity region of the standard Gaussian broadcast channel, but with the noise variance increased by the power of the jammer, as long as the received power of the jammer at each receiver is less than that of the legitimate transmitter. A key aspect of the achievable scheme involves sharing randomness from the transmitter to the receivers by breaking the transmitted sequence into segments, and either transmitting at full power in a segment, or sending zero. By coding over the on/off signal, a small shared randomness can be established without corruption by the jammer, and without interfering with the standard superposition coding strategy for the Gaussian broadcast channel.
Cooperative jamming for multiuser multiple input multiple output (MIMO) broadcast channel is studied to enhance the physical layer security with the help of a friendly jammer. We assume the base station transmits multiple independent data streams to multiple legitimate users. During the transmission, however, there are multiple eavesdroppers with multiple antennas that have interests in the streams from the base station. In order to wiretap the desired streams, the eavesdroppers may collude or not, and maximize the signal-to-interference-plus-noise ratio (SINR) of the desired streams using receive beamforming. The optimal cooperative jammer is designed to keep the achieved SINR at eavesdroppers below a threshold to guarantee that the transmission from the base station to legitimate users is confidential. One main advantage of the proposed cooperative jamming scheme is that no modification is needed for the existing precoding schemes at the base station and decoding schemes at legitimate users. Thus, any existing practical precoding/decoding schemes for multiuser MIMO broadcast channel can be applied directly with the help of a friendly jammer using the proposed cooperative jamming.
This paper considers secure communication in the presence of an eavesdropper and a malicious jammer. The jammer is assumed to be oblivious of the communication signals emitted by the legitimate transmitter(s) but can employ any jamming strategy subject to a given power constraint and shares her jamming signal with the eavesdropper. Four such models are considered: (i) the Gaussian point-to-point wiretap channel; (ii) the Gaussian multiple-access wiretap channel; (iii) the Gaussian broadcast wiretap channel; and (iv) the Gaussian symmetric interference wiretap channel. The use of pre-shared randomness between the legitimate users is not allowed in our models. Inner and outer bounds are derived for these four models. For (i), the secrecy capacity is obtained. For (ii) and (iv) under a degraded setup, the optimal secrecy sum-rate is characterized. Finally, for (iii), ranges of model parameter values for which the inner and outer bounds coincide are identified.
We study the Gaussian MISO wiretap channel with a transmitter, a legitimate receiver, an eavesdropper and an external helper, where the transmitter and the helper have an arbitrary number of antennas but the intended receiver and the eavesdropper have only one antenna. The transmitter sends confidential messages to its intended receiver, while the helper transmits jamming signals independent of the source message to confuse the eavesdropper. The jamming signal is assumed to be treated as noise at both the intended receiver and the eavesdropper. Assuming Gaussian signaling at the helper, we obtain the optimal beamformers at the transmitter and the helper that achieve the secrecy capacity.
The relay networks face with such a circumstance that an eavesdropper overhears every hop of the relay networks. To solve the issue, we propose a full-duplex friendly-jamming relaying (FDFJR) scheme to secure the information transmissions for a two hop relay network, where a malicious eavesdropper attempts to overhear the private messages transferred by the transmitter and the relay. In the scheme, we take advantage of the capacity of simultaneous reception and transmission of fullduplex (FD) relay. Specifically, in the first hop, the full-duplex jamming relay (FDJR) receives the private information from the transmitter while transmitting the jamming signals to the malicious eavesdropper. And in the second hop, FDJR continues transferring the jamming signals to the eavesdropper, rather than merely amplifying and forwarding the information signals previously received. Furthermore, the ergodic secrecy capacity (ESC) of the networks is characterized and its asymptotical expression is derived. To maximize ESC, we formulate a novel power scheduling problem satisfying several key power and rate requirements. By solving the problem, an exact analytic solution regarding power allocation factor is acquired. Finally, numerical results are provided to validate the accuracy of analytical results and the superiority of our proposed scheme.
We consider the broadcast channel with confidential messages (BCCM) over N parallel Gaussian channels. The transmitter aims at maximizing the sum-rate. The system has two combating jammers, each aiming to enhance the secure rate to one receiver only, while hurting the other receiver by sending Gaussian jamming signals. We cast the problem as an extensive-form game and derive the optimal jamming policy. We show that the jamming strategy is a form of generalized water-filling, and provide theoretical insights on the optimal solution. We provide simulation results to show the convergence of the rate and power allocations, and study the effect of increasing the available power of the transmitter and/or the jammers.