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Asilomar Conference on Signals, Systems and Computers (ACSSC)

On the Equivocation Region of Relay Channels with Orthogonal Components

Xiang He, Aylin Yener

Published Nov 1, 2007• 35 citations
Publisher

Abstract

We consider the secrecy rate of a relay network where an eavesdropper is co-located with the relay node. This exemplifies a scenario where the relay node is not malicious by nature, but is located in an "untrusted region", and hence is potentially compromised. Given that the aim now is to keep the relay node completely oblivious to the information sent from the source to the destination, an interesting question is whether the relay node should be deployed at all. We investigate this question for two types of relay networks with orthogonal components. For the first model, we find the equivocation capacity region and prove the relay node should not be deployed. For the second model, we present an achievable secrecy rate based on compress-and-forward, and conclude that the relay node is potentially useful as it can, without being able to decode the source data, facilitate secret communication between the source and the destination that would not be possible without the relay.

DOI
10.1109/acssc.2007.4487345

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We consider the secrecy rate of a relay network where an eavesdropper is co-located with the relay node. This exemplifies a scenario where the relay node is not malicious by nature, but is located in an "untrusted region", and hence is potentially compromised. Given that the aim now is to keep the relay node completely oblivious to the information sent from the source to the destination, an interesting question is whether the relay node should be deployed at all. We investigate this question for two types of relay networks with orthogonal components. For the first model, we find the equivocation capacity region and prove the relay node should not be deployed. For the second model, we present an achievable secrecy rate based on compress-and-forward, and conclude that the relay node is potentially useful as it can, without being able to decode the source data, facilitate secret communication between the source and the destination that would not be possible without the relay.
We consider the communication scenario where a source-destination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. For this scenario, an interesting question is whether the relay node should be deployed at all. That is, whether cooperation with an untrusted relay node can ever be beneficial. We first provide an achievable secrecy rate for the general untrusted relay channel, and proceed to investigate this question for two types of relay networks with orthogonal components. For the first model, there is an orthogonal link from the source to the relay. For the second model, there is an orthogonal link from the relay to the destination. For the first model, we find the equivocation capacity region and show that answer is negative. In contrast, for the second model, we find that the answer is positive. Specifically, we show, by means of the achievable secrecy rate based on compress-and-forward, that by asking the untrusted relay node to relay information, we can achieve a higher secrecy rate than just treating the relay as an eavesdropper. For a special class of the second model, where the relay is not interfering itself, we derive an upper bound for the secrecy rate using an argument whose net effect is to separate the eavesdropper from the relay. The merit of the new upper bound is demonstrated on two channels that belong to this special class. The Gaussian case of the second model mentioned above benefits from this approach in that the new upper bound improves the previously known bounds. For the Cover-Kim deterministic relay channel, the new upper bound finds the secrecy capacity when the source-destination link is not worse than the source-relay link, by matching with achievable rate we present.
We consider the communication scenario where a source-destination pair wishes to keep the information secret from a relay node despite wanting to enlist its help. A class of relay channels with orthogonal components is considered and an upper bound on the secrecy rate is derived. For the class of relay channels in consideration, we prove the relay and the eavesdropper can be separated to obtain an ‘enhanced’ channel in terms of secrecy capacity. We then consider two special cases of this channel model: (i) the Gaussian orthogonal relay channel, and (ii) the Gaussian Cover-Kim deterministic relay channel. For the former, the upper bound found is tighter than the previously known bound. For the latter, we show that the bound yields the secrecy capacity when the source-destination link is not worse than the source-relay link. This second case also provides the first example where secrecy capacity is achieved with compress and-forward at the relay.
In this paper, we consider a state-dependent relay channel with orthogonal components where the message must be kept secret from the relay node and the channel state information is known non-causally at the source node. A lower bound on the secrecy capacity is derived by the state description scheme proposed in this paper. The source node transmits a description of the channel state information (CSI) to the destination. The message that passes through the relay node is encrypted by a key which is generated from this state description and shared between the source and destination nodes. This scheme enables the relay node to cooperate with the source node to send messages to the destination without getting any information of the message. We show that the achievable secrecy rate by the scheme in this paper is larger than that by the scheme of X. He who showed that the relay is useless in the state-independent untrusted relay channel with orthogonal components.
This paper investigates the achievable secrecy regions when employing a friendly jammer in a cooperative scenario employing an untrusted relay. The untrusted relay which helps to forward the source signal towards the destination, could also be regarded as a potential eavesdropper. Our system employs a friendly jammer which sends a known noise signal towards the relay. In this paper, we investigate the effect of jammer and relay locations on the achievable secrecy rate. We consider two scenarios where in the first case we consider no direct transmission between the source and destination, while in the second case we include a source to destination direct link in our communication system.
We consider a source-destination pair that can communicate only through an unauthenticated intermediate relay node. In this two-hop communication scenario, where the cooperation from the relay node is essential, we investigate whether achieving non-zero secrecy rate is possible. Specifically, we treat the relay node as an eavesdropper from whom the source information needs to be kept secret, despite the fact that its cooperation in relaying this information is needed. We find that a positive secrecy rate is indeed achievable, with the aid of the destination node or an external node that jams the relay, i.e., by cooperative jamming. We derive an upper bound on the secrecy rate by means of an eavesdropper-relay separation argument. We remark that this upper bound is the first of its kind in Gaussian channels with cooperative jamming. The upper bound is strictly smaller than the channel capacity without secrecy constraints. The achievable secrecy rates are found using stochastic encoding and compress-and-forward at the relay. Numerical results show that the gap between the bound and the achievable rate is small when the relay's power is larger than the power of the jammer and the source. In essence, this paper shows that a cooperative jammer enables secure communication to take place using an untrusted relay which would be otherwise impossible.
This paper considers a Gaussian multiple access channel aided by a relay. Specifically, the relay facilitates communication between multiple sources and a destination to which the sources have no direct link. In this set up, the relay node is considered to be untrusted, i.e., honest but curious, from whom the source messages need to be kept secret. We identify an achievable secrecy rate region utilizing cooperative jamming from the destination, and using compress-and-forward at the relay. Additionally, an outer bound on the secrecy rate region is derived. Numerical results indicate that the outer bound is tight in some cases of interest.