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IEEE Information Theory Workshop (ITW)

The multiple access channel with an untrusted relay

Ahmed A. Zewail, Aylin Yener

Published Nov 1, 2014• 5 citations
Publisher

Abstract

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.

DOI
10.1109/itw.2014.6970785

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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.
This paper investigates the impact of cooperation with an untrusted relay in multi-source multi-destination networks. The set up considered is one where the relay is the only means of communications due to the absence of direct links between the sources and the destinations. Since the relay is untrusted, all messages from the sources need to be kept secret from the relay. Furthermore, the destinations are assumed to have different levels of security clearance, i.e., some private messages should only be decoded by their intended receiver and should be kept secret from other destinations. An achievable secure rate region is found by using random binning at the sources, cooperative jamming from the destinations, and compress-and-forward at the relay. Additionally, a genie aided outer bound on the secure rate region is derived. Comparison of inner and outer bounds are provided.
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 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.
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.
We consider a Gaussian network consisting of a source that aims to communicate to its legitimate destination via an untrusted relay node in the presence of an external eavesdropper. The source wishes to send two independent messages to the destination: one message must be kept secret from the external eavesdropper only, while the other message must be kept secret from the external eavesdropper and the untrusted relay both. We identify achievable secure rates under these layered secrecy constraints. Considering a two-hop half-duplex setup, we employ the destination as a cooperative jammer in the first phase in order to help provide secrecy from the relay and the external eavesdropper, and the source as a cooperative jammer in the second phase in order to detriment the external eavesdropper. The source encodes its messages using stochastic encoding and security embedding coding. We provide the secrecy analysis and present numerical results to demonstrate the performance of the proposed achievability technique. Our study points to the value of the source serving as a cooperative jammer as well as the need for power control policies at the legitimate nodes in order to ensure secrecy in this system.
We consider a two-source two-destination two-hop relay network, where all data communication must be kept secret from the relay node. The model considered is the simplest primitive that embodies a multi-transmitter multi-receiver network that needs to communicate sharing an untrusted relay node. We focus on two scenarios. In the first scenario, each source aims to send two messages to be kept secret from the relay: a common message that should be decoded by both destinations, and a private message that should be decoded by the first destination while kept secret from the second one. We define an achievable rate region by utilizing stochastic encoding at the sources, the Gaussian noise cooperative jamming from the destinations, and compress-and-forward at the relay. In the second scenario, each source aims to send a confidential message to its intended destination, which should be kept secret from the other one as well as the relay. We define an achievable rate region using a combination of nested lattice codes and random binning at the sources, structured cooperative jamming from destinations, and scaled compute-and-forward at the relay. We also derive genie-aided outer bounds on the secrecy rate regions. We present numerical results that demonstrate the performance of the proposed achievable schemes. Overall, this paper provides insights into how to utilize an untrusted relay to communicate to destinations with different levels of security clearance, and how intentional interference is an enabler of communication.