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Information Theory and Applications Workshop (ITA)

Secrecy capacity of a class of orthogonal relay eavesdropper channels

Vaneet Aggarwal, Lalitha Sankar, A.R. Calderbank, H. Vincent Poor

Published Feb 1, 2009• 47 citations
Publisher

Abstract

The secrecy capacity is developed for a class of relay channels with orthogonal components and a passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multi-antenna channel with a multi-antenna eavesdropper. The outer bounds are shown to be tight for two sub-classes of channels. The first sub-class is one in which the source and relay are clustered and the eavesdropper overhears on only one of the two channels for which the PDF strategy is optimal. The second is a sub-class in which the source does not transmit to the relay for which a noise-forwarding strategy is optimal.

DOI
10.1109/ita.2009.5044960

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The secrecy capacity is developed for a class of relay channels with orthogonal components and a passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multi-antenna channel with a multi-antenna eavesdropper. The outer bounds are shown to be tight for two sub-classes of channels. The first sub-class is one in which the source and relay are clustered and the eavesdropper overhears on only one of the two channels for which the PDF strategy is optimal. The second is a sub-class in which the source does not transmit to the relay for which a noise-forwarding strategy is optimal.
The secrecy capacity of relay channels with orthogonal components is studied in the presence of an additional passive eavesdropper node. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper can overhear either one or both of the orthogonal channels. Inner and outer bounds on the secrecy capacity are developed for both the discrete memoryless and the Gaussian channel models. For the discrete memoryless case, the secrecy capacity is shown to be achieved by a partial decode-and-forward (PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. Two new outer bounds are presented for the Gaussian model using recent capacity results for a Gaussian multiantenna point-to-point channel with a multiantenna eavesdropper. The outer bounds are shown to be tight for two subclasses of channels. The first subclass is one in which the source and relay are clustered, and the eavesdropper receives signals only on the channel from the source and the relay to the destination, for which the PDF strategy is optimal. The second is a subclass in which the source does not transmit to the relay, for which a noise-forwarding strategy is optimal.
The secrecy capacity of relay channels with orthogonal components is studied in the presence of additional passive eavesdropper nodes. The relay and destination receive signals from the source on two orthogonal channels such that the destination also receives transmissions from the relay on its channel. The eavesdropper(s) can overhear either one or both of the orthogonal channels. For a single eavesdropper node, the secrecy capacity is shown to be achieved by apartial decode-and-forward(PDF) scheme when the eavesdropper can overhear only one of the two orthogonal channels. For the case of two eavesdropper nodes, secrecy capacity is shown to be achieved by PDF for a sub-class of channels.
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 investigate the problem of secure communication over parallel relay channel in the presence of a passive eavesdropper. We consider a four terminal relay-eavesdropper channel which consists of multiple relay-eavesdropper channels as subchannels. For the discrete memoryless model, we establish outer and inner bounds on the rate-equivocation region. The inner bound allows mode selection at the relay. For each subchannel, secure transmission is obtained through one of two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. For the Gaussian memoryless channel, we establish lower and upper bounds on the perfect secrecy rate. Furthermore, we study a special case in which the relay does not hear the source and show that under certain conditions the lower and upper bounds coincide. The results established for the parallel Gaussian relay-eavesdropper channel are then applied to study the fading relay-eavesdropper channel. Analytical results are illustrated through some numerical examples.
We investigate the effects of an additional relay node on the secrecy of broadcast channels by considering the model of relay broadcast channels with confidential messages. We show that this additional relay node can increase the achievable secrecy rate region of the broadcast channels with confidential messages. More specifically, first, we investigate the discrete memoryless relay broadcast channels with two confidential messages and one common message. Three inner bounds (with respect to decode-forward, generalized noise-forward and compress-forward strategies) and an outer bound on the capacity-equivocation region are provided. Removing the secrecy constraint, this outer bound can also be served as a new outer bound for the relay broadcast channel. Second, we investigate the discrete memoryless relay broadcast channels with two confidential messages (no common message). Inner and outer bounds on the capacity-equivocation region are provided. Then, we study the Gaussian case, and find that with the help of the relay node, the achievable secrecy rate region of the Gaussian broadcast channels with two confidential messages is enhanced. Finally, we investigate the discrete memoryless relay broadcast channels with one confidential message and one common message. This work generalizes Lai-Gamals work on the relay-eavesdropper channel by considering an additional common message for both the legitimate receiver and the eavesdropper. Inner and outer bounds on the capacity-equivocation region are provided, and the results are further explained via a Gaussian example. Compared with Csiszár-Körner’s work on broadcast channels with confidential messages (BCC), we find that with the help of the relay node, the secrecy capacity region of the Gaussian BCC is enhanced.
We study a four terminal parallel relay-eavesdropper channel which consists of multiple independent relay-eavesdropper channels as subchannels. For the discrete memoryless case, we establish inner and outer bounds on the rate-equivocation region. For each subchannel, secure transmission is obtained through one of the two coding schemes at the relay: decoding-and-forwarding the source message or confusing the eavesdropper through noise injection. The inner bound allows relay mode selection. For the Gaussian model we establish lower and upper bounds on the perfect secrecy rate. We show that the bounds meet in some special cases, including when the relay does not hear the source. We illustrate the analytical results through some numerical examples.