Abstract
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.
Highlights
In wireless networks for which nodes can benefit from cooperation and packet-forwarding, there is a need to preserve the confidentiality of transmitted information from untrusted nodes
An outer bound on the secrecy capacity of the relay eavesdropper channel results from assuming that the source and relay can cooperate over a noiseless link without causality constraints
We have developed bounds on the secrecy capacity of relay eavesdropper channels with orthogonal components in the presence of an additional passive eavesdropper for both the discrete memoryless and Gaussian channel models
Summary
In wireless networks for which nodes can benefit from cooperation and packet-forwarding, there is a need to preserve the confidentiality of transmitted information from untrusted nodes. The orthogonal model implicitly imposes a half-duplex transmission and reception constraint on the relay For this channel, in the absence of an eavesdropper, El Gamal and Zahedi showed that a partial decode-and-forward (PDF) strategy, in which the source transmits two messages on the two orthogonal channels and the relay decodes its received signal, achieves the capacity [14]. We specialize the outer bounds developed in [11] for the orthogonal case and show that, for the discrete memoryless channel, PDF achieves the secrecy capacity for the two cases where the eavesdropper receives signals in only one of the two orthogonal channels.
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