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The reason for the union of these two regions to be the outer bound on the stability region follows from the indistinguishability argument [16, 18].
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The proof is extended from the outer bound in [11, Theorem 1] to include auxiliary random variables corresponding to each of the transmitted signals and is developed in Appendix A. Following Proposition 5, a natural question for the relay-eavesdropper channel with orthogonal components is whether the PDF strategy can achieve the secrecy capacity.
Since the derivation is straightforward, we state the outer bound without proof.
For comparison, the outer bound is also provided.
By increasing the channel gain, a, the achievable rate by lattice codes is within 0.5 bits of the outer bound.
Also, regardless of all channel parameters, the gap between the achievable rate region and the outer bound is at most 0.5 bits.
As a result, the outer bound can be efficiently computed via geometric programming techniques.
By using superposition coding, a scheme which achieves the outer bound within 0.5 bit is proposed.
Under a secrecy constraint, the outer bound in Theorem 17 is based on the assumption of a noiseless source-relay link.
In (41a) and (41c), the maximizing the outer bound on the secrecy capacity is.
Figure 7 The achievable rate regions and the outer bound.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com