Secure degrees of freedom of the Gaussian wiretap channel with helpers
Secure degrees of freedom of the Gaussian wiretap channel with helpers
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DOI：
10.1109/allerton.2012.6483217
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发表时间：
2012-10
期刊：
影响因子：
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通讯作者：
Jianwei Xie;S. Ulukus
中科院分区：
文献类型：
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作者：
Jianwei Xie;S. Ulukus
规范高斯窃听信道的保密容量不与发射功率成比例，因此，安全d.o.f.没有助手的高斯窃听通道的概率为零。严格正安全d.o.f.可以在高斯窃听信道中通过使用发送结构化协作信号的辅助器来获得。我们证明了确切的安全d.o.f.的高斯窃听通道是1/2。我们实现的方案是基于真实的干扰对齐和合作干扰，这使得消息信号和合作干扰信号在合法的接收器处是可分离的，但是在窃听者处将它们完美地对齐，从而防止消息信号的任何可靠解码。我们的匡威是基于两个关键引理。第一个引理量化了保密惩罚，表明窃听者对系统的净影响是它消除了一个独立的信道输入。第二个引理量化的帮助者的作用，通过开发一个直接的合作干扰信号的帮助者和消息速率之间的关系。我们将这个结果推广到M个助手的情况，并证明了精确的安全d.o.f.在这种情况下是M/M+1。
The secrecy capacity of the canonical Gaussian wiretap channel does not scale with the transmit power, and hence, the secure d.o.f. of the Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap channel with a helper is 1/2. Our achievable scheme is based on real interference alignment and cooperative jamming, which renders the message signal and the cooperative jamming signal separable at the legitimate receiver, but aligns them perfectly at the eavesdropper preventing any reliable decoding of the message signal. Our converse is based on two key lemmas. The first lemma quantifies the secrecy penalty by showing that the net effect of an eavesdropper on the system is that it eliminates one of the independent channel inputs. The second lemma quantifies the role of a helper by developing a direct relationship between the cooperative jamming signal of a helper and the message rate. We extend this result to the case of M helpers, and show that the exact secure d.o.f. in this case is M/M+1.