The Secrecy Capacity of Compound Gaussian MIMO Wiretap Channels
The Secrecy Capacity of Compound Gaussian MIMO Wiretap Channels
复制标题
DOI：
10.1109/tit.2015.2458856
复制
发表时间：
2015-07
影响因子：
2.5
通讯作者：
Rafael F. Schaefer;S. Loyka
中科院分区：
文献类型：
--
作者：
Rafael F. Schaefer;S. Loyka
研究了复合窃听信道的强保密容量。在强保密准则下，将离散字母表下复合有限状态无记忆信道保密容量的已知下界推广到任意不确定集和连续字母表.给出了这些界是紧界的条件。在鞍点条件下，证明了复合保密容量等于最坏信道的复合保密容量。在此基础上，研究了谱范数约束下的复合高斯多输入多输出窃听信道，并在不考虑信道退化性假设的情况下进行了仿真。首先，假设只有窃听者信道是未知的，但已知具有有界谱范数（最大信道增益）。建立了复合保密容量的封闭形式，并确定了最优信令。复合容量等于最坏情况下的信道容量，从而建立鞍点属性;最佳信令是高斯的，并且在合法信道的特征向量上，最坏情况下的窃听者是各向同性的。本征模式的功率分配有点类似于标准的注水，但并不完全相同it. More一般的不确定性集被认为是一个最大的元素的存在被证明是足够的鞍点存在，使信令在最坏情况下的信道实现的复合容量的整个类的信道。考虑了等级受限窃听者的情况，建立了相应的复合保密容量。随后，在合法信道的情况下，除了未知的窃听者信道，添加剂的不确定性进行了研究。其复合保密容量和最优信令也被建立在一个封闭的形式，揭示了相同的鞍点性质。当强保密下存在鞍点时，强、弱保密复合容量相等。
Strong secrecy capacity of compound wiretap channels is studied. The known lower bounds for the secrecy capacity of compound finite-state memoryless channels under discrete alphabets are extended to arbitrary uncertainty sets and continuous alphabets under the strong secrecy criterion. The conditions under which these bounds are tight are given. Under the saddle-point condition, the compound secrecy capacity is shown to be equal to that of the worst-case channel. Based on this, the compound Gaussian multiple-input multiple-output wiretap channel is studied under the spectral norm constraint and without the degradedness assumption. First, it is assumed that only the eavesdropper channel is unknown, but is known to have a bounded spectral norm (maximum channel gain). The compound secrecy capacity is established in a closed form and the optimal signaling is identified. The compound capacity equals the worst-case channel capacity and thus establishing the saddlepoint property; the optimal signaling is Gaussian and on the eigenvectors of the legitimate channel and the worst-case eavesdropper is isotropic. The eigenmode power allocation somewhat resembles the standard water-filling but is not identical to it. More general uncertainty sets are considered and the existence of a maximum element is shown to be sufficient for a saddle-point to exist, so that signaling on the worst-case channel achieves the compound capacity of the whole class of channels. The case of rank-constrained eavesdropper is considered and the respective compound secrecy capacity is established. Subsequently, the case of additive uncertainty in the legitimate channel, in addition to the unknown eavesdropper channel, is studied. Its compound secrecy capacity and the optimal signaling are established in a closed form as well, revealing the same saddle-point property. When a saddle-point exists under strong secrecy, strong and weak secrecy compound capacities are equal.