线性向量高斯信道中互信息、微分熵和熵功率的Hessian和Hessian
Hessian and concavity of mutual information, differential entropy, and entropy power in linear vector Gaussian channels
摘要：
在线性矢量高斯信道的框架内，任意信令，最小均方误差和Fisher信息矩阵的雅可比矩阵的封闭形式的表达式相对于任意参数的系统计算。利用先前的研究，其中的最小均方误差和Fisher信息矩阵被连接到信息理论的数量，通过微分，封闭形式的表达式的互信息和微分熵的海森推导。然后，这些表达式被用来评估在不同的信道条件下的互信息和微分熵，并推导出一个多变量版本的熵功率不等式由于科斯塔。
英文摘要：
Within the framework of linear vector Gaussian channels with arbitrary signaling, closed-form expressions for the Jacobian of the minimum mean square error and Fisher information matrices with respect to arbitrary parameters of the system are calculated in this paper. Capitalizing on prior research where the minimum mean square error and Fisher information matrices were linked to information-theoretic quantities through differentiation, closed-form expressions for the Hessian of the mutual information and the differential entropy are derived. These expressions are then used to assess the concavity properties of mutual information and differential entropy under different channel conditions and also to derive a multivariate version of the entropy power inequality due to Costa.
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