Gradient of mutual information in linear vector Gaussian channels
Gradient of mutual information in linear vector Gaussian channels
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DOI：
10.1109/tit.2005.860424
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发表时间：
2006-01-01
影响因子：
2.5
通讯作者：
Verdú, S
中科院分区：
文献类型：
--
作者：
Palomar, DP;Verdú, S
本文考虑一个具有任意信号的一般线性向量高斯信道，并追求两个密切相关的目标：i）关于系统任意参数的互信息梯度的闭式表达式，以及ii）信息论和估计理论之间的基本联系。推广郭（Guo）、沙迈（Shamai）和韦尔杜（Verdu）最近揭示的基本关系，我们表明，互信息关于信道矩阵的梯度等于信道矩阵与给定输出时输入的最佳估计的误差协方差矩阵的乘积。然后通过微分链式法则求出关于其他参数的梯度和导数。
This paper considers a general linear vector Gaussian channel with arbitrary signaling and pursues two closely related goals: i) closed-form expressions for the gradient of the mutual information with respect to arbitrary parameters of the system, and ii) fundamental connections between information theory and estimation theory. Generalizing the fundamental relationship recently unveiled by Guo, Shamai, and Verdu, we show that the gradient of the mutual information with respect to the channel matrix is equal to the product of the channel matrix and the error covariance matrix of the best estimate of the input given the output. Gradients and derivatives with respect to other parameters are then found via the differentiation chain rule.