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首页> 外文期刊>Information Theory, IEEE Transactions on >Data-Processing Inequalities Based on a Certain Structured Class of Information Measures With Application to Estimation Theory
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Data-Processing Inequalities Based on a Certain Structured Class of Information Measures With Application to Estimation Theory

机译：某种结构化的信息测度类别的数据处理不等式及其在估计理论中的应用

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摘要

We study data-processing inequalities that are derived from a certain class of generalized information measures, where a series of convex functions and multiplicative likelihood ratios is nested alternately. While these information measures can be viewed as a special case of the most general Zakai–Ziv generalized information measure, this special nested structure calls for attention and motivates our study. Specifically, a certain choice of the convex functions leads to an information measure that extends the notion of the Bhattacharyya distance (or the Chernoff divergence): While the ordinary Bhattacharyya distance is based on the (weighted) geometric mean of two replicas of the channel's conditional distribution, the more general information measure allows an arbitrary number of such replicas. We apply the data-processing inequality induced by this information measure to a detailed study of lower bounds of parameter estimation under additive white Gaussian noise (AWGN) and show that in certain cases, tighter bounds can be obtained by using more than two replicas. While the resulting lower bound may not compete favorably with the best bounds available for the ordinary AWGN channel, the advantage of the new lower bound, relative to the other bounds, becomes significant in the presence of channel uncertainty, like unknown fading. This different behavior in the presence of channel uncertainty is explained by the convexity property of the information measure.
机译：我们研究了从一类广义信息测度中得出的数据处理不等式，其中一系列凸函数和乘性似然比交替嵌套。虽然这些信息量度可以看作是最一般的Zakai-Ziv广义信息量度的特例，但这种特殊的嵌套结构需要引起注意并激发我们的研究。具体来说，对凸函数的某种选择会导致一种信息量度，该量度扩展了Bhattacharyya距离（或Chernoff散度）的概念：而普通的Bhattacharyya距离基于通道条件的两个副本的（加权）几何平均值分布，更一般的信息量度允许任意数量的此类副本。我们将这种信息量度引起的数据处理不等式应用于对加性高斯白噪声（AWGN）下参数估计下限的详细研究，并表明在某些情况下，可以使用两个以上的副本来获得更严格的界限。尽管所得到的下限可能无法与普通AWGN信道的最佳上限竞争，但是在存在信道不确定性（例如未知衰落）的情况下，相对于其他边界，新下限的优势变得十分明显。在存在信道不确定性的情况下，这种不同的行为可以通过信息度量的凸性来解释。

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