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首页> 外文期刊>Information Theory, IEEE Transactions on >Relations Between Information and Estimation in Discrete-Time Lévy Channels
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Relations Between Information and Estimation in Discrete-Time Lévy Channels

机译：离散时间Lévy频道中信息与估计之间的关系

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摘要

Fundamental relations between information and estimation have been established in the literature for the discrete-time Gaussian and Poisson channels. In this paper, we demonstrate that such relations hold for a much larger class of observation models. We introduce the natural family of discrete-time Lévy channels where the distribution of the output conditioned on the input is infinitely divisible. For Lévy channels, we establish new representations relating the mutual information between the channel input and output to an optimal expected estimation loss, thereby unifying and considerably extending results from the Gaussian and Poisson settings. We demonstrate the richness of our results by working out two examples of Lévy channels, namely the gamma channel and the negative binomial channel, with corresponding relations between information and estimation. Extensions to the setting of mismatched estimation are also presented.
机译：文献中已经为离散时间的高斯和泊松通道建立了信息和估计之间的基本关系。在本文中，我们证明了这种关系适用于更大范围的观察模型。我们介绍了离散时间Lévy通道的自然族，其中以输入为条件的输出分布是无限可分割的。对于Lévy通道，我们建立了新的表示形式，将通道输入和输出之间的互信息与最佳预期估计损失相关联，从而统一并大大扩展了高斯和泊松设置的结果。我们通过计算两个Lévy通道示例（伽马通道和负二项式通道）以及信息与估计之间的对应关系，证明了我们的结果的丰富性。还介绍了失配估计设置的扩展。

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