This paper considers an additive Gaussian noise channel with arbitrarily distributed finite variance input signals. It studies the differential entropy of the minimum mean-square error (MMSE) estimator and provides a new lower bound which connects the entropy of the input, output, and conditional mean. That is, the sum of entropies of the conditional mean and output is always greater than or equal to twice the input entropy. Various other properties such as upper bounds, asymptotics, Taylor series expansion, and connection to Fisher Information are obtained. An application of the lower bound in the remote-source coding problem is discussed, and extensions of the lower and upper bounds to the vector Gaussian channel are given.
翻译：本文考虑一个带有任意分布的有限差异输入信号的加加加高西亚噪声信道。 它研究最小平均方差误( MMSE) 估测器的差倍数, 并提供一个新的下限, 连接输入、 输出和有条件平均值的倍数。 也就是说, 有条件平均值和输出的倍数总和总是大于或等于输入倍数的倍数 。 获取了其他各种属性, 如上限数、 静态、 Taylor 序列扩展 和 与 Fisher 信息的连接 。 正在讨论远程源码问题中下限的应用, 并给出向矢量 Gaussian 频道的下限和上限的扩展 。
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