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arXiv 1702.03590cs.ITmath.IT
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一类信号相关噪声信道的容量

On the Capacity of a Class of Signal-Dependent Noise Channels

Hamid Ghourchian, Gholamali Aminian, Amin Gohari, Mahtab Mirmohseni, Masoumeh Nasiri-Kenari

摘要:

在某些应用中,加性测量噪声的方差取决于我们要测量的信号。例如,加性高斯信号相关噪声(AGSDN)信道模型用于分子和光通信。在这里,我们提供了上下限和上界的附加信号相关噪声(ASDN)信道的容量。第一个下界的思想是优控不等式的推广,第二个下界的思想是基于$h(Y) > h (Y|Z)$。这两种方法都适用于本文定义的所有加性信号相关噪声(ASDN)信道。上限是基于作者以前的想法(“对称相对熵”),并用于加性高斯信号相关噪声(AGSDN)信道。这些界限表明,在ASDN信道(与经典的AWGN信道不同),容量不一定通过使噪声的方差函数更小而变得更大。我们还提供了充分条件下的能力成为无穷大。除此之外,还有一些条件,意味着能力是有限的,而且存在一种独特的能力实现措施(从产出措施的意义上说)。

英文摘要:

In some applications, the variance of additive measurement noise depends on the signal that we aim to measure. For instance, additive Gaussian signal-dependent noise (AGSDN) channel models are used in molecular and optical communication. Herein we provide lower and upper bounds on the capacity of additive signal-dependent noise (ASDN) channels. The idea of the first lower bound is the extension of the majorization inequality, and for the second one, it uses some calculations based on the fact that $h(Y) > h (Y|Z)$. Both of them are valid for all additive signal-dependent noise (ASDN) channels defined in the paper. The upper bound is based on a previous idea of the authors ("symmetric relative entropy") and is used for the additive Gaussian signal-dependent noise (AGSDN) channels. These bounds indicate that in ASDN channels (unlike the classical AWGN channels), the capacity does not necessarily become larger by making the variance function of the noise smaller. We also provide sufficient conditions under which the capacity becomes infinity. This is complemented by a number of conditions that imply capacity is finite and a unique capacity achieving measure exists (in the sense of the output measure).

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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