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On the Capacity of the Carbon Copy onto Dirty Paper Channel

机译：关于脏纸通道上复写纸的容量

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摘要

The “carbon copy onto dirty paper” (CCDP) channel is the compound “writing on dirty paper” channel in which the channel output is obtained as the sum of the channel input, white Gaussian noise and a Gaussian state sequence randomly selected among a set possible realizations. The transmitter has non-causal knowledge of the set of possible state sequences but does not know which sequence is selected to produce the channel output. We study the capacity of the CCDP channel for two scenarios: 1) the state sequences are independent and identically distributed; and 2) the state sequences are scaled versions of the same sequence. In the first scenario, we show that a combination of superposition coding, time-sharing, and Gel’fand-Pinsker binning is sufficient to approach the capacity to within 3 bits per channel use for any number of possible state realizations. In the second scenario, we derive capacity to within 4 bits per channel use for the case of two possible state sequences. This result is extended to the CCDP channel with any number of possible state sequences under certain conditions on the scaling parameters, which we denote as “strong fading” regime. We conclude by providing some remarks on the capacity of the CCDP channel in which the state sequences have any jointly Gaussian distribution.
机译：“复制到脏纸上”（CCDP）通道是复合“在脏纸上书写”通道，其中通道输出是通道输入，白高斯噪声和从一组中随机选择的高斯状态序列之和获得的可能的实现。发射机对可能的状态序列集具有非因果关系知识，但不知道选择哪个序列来产生信道输出。我们针对以下两种情况研究CCDP信道的容量：1）状态序列是独立的并且分布相同； 2）状态序列是相同序列的缩放版本。在第一种情况下，我们证明了叠加编码，分时和Gel'fand-Pinsker分箱的组合足以使容量达到每通道3位以内，以实现任何数量的可能状态实现。在第二种情况下，对于两个可能的状态序列，我们得出的容量为每个通道使用4位以内。在缩放参数的某些条件下，此结果扩展到具有任何数量的可能状态序列的CCDP通道，我们将其称为“强衰落”机制。我们通过对CCDP信道的容量进行一些总结，其中状态序列具有任何联合的高斯分布。

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