This article proposes a write channel model with input-dependent noise, called multiplicative noise, for bit patterned media recording (BPMR). In general, for these types of channels and other channels with memory, the capacity is not known. In channels with unknown capacity (with noise, dependent or independent of the input), the mutual information between channel input and output for any chosen input and output distribution is a capacity lower bound, which is called the information rate. In this article, the dependence of the noise on the channel input is added to the previously studied models. Using this write channel model with input-dependent noise and with memory considered as a binary random state, information rate lower and upper bounds and the gap between them can be found. These lower and upper bounds are calculated for the defined information rate relating to two types of input distribution [independent and uniformly distributed (i.u.d.) process and first-order Markov (foM) process]. The proposed model is shown to include some previous works as special cases and is compared mathematically with the other models, where, the noise is not considered and/or is considered to be independent of the input.

中文翻译：

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一种新的位模式媒体记录写通道模型的信息论分析

本文提出了一种用于位模式媒体记录 (BPMR) 的具有输入相关噪声（称为乘法噪声）的写入通道模型。一般来说，对于这些类型的通道和其他带有内存的通道，容量是未知的。在容量未知（有噪声、依赖或独立于输入）的通道中，对于任何选定的输入和输出分布，通道输入和输出之间的互信息是一个容量下限，称为信息率。在本文中，噪声对通道输入的依赖性被添加到先前研究的模型中。使用这种具有输入相关噪声的写入通道模型，并将内存视为二进制随机状态，可以找到信息率下限和上限以及它们之间的差距。这些下限和上限是针对与两种类型的输入分布 [独立和均匀分布 (iud) 过程和一阶马尔可夫 (foM) 过程] 相关的定义信息率计算的。所提出的模型显示包括一些先前的工作作为特殊情况，并与其他模型进行数学比较，其中不考虑噪声和/或被认为与输入无关。