This paper 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 paper, the dependency 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.

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