On the capacity of high-density recording on a 1-D granular magnetic medium

In terabit-density magnetic recording, several bits of data can be replaced by the values of their neighbors in the storage medium. As a result, errors in the medium are dependent on each other and also on the data written. In an earlier paper we studied a simple one-dimensional model of this situation. In our model binary data is sequentially written on the medium and a bit can erroneously change to the immediately preceding value. Here we define a probabilistic finite-state channel model of the storage medium and derive estimates of its capacity. To derive a lower bound we consider a uniform input distribution, and find an exact expression of the symmetric capacity of the channel. An upper bound is found by showing that the original channel is a stochastic degradation of another, related channel model whose capacity we compute explicitly.