  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. We
consider a simple one-dimensional combinatorial model of this medium. In our
model, we assume a setting where binary data is sequentially written on the
medium and a bit can erroneously change to the immediately preceding value. We
derive several properties of codes that correct this type of errors, focusing
on bounds on their cardinality.
  We also define a probabilistic finite-state channel model of the storage
medium, and derive lower and upper estimates of its capacity. A lower bound is
derived by evaluating the symmetric capacity of the channel, i.e., the maximum
transmission rate under the assumption of the uniform input distribution 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 can
compute explicitly.
