  Many storage channels admit reading and rewriting of the content at a given
cost. We consider rewritable channels with a hidden state which models the
unknown characteristics of the memory cell. In addition to mitigating the
effect of the write noise, rewrites can help the write controller obtain a
better estimate of the hidden state. The paper has two contributions. The first
is a lower bound on the capacity of a general rewritable channel with hidden
state. The lower bound is obtained using a coding scheme that combines
Gelfand-Pinsker coding with superposition coding. The rewritable AWGN channel
is discussed as an example. The second contribution is a simple coding scheme
for a rewritable channel where the write noise and hidden state are both
uniformly distributed. It is shown that this scheme is asymptotically optimal
as the number of rewrites gets large.
