Superposition coding in rewritable channels

We introduce the notions of superposition coding and sequential decoding in the context of rewritable channels. Using these concepts we will show that for ?₁ > ?₀, C(?₁) ? C(?₀) + log(?₁/?₀), where C(?) is the capacity of the rewritable channel for a given cost. A consequence of this result is that C(?) ? C(1) + log ?, where C(1) is the classical channel capacity with no rewrite iterations. Thus this result provides a connection between rewritable and classical channel theory. We also derive a general upper bound on capacity which can be written as an offset plus the logarithm of the average number of write iterations. Closed form bounds on rewritable channel capacity will be given for Gaussian rewritable channels.