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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...
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