Rewritable storage channels with hidden state

TL;DR

This paper investigates the capacity of rewritable storage channels with hidden states, proposing bounds and coding schemes that improve understanding of how to mitigate noise and estimate unknown memory characteristics.

Contribution

It provides a lower bound on the capacity of such channels using combined coding strategies and introduces an asymptotically optimal coding scheme for specific noise and state distributions.

Findings

Lower bound on channel capacity established

Coding scheme combining Gelfand-Pinsker and superposition coding

Asymptotic optimality of the proposed scheme for large rewrites

Abstract

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.