On the Capacity of Multilevel NAND Flash Memory Channels

TL;DR

This paper provides an information-theoretic analysis of multilevel NAND flash memory channels with intercell interference, establishing their capacity properties and linking them to finite-state channel techniques.

Contribution

It proves the indecomposability, asymptotic equipartition property, and capacity convergence of multilevel NAND flash memory channels, connecting their capacity analysis to finite-state channel methods.

Findings

Channel is indecomposable with asymptotic equipartition property.

Stationary processes achieve the channel's information capacity.

Operational capacity equals information capacity.

Abstract

In this paper, we initiate a first information-theoretic study on multilevel NAND flash memory channels with intercell interference. More specifically, for a multilevel NAND flash memory channel under mild assumptions, we first prove that such a channel is indecomposable and it features asymptotic equipartition property; we then further prove that stationary processes achieve its information capacity, and consequently, as its order tends to infinity, its Markov capacity converges to its information capacity; eventually, we establish that its operational capacity is equal to its information capacity. Our results suggest that it is highly plausible to apply the ideas and techniques in the computation of the capacity of finite-state channels, which are relatively better explored, to that of the capacity of multilevel NAND flash memory channels.