Maximum likelihood decoding for multilevel channels with gain and offset mismatch

TL;DR

This paper derives a maximum likelihood decoding formula for a channel with gain and offset mismatch, relevant to flash memory, and introduces a new code distance measure tailored for this channel.

Contribution

It provides the first explicit maximum likelihood decoding formula for channels with gain and offset mismatch and introduces a corresponding minimum distance concept for coding.

Findings

Derivation of a maximum likelihood decoding formula

Definition of a new code distance measure for the channel

Theoretical justification of the proposed decoding approach

Abstract

K.A.S. Immink and J.H. Weber recently defined and studied a channel with both gain and offset mismatch, modelling the behaviour of charge-leakage in flash memory. They proposed a decoding measure for this channel based on minimising Pearson distance (a notion from cluster analysis). The paper derives a formula for maximum likelihood decoding for this channel, and also defines and justifies a notion of minimum distance of a code in this context.