Maximum likelihood decoding for multilevel channels with gain and offset mismatch

Immink and Weber recently defined and studied a channel with both gain and offset mismatch, modeling the behavior of charge-leakage in flash memory. They proposed a decoding measure for this channel based on minimizing Pearson distance (a notion from cluster analysis). This 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.