Maximum Likelihood Decoding for Multi-Level Cell Memories with Scaling and Offset Mismatch

Reliability is a critical issue for modern multi-level cell memories. We consider a multi-level cell channel model such that the retrieved data is not only corrupted by Gaussian noise, but hampered by scaling and offset mismatch as well. We assume that the intervals from which the scaling and offset values are taken are known, but no further assumptions on the distributions on these intervals are made. We derive maximum likelihood (ML) decoding methods for such channels, based on finding a codeword that has closest Euclidean distance to a specified set defined by the received vector and the scaling and offset parameters. We provide geometric interpretations of scaling and offset and also show that certain known criteria appear as special cases of our general setting.