In one embodiment, a data storage system includes a tape channel for reading data from a tape to produce a signal, an adaptive noise whitening filter adapted for receiving the signal, the noise whitening filter being adapted for minimizing variance of noise affecting the signal output from the noise whitening filter, a soft DMAX detector adapted for receiving the signal from the noise whitening filter, the soft detector adapted for calculating first soft information about each bit of the signal and sending the first soft information to a soft decoder, and the soft decoder positioned subsequent to the soft detector, the soft decoder being adapted for calculating second soft information about each bit of the signal and sending the second soft information to the soft DMAX detector, wherein one or more noise whitening coefficients used in the noise whitening filter are updated using a noise whitening filter coefficient updater.