In one embodiment, a data storage system includes a tape channel for reading data from a magnetic tape medium to produce a signal, a noise whitening filter positioned subsequent to the tape channel adapted for receiving the signal, wherein the noise whitening filter is adapted for minimizing variance of its output signal, a soft detector adapted for receiving output 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 detector. Other systems, methods, and computer program products are described according to more embodiments.