Optimal soft-output detector for channels with intersymbol interference and timing errors

We address the issue of detecting transmitted (or recorded) symbols when there is a timing error in the sampled waveform, along with intersymbol interference (ISI) and additive channel noise. We built a special trellis to jointly characterize the timing uncertainty and the channel ISI. The method derived here provides the joint maximum a posteriori probability detection of each input symbol and the quantized timing offset of each sample. It also generates "soft" decisions, which are essential for soft-decision iterative decoding algorithms.