Precoders for message-passing detection of partial-response channels

Parallel message-passing detectors for partial-response channels have the property that a bit is estimated using channel symbols in a window of size W centered upon that bit. Distinct input sequences that produce the same output sequence result in undesirable failure of window decoders, but preceding can eliminate this input-to-output mapping ambiguity. For a class of partial-response channels, we show necessary and sufficient conditions on a precoder to unambiguously map input sequences to output sequences.