Difference-metric Viterbi decoding of multilevel class-IV partial-response signals

The paper describes the decoding of unconstrained L-ary signals (L⩾2) transmitted over a noisy partial-response channel with transfer function 1-D². Signals received at even and odd sampling times are independently decoded in a pipeline fashion. After stating the known results for full-state maximum-likelihood sequence decoding, a 2-state decoding algorithm is introduced in which the difference between the metrics of the retained two most-likely states is iteratively computed. An analysis of its error-event probability shows that two types of error events are most likely, regular free-distance events and induced free-distance events. The latter cause only a rather small degradation of error performance compared to full-state decoding. In addition, the symbol-error probability for modulo-L encoded user symbols and decoding with finite decoding delay is computed. The 2-state decoder can be realized for arbitrary values of L with low hardware complexity