Editing Partial-response maximum-likelihood (section)

=== Generalized PRML ===
PR4 is characterized by an equalization target (+1, 0, -1) in bit-response sample values or (1-D)(1+D) in polynomial notation (here, D is the delay operator referring to a one sample delay). The target (+1, +1, -1, -1) or (1-D)(1+D)^2 is called Extended PRML (or EPRML). The entire family, (1-D)(1+D)^n, was investigated by Thapar and Patel.<ref>H.Thapar, A.Patel, "[https://ieeexplore.ieee.org/document/1065230 A Class of Partial Response Systems for Increasing Storage Density in Magnetic Recording]", IEEE Trans. Magn., vol. 23, No. 5, pp.3666-3668 Sept. 1987</ref> The targets with larger n value tend to be more suited to channels with poor high-frequency response. This series of targets all have integer sample values and form an open [[Eye pattern|eye-pattern]] (e.g. PR4 forms a ternary eye). In general, however, the target can just as readily have non-integer values. The classical approach to maximum-likelihood detection on a channel with intersymbol interference (ISI) is to equalize to a minimum-phase, whitened, matched-filter target.<ref>D. Forney, "[https://ieeexplore.ieee.org/document/1054829 Maximum Likelihood Sequence Estimation of Digital Sequences in the Presence of Intersymbol Interference]", IEEE Trans. Info. Theory, vol. IT-18, pp. 363-378, May 1972.</ref> The complexity of the subsequent Viterbi detector increases exponentially with the target length - the number of states doubling for each 1-sample increase in target length.