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== Further Developments ==
=== Generalized PRML ===
GeneralizedPR4 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 EPMRL). The entire family, (1+D)1-D)^n, was investigated by Thapar and Patel<ref>[https://ieeexplore.ieee.org/document/1065230 H.Thapar, A.Patel, "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>. Minimum 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 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>[https://ieeexplore.ieee.org/document/1054829 D. Forney, "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.
=== Post-processor architecture ===
PostGiven the rapid increase in complexity with longer targets, a post-processor architecture was proposed, firstly for EPRML<ref>[https://ieeexplore.ieee.org/document/281375 R. Wood, "Turbo-PRML, A Compromise EPRML Detector", IEEE Trans. Magn., Vol. MAG-29, No. 6, pp. 4018-4020, Nov. 1993]</ref>. With this approach a relatively simple detector (e.g. PRML) is followed by a post-processor which examines the residual waveform error and looks for the occurrence of likely bit pattern errors. This approach was found to be valuable when it was extended to systems employing a simple parity check<ref>[https://www.researchgate.net/publication/328870436 M. Despotovic, V. Senk, "Data Detection", Chapter 32 in ''Coding and Signal Processing for Magnetic Recording Systems'' edited by B. Vasic, E. Kurtas, CRC Press 2004]</ref>
=== PRML with Nonlinearities and Signal-dependent Noise ===
PatternAs data detectors became more sophisticated, it was found important to deal with any residual signal nonlinearities as well as pattern-dependent noise prediction(noise tends to be largest when there is a magnetic transition between bits) including changes in noise-spectrum with data-pattern. To this end, the Viterbi-detector was modified such that it recognized the expected signal-level and expected noise variance associated with each bit-pattern. As a final step, the detectors were modified to include a 'noise predictor filter' thus allowing each pattern to havve a different noise=-spectrum. Such detectors are referred to as Patter-Dependent Noise-Prediction (PDNP) detectors<ref>[https://ieeexplore.ieee.org/abstract/document/920181 J. Moon, J. Park, “Pattern-dependent noise prediction in signal dependent noise,” IEEE J. Sel. Areas Commun., vol. 19, no. 4, pp. 730–743, Apr. 2001]</ref> or [[noise-predictive maximum-likelihood detection|noise-predictive maximum-likelihood detectors]] (NPML)<ref>[https://ieeexplore.ieee.org/document/539233 E. Eleftheriou, W. Hirt, "Improving Performance of PRML/EPRML through Noise Prediction". IEEE Trans. Magn. Vol. 32, No. 5, pp. 3968–3970, Sept. 1996]</ref> <br><br>
The most advanced detectors today (2019) use all these techniques and furthermore they replace the hard-decision Viterbi algorithm with a detector providing soft-outputs (additional information about the reliability of each bit). Such detectors using a 'soft Viterbi algorithm' or [[BCJR]] algorithm are essential in decoding [[LDPC]] codes used in modern HDDs.
[[noise-predictive maximum-likelihood detection]] (NPML)<ref>[https://ieeexplore.ieee.org/document/539233 E. Eleftheriou, W. Hirt, "Improving Performance of PRML/EPRML through Noise Prediction". IEEE Trans. Magn. Vol. 32, No. 5, pp. 3968–3970, Sept. 1996]</ref>
== See also ==
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