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'Partial Response' refers to the fact that part of the response to an individual bit may occur at one sample instant while other parts fall in other sample instants. 'Maximum-likelihood' refers to the detector finding the bit-pattern most likely to have been responsible for the read-back waveform.
== Theoretical
[[File:Class 4 Partial-Response Eye Diagram.jpg|thumb|Continuous-time Partial-Response (class 4) and corresponding 'eye pattern']]
'''Partial-response''' was first proposed by Adam Lender in 1963.<ref>[https://ieeexplore.ieee.org/abstract/document/6373379 A. Lender, "The duobinary technique for high-speed data transmission", Trans. AIEE, Part I: Communication and Electronics, Vol. 82 , No. 2 , pp. 214-218, May 1963]</ref> The method was generalized by Kretzmer in 1966. Kretzmer also classified the several different possible responses,<ref>[https://ieeexplore.ieee.org/document/1089288 E. Kretzmer, "Generalization of a Techinque for Binary Data Communication", IEEE Trans. Comm., Vol. 14, No. 1, pp. 67-68 Feb. 1966]</ref> for example, PR1 is duobinary and PR4 is the response used in the classical PRML. In 1970, Kobayashi and Tang recognized the value of PR4 for the [[magnetic recording]] channel.<ref>[https://ieeexplore.ieee.org/document/5391640 H. Kobayashi and D. Tang, "Application of Partial-response Channel Coding to Magnetic Recording Systems", IBM J. Res. Dev., Vol, 14, No. 4, pp. 368-375, July 1970]</ref> <br>
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By 1971, [[Hisashi Kobayashi]] at [[IBM]] had recognized that the Viterbi Algorithm could be applied to analog channels with inter-symbol interference and particularly to the use of PR4 in the context of Magnetic Recording<ref>[https://ieeexplore.ieee.org/document/1054689 H. Kobayashi, ”Correlative level coding and maximum-likelihood decoding", IEEE Trans. Inform. Theory, vol. IT-17, PP. 586-594, Sept. 1971]</ref> (later called PRML). (The wide range of applications of the Viterbi algorithm is well described in a review paper by [[Dave Forney]].<ref>[https://www2.isye.gatech.edu/~yxie77/ece587/viterbi_algorithm.pdf D. Forney, “The Viterbi Algorithm”, Proc. IEEE, Vol. 61, No. 3, pp. 268-278, Mar. 1973]</ref>) A simplified algorithm, based upon a difference metric, was used in the early implementations. This is due to Ferguson at [[Bell Labs]].<ref>[https://ieeexplore.ieee.org/document/6774130 M. Ferguson, ”Optimal reception for binary partial response channels” Bell Syst. Tech. J., vol. 51, pp. 493-505, Feb. 1972]</ref>
== Implementation in
[[File:PRML chronology circa 1994 (scanned Nov 1, 2019).pdf|thumb|Early PRML chronology (created around 1994)]]
The first two implementations were in Tape (Ampex - 1984) and then in hard disk drives (IBM - 1990). Both are significant milestones with the [[Ampex]] implementation focused on very high data-rate for a digital instrumentation recorder and [[IBM]] focused on a high level of integration and low power consumption for a mass-market HDD. In both cases, the initial equalization to PR4 response was done with analog circuitry but the Viterbi algorithm was performed with digital logic. In the tape application, PRML superseded 'flat equalization'. In the HDD application, PRML superseded [[run-length limited|RLL]] codes with 'peak detection'.
=== Tape
The first implementation of PRML was shipped in 1984 in the Ampex Digital Cassette Recording System (DCRS). The chief engineer on DCRS was [[Charles Coleman (engineer)|Charles Coleman]]. The machine evolved from a 6-head, transverse-scan, digital [[video tape recorder]]. DCRS was a cassette-based, digital, instrumentation recorder capable of extended play times at very high data-rate.<ref>[http://www.thic.org/pdf/Oct96/ampex.twood.pdf T. Wood, "Ampex Digital Cassette Recording System (DCRS)", THIC meeting, Ellicott City, MD, 16 Oct., 1996 (PDF)]</ref> It became Ampex' most successful digital product.<ref>[https://www.computerhistory.org/collections/catalog/102788145 R. Wood, K. Hallamasek, "Overview of the prototype of the first commercial PRML channel", Computer History Museum, #102788145, Mar. 26, 2009]</ref>
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Petersen was granted a patent on the PRML channel but it was never leveraged by Ampex<ref>[https://patents.google.com/patent/US4504872A/en D. Petersen, "Digital maximum likelihood detector for class IV partial response", US Patent 4504872, filed Feb. 8, 1983]</ref>.
=== Hard
In 1990, IBM shipped the first PRML channel in an HDD in the [https://en.wikipedia.org/w/index.php?title=History_of_IBM_magnetic_disk_drives§ion=44 IBM 0681] (called Redwing during its development). The IBM 0681 was the last HDD product developed at the [[IBM Hursley]], lab. in the UK. It was full-height 5¼-inch form-factor with up to 12 of 130 mm disks and had a maximum capacity of 857 MB.
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The IBM 0681 read/write channel ran at a data-rate of 24 Mbits/s but was more highly integrated with the entire channel contained in a single 68-pin [[Plastic leaded chip carrier|PLCC]] [[integrated circuit]] operating off a 5 volt supply. As well as the fixed analog equalizer, the channel boasted a simple adaptive digital 'cosine equalizer'<ref>[https://ieeexplore.ieee.org/document/1059216 T. Kameyama, S. Takanami, R. Arai, "Improvement of recording density by means of cosine equalizer", IEEE Trans. Magn., Vol. 12, No. 6, pp. 746-748, Nov. 1976]</ref> after the A/D to compensate for changes in radius and/or changes in the magnetic components.
=== Write
The presence of nonlinear transition-shift (NLTS) distortion on [[NRZ]]{{dn|date=November 2019}} recording at high density and/or high data-rate was recognized in 1979.<ref>[https://ieeexplore.ieee.org/document/1060300 R. Wood, R. Donaldson, "The Helical-Scan Magnetic Tape Recorder as a Digital Communication Channel", IEEE Trans. Mag. vol. MAG-15, no. 2, pp. 935-943, March 1979]</ref> The magnitude and sources of NLTS can be identified using the 'extracted dipulse' technique.<ref>[https://ieeexplore.ieee.org/document/1065310 D. Palmer, P. Ziperovich, R. Wood, T. Howell, "Identification of Nonlinear Write Effects Using Pseudo-Random Sequences", IEEE Trans. Magn., Vol. MAG-23, no. 5, pp. 2377-2379, Sept. 1987]</ref><ref>[https://ieeexplore.ieee.org/document/5680698/ D. Palmer, J. Hong, D. Stanek, R. Wood, "Characterization of the Read/Write Process for Magnetic Recording", IEEE Trans. Magn., Vol. MAG-31, No. 2, pp. 1071-1076, Mar. 1995 (invited)]</ref> <br>
Ampex was the first to recognize the impact of NLTS on PR4.<ref>[https://ieeexplore.ieee.org/document/1064566 P. Newby, R. Wood, "The Effects of Nonlinear Distortion on Class IV Partial Response", IEEE Trans. Magn., Vol. MAG-22, No. 5, pp. 1203-1205, Sept. 1986]</ref> and was first to implement [[Write precompensation]] for PRML NRZ recording. 'Precomp.' largely cancels the effect of NLTS. <ref name=8inch />. 'Precomp.'is viewed as a necessity for a PRML system and is important enough to appear in the [[BIOS]] HDD setup<ref>[http://www.kva.kursk.ru/bios1/HTML1/standard.html Kursk: BIOS Settings - Standard CMOS Setup, Feb 12, 2000]</ref> although it is now handled automatically by the HDD.
== Further
=== 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>[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> 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>[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.
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Given 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://ieeexplore.ieee.org/document/917606 R. Cideciyan, J. Coker; E. Eleftheriou; R. Galbraith, "NPML Detection Combined with Parity-Based Postprocessing", IEEE Trans. Magn. Vol. 37, No. 2, pp. 714–720, March 2001]</ref><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
As data detectors became more sophisticated, it was found important to deal with any residual signal nonlinearities as well as pattern-dependent noise (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 have a different noise-spectrum. Such detectors are referred to as Pattern-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>. Such techniques have been more recently applied to digital tape recorders<ref>[https://ieeexplore.ieee.org/document/5438946 E. Eleftheriou, S. Ölçer, R. Hutchins, "Adaptive Noise-Predictive Maximum-Likelihood (NPML) Data Detection for Magnetic Tape Storage Systems", IBM J. Res. Dev. Vol. 54, No. 2, pp. 7.1-7.10, March 2010]</ref>.
== Recent Read/Write Electronics ==
Although the PRML acronym is still occasionally used, the most advanced detectors today (as of 2017) are around a million times more complex (gate-count) than the first PRML channel and operate about 100 times the data-rate (up to 3 Gbit/s). The analog front-end typically includes [[Automatic_gain_control|AGC]], correction for the nonlinear read-element response, and a low-pass filter with control over the high-frequency boost or cut. Equalization is done after the A/D with a digital [[Finite_impulse_response|FIR]] equalizer. ([[Two-Dimensional Magnetic Recording|TDMR]] uses a 2-input, 1-output equalizer.) The detector uses the PDNP/NPML approach but the hard-decision Viterbi algorithm is replaced 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 iteratively decoding [[LDPC]] codes used in modern HDDs. A single integrated circuit contains the entire R/W channel (including the iterative decoder) as well as all the disk control and interface functions. There are currently two suppliers: [[Broadcom]] and [[Marvell Technology Group|Marvell]].<ref>[https://www.marvell.com/storage/assets/Marvell_88i9422_Soleil_pb_FINAL.pdf Marvell 88i9422 Soleil SATA HDD Controller., Sept 2015]</ref>
== See also ==
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