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{{Short description|Method for interpreting data in digital storage systems}}
In [[computer data storage]], '''partial-response maximum-likelihood''' ('''PRML''') is a method for recovering the [[Digital signal (electronics)|digital data]] from the weak analog read-back signal picked up by the [[
Ampex introduced PRML in a tape drive in 1984. IBM introduced PRML in a disk drive in 1990 and also coined the acronym PRML. Many advances have taken place since the initial introduction. Recent [[read/write channel]]s operate at much higher data-rates, are fully adaptive, and, in particular, include the ability to handle nonlinear signal distortion and non-stationary, colored, data-dependent noise ([[noise-predictive maximum-likelihood detection|PDNP or NPML]]).
''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.
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== Theoretical development ==
[[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>A. Lender, "[https://ieeexplore.ieee.org/abstract/document/6373379 The duobinary technique for high-speed data transmission]", Trans. AIEE, Part I: Communication and Electronics, Vol. 82
'''[[Maximum-likelihood]]''' decoding using the eponymous [[Viterbi algorithm]] was proposed in 1967 by [[Andrew Viterbi]] as a means of decoding [[convolutional codes]].<ref>A. Viterbi, "[https://ieeexplore.ieee.org/document/1054010 Error bounds for convolutional codes and an asymptotically optimum decoding algorithm]", IEEE Trans. Info. Theory, Vol. 13, No. 2, pp. 260-269, Apr. 1967</ref>
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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>T. Wood, "[http://www.thic.org/pdf/Oct96/ampex.twood.pdf Ampex Digital Cassette Recording System (DCRS)]", THIC meeting, Ellicott City, MD, 16 Oct., 1996 (PDF)</ref> It became Ampex' most successful digital product.<ref>R. Wood, K. Hallamasek, "[https://www.computerhistory.org/collections/catalog/102788145 Overview of the prototype of the first commercial PRML channel]", Computer History Museum, #102788145, Mar. 26, 2009</ref>
The heads and the read/write channel ran at the (then) remarkably high data-rate of 117
▲The heads and the read/write channel ran at the (then) remarkably high data-rate of 117 Mbits/s.<ref>C. Coleman, D. Lindholm, D. Petersen, and R. Wood, "[https://ieeexplore.ieee.org/document/5261308 High Data Rate Magnetic Recording in a Single Channel]", J. IERE, Vol., 55, No. 6, pp. 229-236, June 1985. (invited) (Charles Babbage Award for Best Paper)</ref> The PRML electronics were implemented with four 4-bit, [[Plessey]] [[analog-to-digital converter]]s (A/D) and [https://en.wikichip.org/wiki/fairchild/100k 100k ECL logic].<ref>Computer History Museum, #102741157, "[https://www.computerhistory.org/collections/catalog/102741157 Ampex PRML Prototype Circuit]", circa 1982</ref> The PRML channel outperformed a competing implementation based on "Null-Zone Detection".<ref>J. Smith, "[https://ieeexplore.ieee.org/document/1089924 Error Control in Duobinary Data Systems by Means of Null Zone Detection]", IEEE Trans. Comm., Vil 16, No. 6, pp. 825-830, Dec., 1968</ref> A prototype PRML channel was implemented earlier at 20 Mbit/s on a prototype 8-inch HDD,<ref name=8inch>R. Wood, S. Ahlgrim, K. Hallamasek, R. Stenerson, "[https://ieeexplore.ieee.org/document/1063460 An Experimental Eight-inch Disc Drive with One-hundred Megabytes Per Surface]", IEEE Trans. Mag., vol. MAG-20, No. 5, pp. 698-702, Sept. 1984. (invited)</ref> but Ampex exited the HDD business in 1985. These implementations and their mode of operation are best described in a paper by Wood and Petersen.<ref>R. Wood and D. Petersen, "[https://ieeexplore.ieee.org/document/1096563 Viterbi Detection of Class IV Partial Response on a Magnetic Recording Channel]", IEEE Trans. Comm., Vol., COM-34, No. 5, pp. 454-461, May 1986 (invited)</ref> Petersen was granted a patent on the PRML channel but it was never leveraged by Ampex.<ref>D. Petersen, "[https://patents.google.com/patent/US4504872A/en Digital maximum likelihood detector for class IV partial response]", US Patent 4504872, filed Feb. 8, 1983</ref>
=== Hard disk drives ===
In 1990, IBM shipped the first PRML channel in an HDD in the [[History of IBM magnetic disk drives#IBM 0681|IBM 0681]] It was full-height 5¼-inch form-factor with up to 12 of 130 mm disks and had a maximum capacity of 857 MB.
The PRML channel for the IBM 0681 was developed in [[IBM Rochester]] lab. in Minnesota<ref>J. Coker, R. Galbraith, G. Kerwin, J. Rae, P. Ziperovich, "[https://ieeexplore.ieee.org/document/278677 Implementation of PRML in a rigid disk drive]", IEEE Trans. Magn., Vol. 27, No. 6, pp. 4538-43, Nov. 1991</ref> with support from the [[IBM Zurich]] Research lab. in [[Switzerland]].<ref>R.Cidecyan, F.Dolvio, R. Hermann, W.Hirt, W. Schott "[https://ieeexplore.ieee.org/document/124468 A PRML System for Digital Magnetic Recording]", IEEE Journal on Selected Areas in Comms, vol.10, No.1, pp.38-56, Jan 1992</ref> A parallel R&D effort at IBM San Jose did not lead directly to a product.<ref>T. Howell, et al. "[https://ieeexplore.ieee.org/document/104703 Error Rate Performance of Experimental Gigabit per Square Inch Recording Components]", IEEE Trans. Magn., Vol. 26, No. 5, pp. 2298-2302, 1990</ref> A competing technology at the time was 17ML<ref>A. Patel, "[https://www.researchgate.net/publication/224663211 Performance Data for a Six-Sample Look-Ahead 17ML Detection Channel]", IEEE Trans. Magn., Vol. 29, No. 6, pp. 4012-4014, Dec. 1993</ref> an example of Finite-Depth Tree-Search (FDTS).<ref>R. Carley, J. Moon, "[https://patents.google.com/patent/US5136593A/en Apparatus and method for fixed delay tree search]", filed Oct. 30th, 1989</ref><ref>R. Wood, "[https://ieeexplore.ieee.org/document/42527 New Detector for 1,k Codes Equalized to Class II Partial Response]", IEEE Trans. Magn., Vol. MAG-25, No. 5, pp. 4075-4077, Sept. 1989</ref>
The IBM 0681 read/write channel ran at a data-rate of 24
=== Write precompensation ===
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Ampex was the first to recognize the impact of NLTS on PR4.<ref>P. Newby, R. Wood, "[https://ieeexplore.ieee.org/document/1064566 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 /> Precompensation is viewed as a necessity for a PRML system and is important enough to appear in the [[BIOS]] HDD setup<ref>{{Cite web |url=http://www.kva.kursk.ru/bios1/HTML1/standard.html |title=Kursk: BIOS Settings - Standard CMOS Setup, Feb 12, 2000 |access-date=October 8, 2019 |archive-date=October 4, 2018 |archive-url=https://web.archive.org/web/20181004103524/http://www.kva.kursk.ru/bios1/HTML1/standard.html |url-status=dead }}</ref> although it is now handled automatically by the HDD.
== Further developments ==
=== 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.
=== Post-processor architecture ===
Given the rapid increase in complexity with longer targets, a post-processor architecture was proposed, firstly for EPRML.<ref>R. Wood, "[https://ieeexplore.ieee.org/document/281375 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>{{Cite journal|last=Conway|first=T.|date=July 1998|title=A new target response with parity coding for high density magnetic recording channels
=== PRML with nonlinearities and signal-dependent noise ===
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>J. Moon, J. Park, "[https://ieeexplore.ieee.org/abstract/document/920181 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>E. Eleftheriou, W. Hirt, "[https://ieeexplore.ieee.org/document/539233 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>E. Eleftheriou, S. Ölçer, R. Hutchins, "[https://ieeexplore.ieee.org/document/5438946 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>
== Modern electronics ==
Although the PRML acronym is still occasionally used, advanced detectors are more complex than PRML and operate at higher data rates. The analog front-end typically includes [[
== See also ==
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