Partial-response maximum-likelihood: Difference between revisions

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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 [[Disk_read-and-write_head|head]] of a magnetic [[Hard disk drive|disk drive]] or [[tape drive]]. PRML was introduced to recover data more reliably or at a greater [[areal_density_(computer_storage)|areal-density]] than earlier simpler schemes such as peak-detection.<ref>G. Fisher, W. Abbott, J. Sonntag, R. Nesin, "[https://ieeexplore.ieee.org/document/542278 PRML detection boosts hard-disk drive capacity]", IEEE Spectrum, Vol. 33, No. 11, pp. 70-76, Nov. 1996</ref>. These advances are important because most of the digital data in the world is stored using [[magnetic recording]] on Hard Disk Drives (HDD) or a digital tape recorders.

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 channels operate a 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]]).

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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&nbsp;mm disks and had a maximum capacity of 857&nbsp;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&nbsp;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>T. Kameyama, S. Takanami, R. Arai, "[https://ieeexplore.ieee.org/document/1059216 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.

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=== 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>R. Cideciyan, J. Coker; E. Eleftheriou; R. Galbraith, "[https://ieeexplore.ieee.org/document/917606 NPML Detection Combined with Parity-Based Postprocessing]", IEEE Trans. Magn. Vol. 37, No. 2, pp. 714–720, March 2001</ref><ref>M. Despotovic, V. Senk, "Data Detection", Chapter 32 in ''[https://www.researchgate.net/publication/328870436 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 ===

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 ==