Partial-response maximum-likelihood: Difference between revisions

Revision as of 15:48, 9 October 2019

Revision as of 17:49, 9 October 2019

Line 1:

In [[computer data storage]], '''partial-response maximum-likelihood''' ('''PRML''') is a method for convertingrecovering a weakthe [[analogDigital 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]]. intoPRML was introduced to recover data more reliably or at a greater [[Digital signal areal_density_(electronicscomputer_storage)|digital signalareal-density]]. PRMLthan attemptsearlier tosimpler correctlyschemes interpretsuch evenas smallpeak-detection. changesThese inadvances theare analogimportant signal,because whereasmost peakof detectionthe reliesdigital ondata fixedin thresholds.the Becauseworld PRMLis canstored correctlyusing decode[[magnetic arecording]] weakeron signal,Hard itDisk allowsDrives higher(HDD) densityor ofa datadigital recordingtape 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]]).

For example, PRML would read the magnetic flux density pattern "70, 60, 55, 60, 70" (where 60 is the baseline signal) as binary "101", and the same for "45, 40, 30, 40, 45" (baseline of 40), whereas a peak detector would decode everything above 50 (for example) as high, and below 50 as low, so the first pattern would read "111" and the second as "000".

'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.

In the presence of colored stationary and nonstationary data-dependent noise, the performance of the PRML detector can be improved by embedding a noise prediction/whitening process into the computation algorithm of the PRML detector. This noise-prediction-based sequence-estimation framework is known as [[noise-predictive maximum-likelihood detection]] (NPML).

== Theoretical Development ==

Line 23:

<br>

The PRML channel for the IBM 0681 was developed in [[IBM Rochester]] lab. in Minnesota<ref>[https://ieeexplore.ieee.org/document/278677 J. Coker, R. Galbraith, G. Kerwin, J. Rae, P. Ziperovich, "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>[https://ieeexplore.ieee.org/document/124468 R.Cidecyan, F.Dolvio, R. Hermann, W.Hirt, W. Schott "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>[https://ieeexplore.ieee.org/document/104703 T. Howell, et al. "Error Rate Performance of Experimental Gigabit per Square Inch Recording Components", IEEE Trans. Magn., Vol. 26, No. 5, pp. 2298-2302, 1990]</ref> <br>

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 Precompensation ===

Line 31:

== 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 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> 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.

=== Post-processor architecture ===

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 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 havve 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]<br/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. ([https://en.wikipedia.org/wiki/Draft: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 ==

Line 47:

== References ==

{{Reflist}}

== Further Reading ==

* [http://pcguide.com/ref/hdd/geom/dataPRML-c.html The PC Guide: PRML]

* [http://www.guzik.com/solutions_chapter9.asp Online Chapter "Introduction to PRML"], from Alex Taratorin's book ''Characterization of Magnetic Recording Systems: A Practical Approach''