fbpx
Wikipedia

Partial-response maximum-likelihood

May 02, 2024

In computer data storage, partial-response maximum-likelihood (PRML) is a method for recovering the digital data from the weak analog read-back signal picked up by the head of a magnetic disk drive or tape drive. PRML was introduced to recover data more reliably or at a greater areal-density than earlier simpler schemes such as peak-detection.[1] These advances are important because most of the digital data in the world is stored using magnetic storage on hard disk or tape drives.

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 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 (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.

Theoretical development edit

 
Continuous-time Partial-Response (class 4) and corresponding 'eye pattern'

Partial-response was first proposed by Adam Lender in 1963.[2] The method was generalized by Kretzmer in 1966. Kretzmer also classified the several different possible responses,[3] 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.[4]

Maximum-likelihood decoding using the eponymous Viterbi algorithm was proposed in 1967 by Andrew Viterbi as a means of decoding convolutional codes.[5]

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[6] (later called PRML). (The wide range of applications of the Viterbi algorithm is well described in a review paper by Dave Forney.[7]) A simplified algorithm, based upon a difference metric, was used in the early implementations. This is due to Ferguson at Bell Labs.[8]

Implementation in products edit

 
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 RLL codes with 'peak detection'.

Tape recording edit

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. 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.[9] It became Ampex' most successful digital product.[10]


The heads and the read/write channel ran at the (then) remarkably high data-rate of 117 Mbits/s.[11] The PRML electronics were implemented with four 4-bit, Plessey analog-to-digital converters (A/D) and 100k ECL logic.[12] The PRML channel outperformed a competing implementation based on "Null-Zone Detection".[13] A prototype PRML channel was implemented earlier at 20 Mbit/s on a prototype 8-inch HDD,[14] 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.[15] Petersen was granted a patent on the PRML channel but it was never leveraged by Ampex.[16]

Hard disk drives edit

In 1990, IBM shipped the first PRML channel in an HDD in the 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[17] with support from the IBM Zurich Research lab. in Switzerland.[18] A parallel R&D effort at IBM San Jose did not lead directly to a product.[19] A competing technology at the time was 17ML[20] an example of Finite-Depth Tree-Search (FDTS).[21][22]

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 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[23] after the A/D to compensate for changes in radius and/or changes in the magnetic components.

Write precompensation edit

The presence of nonlinear transition-shift (NLTS) distortion on NRZ recording at high density and/or high data-rate was recognized in 1979.[24] The magnitude and sources of NLTS can be identified using the 'extracted dipulse' technique.[25][26]

Ampex was the first to recognize the impact of NLTS on PR4.[27] and was first to implement Write precompensation for PRML NRZ recording. 'Precomp.' largely cancels the effect of NLTS.[14] Precompensation is viewed as a necessity for a PRML system and is important enough to appear in the BIOS HDD setup[28] although it is now handled automatically by the HDD.

Further developments edit

Generalized PRML edit

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.[29] 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 (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.[30] 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 edit

Given the rapid increase in complexity with longer targets, a post-processor architecture was proposed, firstly for EPRML.[31] 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[32][33][34]

PRML with nonlinearities and signal-dependent noise edit

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[35] or noise-predictive maximum-likelihood detectors (NPML).[36] Such techniques have been more recently applied to digital tape recorders.[37]

Modern electronics edit

Although the PRML acronym is still occasionally used, advanced detectors are more complex PRML operate at higher data-rates. The analog front-end typically includes 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 ADC with a digital FIR filter. (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 the low-density parity-check code used in modern HDDs. A single integrated circuit contains the entire read and write channels (including the iterative decoder) as well as all the disk control and interface functions. There are currently two suppliers: Broadcom and Marvell.[38]

See also edit

References edit

  1. ^ G. Fisher, W. Abbott, J. Sonntag, R. Nesin, "PRML detection boosts hard-disk drive capacity", IEEE Spectrum, Vol. 33, No. 11, pp. 70-76, Nov. 1996
  2. ^ 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
  3. ^ E. Kretzmer, "Generalization of a Technique for Binary Data Communication", IEEE Trans. Comm., Vol. 14, No. 1, pp. 67-68 Feb. 1966
  4. ^ 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
  5. ^ A. Viterbi, "Error bounds for convolutional codes and an asymptotically optimum decoding algorithm", IEEE Trans. Info. Theory, Vol. 13, No. 2, pp. 260-269, Apr. 1967
  6. ^ H. Kobayashi, "Correlative level coding and maximum-likelihood decoding", IEEE Trans. Inform. Theory, vol. IT-17, PP. 586-594, Sept. 1971
  7. ^ D. Forney, “The Viterbi Algorithm”, Proc. IEEE, Vol. 61, No. 3, pp. 268-278, Mar. 1973
  8. ^ M. Ferguson, ”Optimal reception for binary partial response channels” Bell Syst. Tech. J., vol. 51, pp. 493-505, Feb. 1972
  9. ^ T. Wood, "Ampex Digital Cassette Recording System (DCRS)", THIC meeting, Ellicott City, MD, 16 Oct., 1996 (PDF)
  10. ^ R. Wood, K. Hallamasek, "Overview of the prototype of the first commercial PRML channel", Computer History Museum, #102788145, Mar. 26, 2009
  11. ^ C. Coleman, D. Lindholm, D. Petersen, and R. Wood, "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)
  12. ^ Computer History Museum, #102741157, "Ampex PRML Prototype Circuit", circa 1982
  13. ^ J. Smith, "Error Control in Duobinary Data Systems by Means of Null Zone Detection", IEEE Trans. Comm., Vil 16, No. 6, pp. 825-830, Dec., 1968
  14. ^ a b R. Wood, S. Ahlgrim, K. Hallamasek, R. Stenerson, "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)
  15. ^ R. Wood and D. Petersen, "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)
  16. ^ D. Petersen, "Digital maximum likelihood detector for class IV partial response", US Patent 4504872, filed Feb. 8, 1983
  17. ^ 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
  18. ^ 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
  19. ^ 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
  20. ^ A. Patel, "Performance Data for a Six-Sample Look-Ahead 17ML Detection Channel", IEEE Trans. Magn., Vol. 29, No. 6, pp. 4012-4014, Dec. 1993
  21. ^ R. Carley, J. Moon, "Apparatus and method for fixed delay tree search", filed Oct. 30th, 1989
  22. ^ R. Wood, "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
  23. ^ 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
  24. ^ 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
  25. ^ 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
  26. ^ 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)
  27. ^ 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
  28. ^ . Archived from the original on October 4, 2018. Retrieved October 8, 2019.
  29. ^ 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
  30. ^ 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.
  31. ^ R. Wood, "Turbo-PRML, A Compromise EPRML Detector", IEEE Trans. Magn., Vol. MAG-29, No. 6, pp. 4018-4020, Nov. 1993
  32. ^ Conway, T. (July 1998). "A new target response with parity coding for high density magnetic recording channels". IEEE Transactions on Magnetics. 34 (4): 2382–2386. doi:10.1109/20.703887.
  33. ^ 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
  34. ^ 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
  35. ^ 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
  36. ^ E. Eleftheriou, W. Hirt, "Improving Performance of PRML/EPRML through Noise Prediction". IEEE Trans. Magn. Vol. 32, No. 5, pp. 3968–3970, Sept. 1996
  37. ^ 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
  38. ^ (PDF). September 2015. Archived from the original (PDF) on 2016-12-13. Retrieved 2019-10-09.

Further reading edit

  • The PC Guide: PRML
  • Online Chapter "Introduction to PRML", from Alex Taratorin's book Characterization of Magnetic Recording Systems: A Practical Approach

May 02, 2024
partial, response, maximum, likelihood, computer, data, storage, partial, response, maximum, likelihood, prml, method, recovering, digital, data, from, weak, analog, read, back, signal, picked, head, magnetic, disk, drive, tape, drive, prml, introduced, recove. In computer data storage partial response maximum likelihood PRML is a method for recovering the digital data from the weak analog read back signal picked up by the head of a magnetic disk drive or tape drive PRML was introduced to recover data more reliably or at a greater areal density than earlier simpler schemes such as peak detection 1 These advances are important because most of the digital data in the world is stored using magnetic storage on hard disk or tape drives 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 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 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 Contents 1 Theoretical development 2 Implementation in products 2 1 Tape recording 2 2 Hard disk drives 2 3 Write precompensation 3 Further developments 3 1 Generalized PRML 3 2 Post processor architecture 3 3 PRML with nonlinearities and signal dependent noise 4 Modern electronics 5 See also 6 References 7 Further readingTheoretical development edit nbsp Continuous time Partial Response class 4 and corresponding eye pattern Partial response was first proposed by Adam Lender in 1963 2 The method was generalized by Kretzmer in 1966 Kretzmer also classified the several different possible responses 3 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 4 Maximum likelihood decoding using the eponymous Viterbi algorithm was proposed in 1967 by Andrew Viterbi as a means of decoding convolutional codes 5 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 6 later called PRML The wide range of applications of the Viterbi algorithm is well described in a review paper by Dave Forney 7 A simplified algorithm based upon a difference metric was used in the early implementations This is due to Ferguson at Bell Labs 8 Implementation in products edit nbsp 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 RLL codes with peak detection Tape recording edit 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 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 9 It became Ampex most successful digital product 10 The heads and the read write channel ran at the then remarkably high data rate of 117 Mbits s 11 The PRML electronics were implemented with four 4 bit Plessey analog to digital converters A D and 100k ECL logic 12 The PRML channel outperformed a competing implementation based on Null Zone Detection 13 A prototype PRML channel was implemented earlier at 20 Mbit s on a prototype 8 inch HDD 14 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 15 Petersen was granted a patent on the PRML channel but it was never leveraged by Ampex 16 Hard disk drives edit In 1990 IBM shipped the first PRML channel in an HDD in the IBM 0681 It was full height 5 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 17 with support from the IBM Zurich Research lab in Switzerland 18 A parallel R amp D effort at IBM San Jose did not lead directly to a product 19 A competing technology at the time was 17ML 20 an example of Finite Depth Tree Search FDTS 21 22 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 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 23 after the A D to compensate for changes in radius and or changes in the magnetic components Write precompensation edit The presence of nonlinear transition shift NLTS distortion on NRZ recording at high density and or high data rate was recognized in 1979 24 The magnitude and sources of NLTS can be identified using the extracted dipulse technique 25 26 Ampex was the first to recognize the impact of NLTS on PR4 27 and was first to implement Write precompensation for PRML NRZ recording Precomp largely cancels the effect of NLTS 14 Precompensation is viewed as a necessity for a PRML system and is important enough to appear in the BIOS HDD setup 28 although it is now handled automatically by the HDD Further developments editGeneralized PRML edit 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 29 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 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 30 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 edit Given the rapid increase in complexity with longer targets a post processor architecture was proposed firstly for EPRML 31 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 32 33 34 PRML with nonlinearities and signal dependent noise edit 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 35 or noise predictive maximum likelihood detectors NPML 36 Such techniques have been more recently applied to digital tape recorders 37 Modern electronics editAlthough the PRML acronym is still occasionally used advanced detectors are more complex PRML operate at higher data rates The analog front end typically includes 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 ADC with a digital FIR filter 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 the low density parity check code used in modern HDDs A single integrated circuit contains the entire read and write channels including the iterative decoder as well as all the disk control and interface functions There are currently two suppliers Broadcom and Marvell 38 See also editMaximum likelihood Viterbi algorithmReferences edit G Fisher W Abbott J Sonntag R Nesin PRML detection boosts hard disk drive capacity IEEE Spectrum Vol 33 No 11 pp 70 76 Nov 1996 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 E Kretzmer Generalization of a Technique for Binary Data Communication IEEE Trans Comm Vol 14 No 1 pp 67 68 Feb 1966 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 A Viterbi Error bounds for convolutional codes and an asymptotically optimum decoding algorithm IEEE Trans Info Theory Vol 13 No 2 pp 260 269 Apr 1967 H Kobayashi Correlative level coding and maximum likelihood decoding IEEE Trans Inform Theory vol IT 17 PP 586 594 Sept 1971 D Forney The Viterbi Algorithm Proc IEEE Vol 61 No 3 pp 268 278 Mar 1973 M Ferguson Optimal reception for binary partial response channels Bell Syst Tech J vol 51 pp 493 505 Feb 1972 T Wood Ampex Digital Cassette Recording System DCRS THIC meeting Ellicott City MD 16 Oct 1996 PDF R Wood K Hallamasek Overview of the prototype of the first commercial PRML channel Computer History Museum 102788145 Mar 26 2009 C Coleman D Lindholm D Petersen and R Wood 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 Computer History Museum 102741157 Ampex PRML Prototype Circuit circa 1982 J Smith Error Control in Duobinary Data Systems by Means of Null Zone Detection IEEE Trans Comm Vil 16 No 6 pp 825 830 Dec 1968 a b R Wood S Ahlgrim K Hallamasek R Stenerson 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 R Wood and D Petersen 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 D Petersen Digital maximum likelihood detector for class IV partial response US Patent 4504872 filed Feb 8 1983 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 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 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 A Patel Performance Data for a Six Sample Look Ahead 17ML Detection Channel IEEE Trans Magn Vol 29 No 6 pp 4012 4014 Dec 1993 R Carley J Moon Apparatus and method for fixed delay tree search filed Oct 30th 1989 R Wood 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 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 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 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 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 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 Kursk BIOS Settings Standard CMOS Setup Feb 12 2000 Archived from the original on October 4 2018 Retrieved October 8 2019 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 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 R Wood Turbo PRML A Compromise EPRML Detector IEEE Trans Magn Vol MAG 29 No 6 pp 4018 4020 Nov 1993 Conway T July 1998 A new target response with parity coding for high density magnetic recording channels IEEE Transactions on Magnetics 34 4 2382 2386 doi 10 1109 20 703887 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 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 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 E Eleftheriou W Hirt Improving Performance of PRML EPRML through Noise Prediction IEEE Trans Magn Vol 32 No 5 pp 3968 3970 Sept 1996 E Eleftheriou S Olcer 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 Marvell 88i9422 Soleil SATA HDD Controller PDF September 2015 Archived from the original PDF on 2016 12 13 Retrieved 2019 10 09 Further reading editThe PC Guide PRML Online Chapter Introduction to PRML from Alex Taratorin s book Characterization of Magnetic Recording Systems A Practical Approach Retrieved from https en wikipedia org w index php title Partial response maximum likelihood amp oldid 1220805060, wikipedia, wiki, book, books, library,

article

, read, download, free, free download, mp3, video, mp4, 3gp, jpg, jpeg, gif, png, picture, music, song, movie, book, game, games.