Partial-response maximum-likelihood: Difference between revisions

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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 ===

'''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>

'''[[Maximum-likelihood]]''' decoding using the eponymous [[Viterbi algorithm]] was proposed in 1967 by [[Andrew Viterbi]] as a means of decoding [[convolutional codes]].<ref>[https://ieeexplore.ieee.org/document/1054010 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]</ref>. <br>

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 G. 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 Products ===

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 Recording ====

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_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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The heads and the read/write channel ran at the remarkably high data-rate of 117 Mbits/s.<ref>[https://ieeexplore.ieee.org/document/5261308 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)]</ref>. The PRML electronics were implemented with four 4-bit, [[Plessey]] [[analog-to-digital converter]]s and [https://en.wikichip.org/wiki/fairchild/100k 100k ECL logic].<ref>[https://www.computerhistory.org/collections/catalog/102741157 Computer History Museum, #102741157, "Ampex PRML Prototype Circuit", circa 1982]</ref>. Its mode of operation is best described in a paper by Wood and Petersen.<ref>[https://ieeexplore.ieee.org/document/1096563 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)]</ref>.

Petersen was granted a patent on the PRML channel but Ampex never took advantage of it.<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 Disk Drives (HDD) ====

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&section=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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=== Further Developments ===

Generalized PRML

[[NPML]]

PDNP

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== References ==

{{Reflist}}

* [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''