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Partial-response maximum-likelihood


Jan 20, 2022

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.

Method for interpreting data in digital storage systems

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.

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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]

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’.

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