CODING AND SIGNAL
`PROCESSING FOR MAGNETIC
`RECORDING SYSTEMS
`
`EDITED BY
`
`· Bane Vasic
`
`University of Arizona
`Tucson,AZ
`
`Erozan M. Kurtas
`
`Seagate Technology
`Pittsburgh, PA
`
`. \ ...
`
`CRC PRESS
`Boca Raton London New York Washington, D.C.
`
`UMN EXHIBIT 2036
`LSI Corp. et al. v. Regents of Univ. of Minn.
`IPR2017-01068
`
`
`Page 1 of 17
`
`

`

`Library of Congress Cataloging-in-Publication Data
`Coding and signal processing for magnetic recording systems / edited by Bane Vasic and Erozan M. Kurtas.
`(Computer engineering; 2)
`p. cm. -
`Includes bibliographical references and index.
`ISBN 0-8493-1524-7 (alk paper)
`1. Magnetic recorders and recording. 2. Signal processing. 3. Coding theory:
`I. Vasic, Bane II. Kurtas, M. Erozan III. Title IV. Series: Computer engineering ( CRC Press); 2.
`
`TK7881.6C62 2004
`621.39-dc22
`
`2004050269
`
`This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with
`permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish
`reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials
`or for the consequences of their use.
`Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical,
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`@ 2005 by CRC Press I.LC
`
`No claim to original U.S. Government works
`International Standard Book Number 0-8493-1524-7
`Library of Congress Card Number 2004050269
`Printed in the United States of America 1 2 3 4 5 6 7 8 9 0
`Printed on acid-free paper
`
`A
`is
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`
`
`Page 2 of 17
`
`

`

`Contents
`
`Section I: Recording Systems
`
`1 A Brief History of Magnetic Storage
`Dean Palmer ........................................................................ 1-1
`
`2 Physics of Longitudinal and Perpendicular Recording
`Hong Zhou, Tom Roscamp, Roy Gustafson, Eric Boernern, and Roy Chantrell ....... 2-1
`
`3 The Physics of Optical Recording
`William A. Challener and Terry W. McDaniel ....................................... 3-1
`
`4 Head Design Techniques for Recording Devices
`Robert E. Rottmayer . ................................................................ 4-1
`
`Section II: Communication and Information Theory
`of Magnetic Recording Channels
`
`5 Modeling the Recording Channel
`Jaekyun Moon . ................................................................. .- .... 5-1
`
`6 Signal and Noise Generation for Magnetic Recording Channel Simulations
`Xueshi Yang and Brazan M. Kurtas .................................................. 6-1
`
`7 Statistical Analysis of Digital Signals and Systems
`Dragana Bajic and Dusan Drajic .................................................... 7-1
`
`8 Partial Response Equalization with Application to High Density
`Magneti'c Recording Channels
`John G. Proakis ............................................... : ..................... . 8-1
`
`9 An Introduction to Error-Correcting Codes
`Mario Blaum .................................................................. : .... . 9-1
`
`xv
`
`
`Page 3 of 17
`
`

`

`10 Message-Passing Algorithm
`Sundararajan Sankaranarayanan and Bane Vasic . ................................. 10-1
`
`11 Modulation Codes for Storage Systems
`Brian Marcus and Emina Soljanin ................................................. 11-1
`
`12
`
`Information Theory of Magnetic Recording Channels
`Zheng Zhang, Tolga M. Duman, and Brazan M. Kurtas ............................ 12-1
`
`13 Capacity of Partial Response Channels
`Shaohua Yang and Aleksandar Kavci c .............................................. 13-1
`Introduction to Read Channels
`
`Section III:
`
`14 Recording Physics and Organization of Data on a Disk
`Bane Vasic, Miroslav Despotovit, and Vojin Senk . .................................. 14-1
`
`15 Read Channels for Hard Drives
`Bane Vasic, Pervez M. Aziz, and Necip Sayiner . .................................... 15-1
`16 An Overview of Hard Ddve Controller Functionality
`Bruce Buch . ........................................................................ 16-1
`
`Section IV: Coding for Read Channels
`
`17 Runlength Limited Sequences
`Kees A. Schouhamer Immink ....................................................... 17-1
`
`20
`
`18 Maximum Transition Run Coding
`Barrett J. Brickner . ................................................................. 18-1
`19 Spectrum Shaping Codes
`Stojan Denic and Bane Vasic . ...................................................... 19-1
`Introduction to Constrained Binary Codes with Error Correction Capability
`Hendrik C. Ferreira and Willem A. Clarke ......................................... 20-1
`21 Constrained Coding and Error-Control Coding
`John L. Fan ........................................................................ 21-1
`22 Convolutional Codes for Partial-Response Channels
`Bartolomeu F. Uchoa-Filho, Mark A. Herra, Miroslav Despotovit,
`and Vojin Senk .......... ' ...................................... · .................... 22-1
`23 Capacity-Approaching Codes for Partial Response Channels
`Nedeljko Varnica, Xiao Ma, and Aleksandar Kavci c ................................ 23-1
`
`xvi
`
`C-
`
`
`Page 4 of 17
`
`

`

`....... 10-1
`
`....... 11-1
`
`....... 12-1
`
`....... 13-1
`
`....... 14-1
`
`....... 15-1
`
`....... 16-1
`
`....... 17-1
`
`....... . 18-1
`
`....... 19-1
`
`ity
`....... 20-1
`
`....... 21-1
`
`....... 22-1
`
`....... 23-1
`
`24 Coding and Detection for Multitrack Systems
`Bane Vasic and Olgica Milenkovic ................................................. 24-1
`25 Two-Dimensional Data Detection and Error Control
`Brian M. King and Mark A. Neifeld ................................................ 25-1
`Section V: Signal Processing for Read Channels
`
`26 Adaptive Timing Recovery for Partial Response Channels
`Pervez M. Aziz and Viswanath Annampedu ........................................ 26-1
`2 7 Interpolated Timing Recovery
`Piya Kovintavewat, John R. Barry, M. Fatih Brden, and Brazan M. Kurtas ......... 27-1
`28 Adaptive Equalization Architectures for Partial Response Channels
`Pervez M. Aziz ..................................................................... 28-1
`29 Head Position Estimation
`Ara Patapoutian ................................................................... 29-1
`30 Servo Signal Processing
`Pervez M. Aziz and Viswanath Annampedu ........................................ 30-1
`31 Evaluation of Thermal Asperity in Magnetic Recording
`M. Fatih Brden, Brazan M. Kurtas, and Michael J. Link ............................ 31-1
`3 2 Data Detection
`Miroslav Despotovic and Vojin Senk . ............................................... 32-1
`33 Detection Methods for Data-dependent Noise in Storage Channels
`Brazan M. Kurtas, Jongseung Park, Xueshi Yang, William Radich,
`and Aleksandar Kavci c ............................................................ 33-1
`34 Read/Write Channel Implementation
`Borivoje Nikolic, Michael Leung, Bngling Yeo, and Kiyoshi Fukahori ................ 34-1
`
`Section VI:
`
`Iterative Decoding
`
`35 Turbo Codes
`Mustafa N. Kaynak, Taiga M. Duman, and Brazan M. Kurtas ...................... 35-1
`36 An Introduction to LDPC Codes
`William B. Ryan ................................................................... 36-1
`
`xvii
`
`
`Page 5 of 17
`
`

`

`37 Concatenated Single-Parity Check Codes for High-Density
`.
`Digital Recording Systems
`Jing Li, Krishna R. Narayanan, Brazan M. Kurtas, and Travis R. Oenning .......... 37-1
`
`3 8 Structured Low-Density Parity-Check Codes
`Bane Vasic, Brazan M. Kurtas, Alexander Kuznetsav, and Olgica Milenkavic ....... 38-1
`
`39 Turbo Coding for Multitrack Recording Channels
`Zheng Zhang, Talga M. Duman, and Brazan M. Kurtas . ........................... 39-1
`
`Index ..................................................................................... 1-1
`
`xviii
`
`
`Page 6 of 17
`
`

`

`Read Channels for
`Hard Drives
`
`15.1 Analog Front End .................................. . 15-3
`15.2
`Partial Response Signaling with Maximum
`Likelihood Sequence Estimation .................... . 15-3
`15.3 Adaptive Equalization .............................. . 15-4
`15.4 Viterbi Detection .. ·~· ............................. . 15-4
`15.5
`Timing Recovery ................................... . 15-5
`15.6
`Read Channel Servo Information Detection ......... . 15-6
`15.7
`Precompensation .......... · ........................ . 15-7
`15.8
`The Effect of Thermal Asperites .................... . 15-7
`15.9
`Postprocessor ...................................... . 15-7
`15.10 Modulation Coding ................................ . 15-8
`15.11 Error Control Coding .............................. . 15-9
`15.12 Error Performance Measures ....................... . 15-9
`
`e read channel is a device situated between the drive's controller and the recording head's preamplifier
`gure 15.1). The read channel provides an interface between the controller and the analog recording
`, so that digital data can be recorded and read back from the disk. Furthermore it reads back the
`positioning information from a disk and presents it to the head positioning servo system that
`es in the controller. A typical read channel architecture is shown in Figure 15.2. During a read
`ation, the head generates a pulse in response to magnetic transitions on the media. Pulses are then
`~ified by the preamplifier that resides in the arm electronics module, and fed to the read channel. In
`ead channel the readback signal is additionally amplified and filtered to remove noise and to shape the
`orm, and then the data sequence is detected (Figure 15.2). The data to be written on a disk are sent
`a read channel to a write driver that converts them into a bipolar current that is passed through the
`magnet coils. Priorto sending to read channel, user data coming from computer ( or from a network
`network attached storage devices) are encoded by an error control system. Redundant bits are added
`a way to enable a recovery from random errors that may occur during reading data from a disk. The
`occur due to a number of reasons including: demagnetization effects, magnetic field fluctuations,
`n electronic components, dust and other contaminants, thermal effects etc. Traditionally, the read
`I and drive controller have been separate chips. The latest architectures have integrated them into
`d "super-chips:'
`
`. -,,
`
`15-1
`
`
`Page 7 of 17
`
`

`

`15-2
`
`Disk Drive
`
`Coding and Signal Processing for Magnetic Recording Systems
`to Computer or Network
`
`Drive Controller
`Error
`Head-Positioning
`Control
`Servo
`System
`System
`
`Head
`~ Positioning
`Information
`
`Rea
`
`15
`
`1>-s;
`sigi
`ma
`en,
`hit
`of
`ap
`"t
`fil
`
`tl
`
`FIGURE 15.1 The block diagram o f a disk drive.
`
`to the Controller
`
`Gain
`Control
`Offset _ _ _ _ _ _ _ _ _ __,_.._ Quality
`Monitor
`Control
`Servo
`Address
`Mark
`&
`Burst
`Detector
`
`Preamplifier
`
`Variable
`Gain
`Amplifier
`
`Low-Pass
`Filter
`
`Thermal
`Asperity
`Compen-
`sation
`
`Analog
`FIR
`Filter
`
`Adaptive
`Equalizer
`
`Read Channel
`
`FIGURE 15.2 A typical read channel architecture.
`
`
`Page 8 of 17
`
`

`

`jc Recording Systems
`
`Read Channels for Hard Drives
`
`15-3
`
`,ork
`
`lier
`
`Error
`Control
`System
`
`Data
`
`15.1 Analog Front End
`
`As a first step, the read signal is normalized with respect to gain and offset so that it falls into an expected
`signal range. Variation of gain and offset is a result of variations in the head media spacing, variations in
`magnetic and mechanical and electronic components in the drive, preamplifier and read channel. The front
`end also contains a thermal asperity (TA) circuit compensation. A thermal asperity occurs when the head
`hits a dust particle or some other imperfection on a disk surface. At the moment of impact, the temperature
`of the head rises, and a large signal at the head's output is generated. During a TA a useful readback signal
`appears as riding on the back of a low frequency signal of much higher energy. The beginning of this
`"background" signal can be easily predicted and the TA signal itself suppressed by a relatively simple
`filter.
`High frequency noise is then removed with a continuous-time low pass filter to permit a sampling of
`the signal without aliasing of high frequency noise back into the signal spectrum. The filter frequently
`includes programmable cut-off frequencywhich can be used to shape the signal to optimize data detection.
`A programmable cut-off frequency is essential since the disk rotates with constant angular velocity, and
`data rate varies by approximately a factor of2 from the inner to outer radius of the disk. It is also important
`for the analog filter bandwidth to be switched to allow for low cut-off frequencies when processing servo
`sector information.
`
`the Controller
`
`Partial Response Signaling with Maximum
`Likelihood Sequence Estimation
`
`:After sampling with a rate 1/T, the read signal is passed trough an analog or digital front end filter and
`aetected using a maximum likelihood sequence detector. The partial response signaling with maximum
`elihood sequence estimation PRML was proposed for use in magnetic recording by Kobayashi 30
`ars ago [15, 16]. In 1990 IBM produced the first disk drives employing partial-response signaling with
`aximum-likelihood detection. Today's all read channels are based on some version of the PRML. Cidecyan
`al. (3] described a complete PRML system including equalization, gain and timing control, and Viterbi
`tector. All basic functions of a PRML system have remained practically unchanged, until the introduction
`a postprocessor that performs a special type of soft error correction after maximum likelihood sequence
`tection. Also, significant improvements in all the subsystems have been made during last· 10 years. The
`m "partial response" comes from the fact that the sample of the equalized signal at, say, time nT (Tis
`· aling interval), contains information not only on data bits at time nT, but also on neighboring bits,
`is magnetic transitions. The number of adjacent bits that determine the sample at nT is referred to
`1a1111el memory. The channel memory is a parameter that can be selected in the process of defining
`d channel architecture. The channel memory and the details of the partial response selection are
`based on an attempt to have the partial response be as close a match to the channel as possible.
`the complexity of a maximum likelihood detector is an exponential function of a memory, it is :..,
`ble to keep the memory low, but, the equalization required to achieve this might boost the high
`ency noise, which result in decrease of signal to noise ratio, called equalization loss. The typical value
`annel memory in 'today's read channels is four. The value of an equalized sample at time nT, Yn can
`ritten as
`
`Lh
`
`Y. = L hk · Xn-k
`
`k=O
`
`X11 isa user-data bit recorded attime n(xn E {-1, + l}), and Lh is a channel memory. The coefficients
`1• h(D) = Lf!o hk • Dk, a partial response polynomial or partial response target (Dis a formal,
`elay variable). The main idea in partial response equalization is to equalize the channel to a known
`
`
`Page 9 of 17
`
`

`

`15-4
`
`Coding and Signal Processing for Magnetic Recording Systems
`
`and short target that is matched to the channel spectrum so that noise enhancement is minimum. There(cid:173)
`fore, the deliberate intersymbol interference is intr9duced, but since the target is known, the data can be
`recovered, as explained in the previous article.
`
`15.3 Adaptive Equalization
`To properly detect the user-data it is of essential importance to maintain the partial response target during
`the detection. This implies that channel gain, finite-impulse response (FIR) filter coefficients, and sampling
`phase must be adaptively controlled in real-time. Continuous automatic adaptation allows the read channel
`to compensate for signal variations and changes that occur when drive operation is affected by changes in
`temperature and when the input signals is altered by component aging. Comparing the equalizer output
`samples with the expected partial response samples generates an error signal, which is used to produce
`adaptive control signals for each of the adaptive loops. For filter coefficients control, a lea§t-mean square
`(LMS) algorithm is used [ 4]. LMS operates in the time domain to find filter coefficients that minimize the
`mean-squared errorbetween the samples and the desired response. Initial setting of the filter coefficients
`is accomplished by training the filter with an on-board training sequence, and the adaptation is continued
`while the chip is reading data. Adaptation can be in principle performed on all coefficients simultaneously
`at the lower clock rate or on one coefficient at a time. Since disk channel variations are slow relative to
`the data rate, the time-shared coefficient adaptation achieve; the same optimum filter response while
`consuming less power and taking up less chip area. Sometimes, to achieve better loop stability, not all filter
`coefficients are adapted during reading data. Also, before writing, data are scrambled to whiten the power
`spectral density and ensure proper adaptation filter adaptation.
`The FIR filter also compensates for the large amount of group-delay variation that may be caused
`by a low-pass filter with a nonlinear phase characteristic. Filters with nonlinear characteristics, such as a
`Butterworth filter, are preferred over, say, an equi-ri pp le design of the same circuit complexity, because they
`have much better roll-off characteristics. The number of FIR filter coefficients in practical read channels
`has been as low as 3 and as high as 10 with various tradeoffs associated with the different choices which
`can be made.
`
`15.4 Viterbi Detection
`In many communications systems a symbol by symbol detector is used to convert individual received
`samples at the output of the channel to corresponding detected bits. In today's PRML channels, a Viterbi
`detector is a maximum likelihood detector which converts an entire sequence of received equalized samples
`to a corresponding sequence of detected bits. Let y = (yn) be the sequence of received equalized samples
`corresponding to transmitted bit sequence x = (xn). Maximum likelihood sequence estimation maximizes
`the probability density p(y Ix) across all choices of transmitted sequence x [7]. In the absence of noise
`and mis-equalization, the relationship between the noiseless equalized samples, Zn and the corresponding
`transmitted bits is known by the Viterbi detector and is given by
`
`L
`
`Zn = ~ hk · Xn-k
`k=O
`
`(15.1)
`
`In the presence of noise and mis-equalization the received samples will deviate from the noiseless values.
`The Viterbi detector considers various bit sequences and efficiently compares the corresponding expected
`PR channel output values with those actually received. For Gaussian noise at the output of the equalizer
`and equally probable input bits, maximizing p(y Ix) is equivalent to choosing as the correct bit sequence
`the one closest in a (squared) Euclidean distance sense to the received samples. Therefore, we wish to
`
`
`Page 10 of 17
`
`

`

`Systems
`
`Read Channels for Hard Drives
`
`minimize
`
`l 2)
`~!11 ~ Yn - 8 hk · Xn-k
`P-1 [
`(
`
`L
`
`n. There(cid:173)
`tta can be
`
`-et during
`
`,ampling
`I channel
`tangesin
`T output
`produce
`n square
`mizethe
`fficients
`
`,e while
`all filter
`epower
`
`imizes
`f noise
`mdirtg
`
`'.15.1)
`
`alues.
`1ected
`alizer
`1ence
`.sh to
`
`15-5
`
`(15.2)
`
`The various components of Equation 15.3 are also known as branch metrics.
`The Viterbi detector accomplishes the minimization in an efficient manner using a trellis based search
`rather than an exhaustive search. The search is effectively performed over a finite window known as the
`decision delay or path memory length of the Viterbi detector. Increasing the window length beyond a
`certain value leads to only insignificant improvements of the bit detection reliability or bit error rate
`(BER).
`Despite the efficient nature of the Viterbi algorithm the complexity of a Viterbi detector increases
`exponentially with the channel memory of the PR target. A target with channel memory of L - 1 requires
`for example a zL-l state Viterbi detector trellis. For a fully parallel Viterbi implementation, each Viterbi
`state contains an add-compare-select (ACS) computational unit which is used to sum up the branch
`metrics of Equation 15.2 and keep the minimum metric paths for different bit sequences. Also required
`for the hardware is a zL-l • P bit memory to keep a history of potential bit sequences considered across
`the finite decision delay window.
`
`15.5 Timing Recovery
`A phase-locked loop (PLL) is used to regenerate a synchronous clock from the data stream. The PRML
`detector uses decision directed timirtg recovery typically with a digital loop filter. The digital loop filter
`parameters can be easily controlled using programmable registers and changed when a read channel
`switches from acquisition to tracking mode. Because significant pipelining is necessary irt the loop logic
`to operate at high speeds, the digital loop filter architecture exhibits a relatively large amount of latency.
`It can affect considerably the acquisition time when the timing loop must acquire significant phase and
`frequency offsets. To ensure that only small frequency offsets are present, the synchronizer VCO is phase(cid:173)
`locked to the synthesizer during nonread times. For fast irtitial adjustment of the samplirtg phase, a known
`preamble is recorded prior to user data. The time adjustment scheme is obtairted by applyirtg the stochastic
`gradient technique to minimize the mean squared difference between equalized samples and data signal
`
`ifg
`Frequency
`®-+ Integrator
`
`Phase
`Detector
`
`. :_,,
`
`Digital PLL
`
`Recovered
`Clock
`
`Synthesized
`Clock
`
`
`Page 11 of 17
`
`

`

`15-6
`
`Coding and Signal Processing for Magnetic Recording Systems
`
`estimates. To compensate for offset between the rate of the signal received and the frequency of the local
`timing source the loop filter design allows for a factor I':,. Tn to b~ introduced, so that the sample at discrete
`time n is taken T + I':,. Tn seconds after the sample at discrete time n -
`l. In acquisition mode, in order to
`quickly adjust the timing phase, large values for loop gains are chosen. In tracking mode, the loop gains
`are lowered to reduce loop bandwidth.
`
`15.6 Read Channel Servo Information Detection
`In an embedded servo system (introduced in the previous article), the radial position of the read head
`is estimated from two sequences recorded on servo wedges:· track addresses and servo-bursts. The track
`address provides a unique number for every track on a disk, while a servo-burst pattern is repeated on each
`track or on a group of tracks. Determining the head position using only the track number is not sufficient
`because the head has to be centered exactly on a given track. Therefore, the servo-burst waveform is used
`in conjunction with the track address to determine the head position. Using the servo-burst pattern, it is
`possible to determine the off-track position of a head with respect to a given track with a high resolution.
`While positioning the head over a surface, the disk drive can be in either seeking or tracking operation
`mode. In seeking mode, the head moves over multiple tracks, trying to reach the track with a desired
`address as quickly as possible, while in tracking mode, the head tries to maintain its position over a track.
`The track addresses are therefore used mostly in the seeking mode, while servo-burst information is usually
`used in the tracking mode [25, 30].
`In read channels periodic servo-burst waveforms are detected and used to estimate radial position. The
`radial position error signal is calculated based on the current estimated position and the position of the
`track to be followed, and then used in an external head positioning servo system. Generally two types
`of position estimators are in use: maximum likelihood estimators that are based on a matched filtering,
`and suboptimal estimators based on averaging the area or the peaks of the incoming periodic servo-burst
`waveform. A variety of techniques have been used to demodulate servo bursts including amplitude, phase
`and null servo detectors. Today, most read channels use an amplitude modulation with either peak or area
`detection demodulators.
`Older generation channels generally implemented the servo functions in analog circuitry. The analog
`circuitry of these servo channels partially duplicates functions present in the digital data channel. Now,
`several generations of read-channel chips have switched from analog to digital circuits and digital signal
`processing [8, 34]: These channels reduce duplication of circuits used for servo and data and provide a
`greater degree of flexibility and programmability in the servo functions.
`Typically a single analog to digital converter (ADC) or quantizer is used for both data detection and
`servo position error signal estimation [8, 20, 27, 34]. However, quantizer requirements are different in
`data and servo fields. Compared to position error signal estimators, data detectors require a quantizer
`with higher sampling clock rate. On the other hand position error signal estimators require_a quantizer
`with finer resolution. A typical disk drive has a data resolution requirement of around six bits, and a servo
`resolution requirement of around seven or eight bits. Furthermore, servo·bursts are periodic waveforms
`as opposed to data streams. In principle, both the lower sampling clock rate requirement in the servo field
`and the periodicity property of servo-burst signals can be exploited to increase the detector quantization
`resolution for position error signal estimation. The servo field is oversampled asynchronously to increase
`the effective quantizer resolution.
`Track densities in today's hard drives are higher than 25000 tracks per inch and, and the design of a
`tracking servo system is far from trivial. Some of the recent results include [2, 24, 25, 26, 31]. Increasing
`the drive level servo control loop bandwidth is extremely important. Typical bandwidth of a servo system
`is about 1.5 kHz, and is mainly limited by the parameters that are out of reach of a read channel designer,
`such as mechanical resonances of voice coil motor, arm holding a magnetic head, suspension, and other
`mechanical parameters.
`Another type of disturbance with mechanical origins, that has to be also detected and controlled in
`a read channel is repeatable runout (RRO) /n the position of the head with respect to the track center.
`
`I
`
`
`Page 12 of 17
`
`

`

`!ecording Systems
`
`Read Channels for Hard Drives
`
`15-7
`
`equency of the local
`1e sample at discrete
`,n mode, in order to
`10de, the loop gains
`
`m of the read head
`vo-bursts. The trackL
`1 is repeated on each
`1ber is not sufficient
`st waveform is used.
`J-burst pattern, it is
`h a high resolutio
`
`radial position."
`the position of
`;enerally two
`1 matched filte
`
`These periodic disturbances are inherent in any rotating machine, and can be as a result of an eccentricity
`of the track, offset of the track center with respect to the spindle center, bearing geometry and wear and
`rnotor geometry. The frequencies of the periodic disturbances are integer multiplies of the frequency of
`rotation of the disk, and if not compensated they can be a considerable source of tracking error. In essence
`the control system possesses an adaptive method to learn on-line the true geometry of the track being
`followed, and a mechanism of continuous-time adaptive runout cancellation [31].
`
`Precompensation
`
`Nonlinear bit shift in magnetic recording is the shift in position of a written transition due to the de(cid:173)
`magnetizing field from adjacent transitions. In a PRML channel, the readback waverofrn is synchronously
`.sampled at regular intervals, and the sample values depend on the position of written transitions. There(cid:173)
`ore nonlinear bit shift leads to error in sample values which, in turn, degrades the channel performance.
`e write precompensation is employed to counteract the nonlinear bit shift. However, determining the
`onlinear bit shift is not simple and straightforward especially when one tries to fine tune each drive for
`optimum precompensation. The precompensation circuit generates the write clock signal whose indi(cid:173)
`ual transition timing is delayed from its.nominal position by the required precompensation amount.
`e amount of precompensation and the bit patterns requiring precompensation can be found using
`extracted pulse shape [10, 18]. Another approach is a frequency-domain technique that offers simple
`_asurement procedure and a possible hardware implementation using a band-pass filter [32] or using
`L sample values [ 3 3].
`
`The Effect of Thermal Asperites
`lained earlier, if a head hits a dust particle, a long thermal asperity will occur, producing a severe
`· nt noise burst, loss of timing synchronization, or even off-track perturbation. Error events caused
`ermal asperities (TA) are much less frequent than random error events, but they exist and must be
`into account during read channel design. If there were no TA protection in the read channel, a
`flock in timing recovery system would occur, causing massive numbers of data errors well beyond
`or correction capability of any reasonable ECC system. Despite TA protection, the residual error
`t be completely eliminated, and many bits will be detected incorrectly. However, the read channel
`be designed to enable proper functioning of timing recovery in the presence of bogus samples.
`ly the read channel estimates the beginning and length of TA and sends this information to the
`· tern, which may be able to improve its correction capability using so-called erasure information.
`r, since the TA starting location is not lmown precisely, and the probability of random error in the
`tor is not negligible, the ECC system can misscorrect, which is more dangerous than not to detect
`
`Postprocessor
`
`e channel memory and noise coloration, maximum likelihood sequence detector (Viterbi de-
`roduces some error patterns more often than others. They are referred to as dominant error
`or error events, and can be obtained analytically or through experiments and/or simulation.
`equencies of error events strongly depend on a recording density.
`eek processors combine syndrome decoding and soft-decision decoding. Error eventlikelilioods
`soft decoding can be computed from a channel sequence by some kind of soft-output Viterbi
`By using a syndrome calculated for a received codeword, a list is created of all possible positions
`r events can occur, and then error event likelihoods are used to select the most likely position
`ly type of the error event. Decoding is completed by finding the error event position and type.
`can make two type of errors: it fails to correct if the syndrome is zero, or it makes a wrong
`
`
`Page 13 of 17
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`15-8
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`Coding and Signal Processing for Magnetic Recording Systems
`
`correction if the syndrome is nonzero but the most likely error event or combination of error events do
`not produce right syn