Nonlinear Transition Shift Research Articles

Pattern constraints limiting nonlinear transition shift in high density magnetic recording

Nonlinear transition shift (NLTS) produced by the interaction between transitions is a major source of distortions in magnetic recording. NLTS must be reduced to realize higher density and maintain signal quality. However, there is some confusion about the production and behavior of NLTS in previous reports. In this paper, combined with micromagnetic simulation, we have developed a complete theoretical model to predict NLTS on perpendicular magnetic media. The results show that one-level NLTS (caused by one previous transition) will monotonically decrease as the present transition becomes further away from the previous one, and multilevel NLTS (caused by consecutive previous transitions) will firstly increase and quickly approach a constant value as there are more consecutive transitions. Particularly, it is demonstrated that NLTS and its impact on the media signal-to-noise ratio can be significantly limited by pattern constraints.

A Graded Precompensation Scheme by Pattern Classification on Nonlinear Transition Shift for Perpendicular Magnetic Recording

To achieve higher magnetic recording areal densities, signal distortions caused by the crosstalk among consecutive magnetized transitions that lead to nonlinear transition shifts (NLTS) must be eliminated. We calculated and sorted the transition shifts of different recorded patterns and classified corresponding patterns based on an analytical method. We proposed a graded write precompensation scheme according to the classified patterns and compared the detecting performance of a perpendicular magnetic recording system using the graded compensation and traditional pattern-aware compensation during the writing process. Simulation results show our proposed graded precompensation can effectively mitigate the nonlinear distortion effect caused by NLTS and outperforms the traditional pattern-aware compensation method. The detecting BER decreases by 14.7% when the SNR of electronic noise is only 20 dB and the bit length is 10nm.

Optimal Neuro-Fuzzy Equalizers for Detecting Nonlinear Distortion Channels of the Perpendicular Magnetic Recording System

Nonlinear distortions caused by partial erasure and nonlinear transition shifts interacting with inter-symbol interference, are a major hindrance to data storage systems, since they degrade detector performance. This work aims to design and optimize the neuro-fuzzy equalizer (NFE) using the multi-objective genetic algorithm (MOGA) to detect nonlinear high-density magnetic recording (MR) channels. Through the GA-assisted back-propagation algorithm and least mean square optimization, the complexity in terms of decision rules is reduced by 25% and significantly provides 65% lower signal processing computation. When applied to the perpendicular (MR) system, the proposed NFE outperforms existing equalizers such as the neural network-based equalizer, fuzzy logic equalizer, and conventional NFE for the Volterra and jitter media noise channels using 1–3 dB and 1.5–3.5 dB signal-to-noise ratio gains at the bit-error-rate of 10-4, respectively. Furthermore, compared to the other models, the NFE provides a more effective output mean square error performance for retrieving the original bit data.

Micromagnetics-Based Analysis of Multi-Track Detection With Simplified 2-D Write Precompensation on Shingled Magnetic Recording

In shingled magnetic recording systems, a shingled writer is used to write narrow tracks by overlapping the previous tracks, which also leads to severe inter-track interference, jitter, and nonlinear transition shift (NLTS) in the cross-track direction. To deal with these challenges, we propose a simplified 2-D write precompensation (WPC) scheme that adjusts the write current magnitude instead of the timing, to mitigate the 2-D NLTS in the writing process. In the proposed WPC scheme, the WPC is only implemented for the few specific patterns that seem to cause large media noise mean and variance. During the training period, the optimum write field for current transition being written is obtained by subtracting demagnetizing field from the previous neighboring bits in the current and nearest previous tracks from a fixed write field, and the optimum writing current is determined by minimizing the mean-squared error between the needed field and the available fields within a writer field library. Then, the specific bits producing the dominant demagnetizing field and the obtained optimum writing current are stored in a lookup table during the training period. During the writing process, we can obtain the optimum writing current by matching the specific previous written bits against the bit patterns in the lookup table, avoiding the need for computing the demagnetizing field and optimum writing current for every written bit. Here, two simplified WPC schemes are investigated corresponding to precompensating two sets of data patterns. For readback, a joint pattern-dependent noise-predictive (PDNP) detector is investigated to further whiten the 2-D media noise. Simulations indicate that at the target bit error rate of $10^{-2}$ , the proposed simplified WPC schemes combined with the joint PDNP detector can provide the density gains of as high as 22% compared with the system without WPC and detected with a joint Bahl–Cocke–Jelinek–Raviv detector.

2-D Data-Dependent Media Noise in Shingled Magnetic Recording

This paper investigates 2-D media noise in shingled magnetic recording (SMR) systems. The media noises caused by the overwriting of the next track and the residual information from the previous track are asymmetric in the cross-track (CT) direction and are found to vary with the linear density. The media noise after equalization is found to be 2-D data dependent, with its mean and variance affected by the nonlinear transition shift in the CT and down-track directions, respectively. Also the effect of media noise on the bit error rate (BER) is studied for increased track densities during the writing process. The effect of jitter on the BER is always significant with increased track density in SMR systems, while the effect of overwriting and inter-track interference on the BER performance are quite different for readback with rotated and normally oriented readers, even though the same writer is used during the writing process.

Signal Processing for Dedicated Servo Recording System

Perpendicular magnetic recording (PMR) in the hard disk drive is approaching its physical limits. In an earlier work, the dedicated servo (DS) recording system has been proposed to provide continuous position error signal for servo, enable higher servo sampling rate, and improve the overall servo performance. A further benefit is that the DS layer results in surface area savings at the data layer. However, it was also reported that the embedded servo layer introduces baseline variation and non-linear transition shift (NLTS) to the readback signal of the data layer. In this paper, we propose novel signal processing techniques to improve the bit error rate (BER) in DS recording. The synchronous averaging technique is proposed to improve the BER in the presence of baseline variation distortions. Further, the servo and data-dependent noise prediction method is proposed to mitigate the effect of the NLTS. Through the use of these techniques the linear density loss from the conventional PMR media is reduced.

Two-Dimensional Magnetic Recording With a Novel Write Precompensation Scheme for 2-D Nonlinear Transition Shift

This paper proposes a novel write precompensation scheme that adjusts the current magnitude, not the timing, to mitigate the serious 2-D nonlinear transition shift (NLTS) during the shingled writing process in a two-dimensional magnetic recording (TDMR) system. This scheme calculates the needed optimum write field for the current transition being written by subtracting the demagnetizing field produced by the previous written bits from a fixed write field and determines the optimum writing current based on the minimum mean-squared-error criterion between the needed field and the available fields within an established field library. Such a write precompensation scheme is tested with a micromagnetic writer and exchange coupled composite media, and readback with a rotated reader array combined with a read channel. Simulation indicates that the proposed write precompensation technique can decrease bit error rate compared with the case without write precompensation and approach the performance of a system with negligible NLTS. Correspondingly, the maximum user areal density is increased from 3.2 to 4.1 Tbits/in $^{\mathrm {\mathbf {2}}}$ for a TDMR system with 8 nm Voronoi grains due to the proposed write precompensation.

Reduced-Nonlinear Effect on Magnetic Recording Channels Using MMSE Equalizers

This paper considers the nonlinear effect on magnetic recording channels in order to reduce the system distortion. In this work, we propose the designed MMSE equalizer and target for a high density perpendicular magnetic recording to combat the nonlinear transition shift (NLTS) in a channel characterized by jitter noise and additive white Gaussian noise (AWGN). Due to a complex nature of nonlinear effects, the nonlinearity of a read-back signal is designed by the second order Volterra model consisting of linear and nonlinear part. The bit-error rate (BER) of the nonlinear-affected system using the designed MMSE equalizer is significantly decreased. The results show that the proposed minimum mean square error (MMSE) equalizer with constraint can decrease the inter-symbol interference (ISI) that causes nonlinearity and also improve performance.

Nonlinear Transition Shift in Heat Assisted Magnetic Recording

To achieve high linear densities in magnetic recording noise as well as distortions must be reduced. A significant source of distortions is the interaction between consecutive magnetic transitions that produces a nonlinear transition shift (NLTS). Using a heat assisted magnetic recording system we measured the dibit response for pseudo-random bit sequences. We find that the sign of the echo corresponding to first order NLTS is inversed with respect to conventional perpendicular magnetic recording. A simple physical explanation is given for this experimental finding.

A Study of Nonlinear Partial Erasure Versus Frequency and Side Track Erasure in a Modern Perpendicular Magnetic Recording System

The following study examines nonlinear signal losses in a perpendicular magnetic recording (PMR) system using tunneling magneto-resistive heads (TuMR) and exchange coupled multi-layered media capable of operating at recording density greater than 400 GB/in2. This study differs from previous total nonlinear distortion (TNLD) and nonlinear transition shift (NLTS) studies in that it focuses on nonlinear partial erasure (NLPE) using constant tones. Constant-tone NLPE is often considered negligible compared to pattern-dependent NLTS, but this study shows this is not the case at high linear densities. This study will further show that NLPE behavior at low linear density appears similar when using high density writes combined with track edge trimming. This novel finding suggests on-track NLPE and cross-track data width may simply be different aspects of track edge curvature and/or percolation.

Linearity for Superposed Waveforms between Adjacent Tracks in Shingled Writing

In shingled writing, cross-talk noise from an adjacent track occurs when a rather wide track read-head is used, which causes inter-track-interference (ITI). A compensation method has been proposed. However, the linearity of the superposed response from the tracks should be examined for such signal processing. Experimental studies on the superposition of readback waveforms and nonlinearity caused by overwriting of adjacent tracks were carried out. The superposition of the readback waveform was almost precisely maintained. The off-track overwrite performance showed a large track edge over-write noise. Overwrite noise caused by a nonlinear transition shift was also observed.

Analysis of Nonlinear Transition Shift and Write Precompensation in Perpendicular Recording Systems

In high density perpendicular magnetic recording channels, nonlinear transition shift (NLTS) is one of the distortions that can degrade the system performance. Write precompensation is a standard method used to combat the negative effect of NLTS. In this paper, we present an analysis of the bit-error-rate (BER) for perpendicular recording systems with NLTS and write precompensation. Media jitter noise and additive white Gaussian noise are also considered in the model. A BER lower bound is derived, as well as a more easily computed estimate of the bound. The write precompensation values that numerically minimize the estimate of the BER lower bound prove to be very close to those found using Monte-Carlo channel simulation. We then apply these methods to the design of multilevel precompensation schemes, for which the optimization of precompensation values by Monte-Carlo channel simulation is computationally infeasible. The results show that for higher recording densities subject to increased ISI and noise, the use of more complex precompensation schemes does not significantly improve the system performance.

Effect of Head Field Gradient on Nonlinear Transition Shift in Perpendicular Recording

A modified test of the fifth harmonic measurement for nonlinear transition shift (NLTS) is used to study the influence of the head field properties on some parametric data and signal-to-noise ratio (SNR) performances in perpendicular recording. Particularly, the NLTS properties of two different writer head designs were evaluated in connection with their recording performances. It was revealed that the NLTS properties are sensitive to both the head field strength and head field gradient and thus affect the SNR and bit error rate (BER) performances strongly, especially at high linear density.

Micromagnetic Study of Medium Noise Plateau

Medium noise characteristics and transition jitter in perpendicular magnetic recording are explored using micromagnetic simulation. A noise plateau for intermediate recording densities is observed for a recording layer of typical magnetization. The plateau is replaced by a normal linear dependence of noise on recording density for a low magnetization recording layer. We show analytically that a source of the plateau is similar to that producing the non-linear transition shift of signal. In particular, magnetostatic effects are predicted to produce positive correlation of jitter and thus negative correlation of noise at the densities associated with the plateau.

Micromagnetic Study of Short and Long Yoke PMR Head With Trailing Shield

The response of a trailing shielded perpendicular magnetic recording (PMR) write head with a three-turn two-layer coils is calculated using a full micromagnetic large scale model including return pole and soft underlayer. We study the effect of PMR yoke length and write current overshoot on the dynamic response of the head at high frequency. In particular, recording performance parameter, nonlinear transition shift (NLTS) is simulated using micromagnetic media model. Shorter yoke length head improves NLTS as compared with longer yoke length. Measured NLTS has qualitative agreement with micromagnetic model results.

Mean-Adjusted Pattern-Dependent Noise Prediction for Perpendicular Recording Channels With Nonlinear Transition Shift

In high-density perpendicular magnetic recording channels, nonlinear transition shift (NLTS) is one of the distortions that can degrade the system performance. Write precompensation is a standard method used to combat the negative effect of NLTS. In this paper, we propose a modified pattern-dependent noise predictive (PDNP) detection algorithm for use on channels with electronics noise, transition jitter noise, and NLTS. We show that this detector can offer significant improvement in bit-error-rate (BER) compared to conventional Viterbi and PDNP detectors. Moreover, the system performance can be further improved by combining the new detector with a simple write precompensation scheme.

Dependence of error patterns and BER performance on write pre-compensation in GPRML channels

Nonlinear transition shift (NLTS) influences the performance of PRML channels in perpendicular magnetic recording. For NLTS, it is thought that write pre-compensation is useful to write the transition at the intended position. In this paper, we study the influence of NLTS on the BER performance of GPRML channels and show the appropriate amount of pre-compensation for GPRML channels both with and without a post-processor (PP) to achieve better BER performance. The results show that the widening the shortest bit length by NLTS brings the BER improvement to GPRML channel and the write pre-compensation is useful for a GPRML channel with PP.

Characterization of transition shifts in perpendicular magnetic recording using 3D FEM

Transition shift can create serious timing problems for high density recording environments. However, it is possible to use techniques such as write precompensation to offset the timing error introduced if the magnitude and the behaviour of the transition shift are properly understood. This paper introduces a 3D finite element method (FEM) to analyse the transition shift in perpendicular magnetic recording (PMR) quantitatively, allowing the combinational effects of the transition shifts from non-linear transition shift (NLTS), HTS, and neighbourhood-induced transition shift (NITS) to be examined. The consideration of all contributing factors to the final written transition position is important in determining the precompensation scheme of magnetic data recording, and 3D FEM can facilitate such quantitative analysis.

Analytical Method for Perpendicular Recording Field Calculation to Examine Nonlinear Transition Shift

This paper presents a theoretical study of nonlinear transition shift (NLTS) in perpendicular recording process. The study is carried out using numerical simulations, and an analytical method is introduced in this paper. In analyses of the effect of recorded transitions, the demagnetization field due to written patterns on the recording medium is taken into consideration in the field solution for a write head with shield poles. The influence of the gap length between the shield and the pole-tip is also studied using the new analytical model

Evaluation of Low-Density Parity-Check Codes on Perpendicular Magnetic Recording Model

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Low-density parity-check (LDPC) codes have shown superior error-correcting performance in a variety of data storage system studies, including traditional longitudinal magnetic recording systems. However, perpendicular magnetic recording systems (of increasing interest) exhibit impairments different from longitudinal magnetic recording systems, and thus present new challenges for error-correcting codes. In this effort, we evaluate a structured LDPC code using a perpendicular magnetic recording channel model that includes impairments such as transition noise, nonlinear transition shift, transition percolation, and baseline wander (BLW). The channel model, as well as the LDPC encoder and the decoder are implemented in field-programmable gate array (FPGA) hardware. The LDPC coded system is evaluated down to bit error rate (BER) of 10<formula formulatype="inline"> <tex>$^{-12}$</tex></formula> and frame error rate (FER) of 10<formula formulatype="inline"> <tex>$^{-8}$</tex></formula>. The impact of individual impairments on coding performance is studied separately. The soft output Viterbi algorithm (SOVA) <formula formulatype="inline"><tex>$+$</tex></formula> LDPC system maintains its superior error-correcting performance under the perpendicular recording channel. </para>