High-density Magnetic Recording Channels Research Articles

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.

Optimization and implementation of an equalized maximum likelihood receiver for a simple partial erasure model

In a high-density magnetic recording channel, nonlinear effects such as transition shift and partial erasure arise, and these effects limit the detector performance. The transition shift can be precompensated by using an appropriate write current; however, partial erasure still degrades the detector performance. To mitigate this problem, the partial response maximum likelihood (PRML) receiver with a specific target response is widely used; it has acceptable performance for a reasonable realization complexity. Furthermore, the equalized maximum likelihood (EML) receiver is proposed, and its performance is improved because of the optimized target response. However, the conventional design for optimization often ignores nonlinear effects or minimizes the cost function in the sense of least-squared error because of lacking a closed-form expressions of the correlation functions. Herein, we apply the closed-form correlation functions for a simple partial erasure model (SPEM) to jointly optimize the coefficients of the partial equalizer and the target response to minimize the mean squared error (MSE) between the outputs of the partial equalizer and the target response. The corresponding Viterbi decoder (VD) with a nonlinear trellis diagram is realized. Computer simulations indicate that the EML receiver yields a smaller bit error rate (BER); in fact, it outperforms the conventional PRML receiver by around 1.5 dB when the BER is lower than 10 − 4 .

Evaluation of correlation functions and design of minimum mean squared error equaliser for a high-density magnetic recording channel with partial erasure effect

In a high-density magnetic recording channel, non-linear effects such as transition shift and partial erasure arise, and these effects limit detector performance. The transition shift can be precompensated by using an appropriate write current; however, partial erasure still degrades detector performance. In this study, the authors obtained the correlation functions of the stored data in the presence of partial erasure under the assumption that the transition shift has been precompensated. The correlation functions are applied in designing a minimum mean squared error equaliser for both the linear partial response and the non-linear partial response, and the corresponding partial response maximum likelihood (PRML) sequence detector, realised by the Viterbi decoder, is also examined. Computer simulations indicate that the mean squared error of the proposed equaliser can be improved and the bit error rate of the PRML sequence detector is also reduced as compared with the conventional one in the presence of partial erasure.

Closed-form timing function for a high-density magnetic recording channel with partial erasure effect

Abstract As magnetic recording densities grow, the nonlinear distortions, known as transition shift and partial erasure, arise and limit the performance of the detector. In this article, the closed-form timing function of the Muller and Mueller’s phase detector is derived in the presence of the partial erasure under the assumption that the transition shift has been precompensated. The derived timing function is a weighted combination of two odd functions. One of these two functions is identical to that of a magnetic recording channel in the absence of the nonlinear distortions, and the other is itself a suitable candidate for a timing function. In addition, the weighting coefficients are functions of the reduction parameters. The timing function in the presence of the partial erasure is thus a suitable timing function. The timing functions for both the partial response class IV (PR4) and the extended partial response class IV (EPR4) are explicitly derived, and computer simulations are given to verify the derived results. The closed-form timing function for the nonlinear magnetic recording channel is obtained and discussed; in summary, the slope of the timing function at the origin roughly decreases as the partial erasure effect is prominent.

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.

Maximum a Posteriori Estimation Using the EM Algorithm for Linear Codes With Low-Density Generator Matrix in Magnetic Recording Systems

In high-density digital magnetic recording channels, magnetic recording systems are influenced by media noise. It is known that jitter noise is one of the principal sources of the media noise and depends on recording signal patterns. For such a jitter-noise dominant recording channel with continuous erasures, maximum a posteriori (MAP) decoding is hard to minimize the error rate performance of signal processing systems. To improve MAP decoding performance, sequence estimation using the expectation maximization (EM) algorithm is introduced to identify each distribution of the jitter noise in the normal mixture model and estimates the missing sequences which are caused by continuous erasures

Optimal detection for perpendicular recording channels with transition noise

This paper proposes a jitter-sensitive-sequence-detection scheme based on a realistic transition noise model for high-density perpendicular magnetic recording channels. In this scheme, the transition jitter is assumed to have one of the Q discrete values, and the discretized jitter sequence is estimated jointly with the recorded bit sequence using maximum a posteriori criterion. The detection performance is compared with that of the pattern dependent noise predictive scheme based on an autoregressive Gaussian noise model. Simulation results show that the scheme provides a significant gain when the transition jitter is large and the resulting transition noise dominates over the electronic noise.

Detection techniques for high-density magnetic recording

In this paper, we present techniques for improving the performance of Viterbi detector in the presence of channel nonlinearities and media noise, which are the dominant source of errors in high density magnetic recording channels. Instead of treating these distortions separately, we combine them into a "high-density (HD) noise", which is signal dependent and correlated in nature. To compensate for signal-dependent mean and correlation of HD noise, we modify the branch metrics by subtracting an estimate of the mean from the signals on each branch and optimize the equalization target by minimizing the dominant error event probability, respectively. Simulation results show that these modifications yield significant performance gains.

Hybrid equalized partial response path-feedback maximum likelihood toward higher density Blu-ray disc

Recently, high density optical recording systems like BD (Blu-ray disc) have been standardized regarding a PRML (partial response maximum likelihood) signal processing technology, which has been thoroughly investigated on high density magnetic recording channels for many years. In order to gain a margin of optical disc drives, PFML (path-feedback maximum likelihood), which is also known as adaptive Viterbi, has been also developed in recent years. In this paper, we propose a new signal processing system, which equalizes the waveform causally, enhances the performance of the PFML detector and provides a stable PLL (phase locked loop) towards much higher density formats than standard BDs.

A PRML with modified branches of a dual MTR code for high-density PMR channels

Maximum transition run (MTR, j) code is a modulation code that limits the consecutive transitions. We present a dual MTR code that can be applicable to high-density perpendicular magnetic recording (PMR) channels. The code restricts j=2 in each codeword and allows j=3 when codewords are connected. Furthermore, to improve the detection performance of the PMR systems, we propose a partial response maximum likelihood (PRML) detection scheme with modified branches of the Viterbi trellis for the code. The PRML detection of the dual MTR code achieves an SNR gain of more than 2 and 0.3dB over the conventional fourth-order PRML detections with rate 8/9 code and rate 6/7 MTR (j=2) code at 10−5 bit error rate (BER) in the PMR channel model, respectively.

An extended dual decision-feedback equalizer for high-density perpendicular magnetic recording channels

Partial-response maximum-likelihood (PRML) systems are powerful and indispensable for high-density perpendicular magnetic recording channels. However, high-order partial-response (PR) targets must be considered because of severe intersymbol interference (ISI). On the other hand, decision feedback equalization (DFE) has very low complexity. DFE can be used with high code rate modulation codes, thanks to the fact that DFE does not use a minimum run constraint as a multilevel DFE (MDFE). At high recording densities, dual detection schemes such as dual DFE (DDFE) significantly improve performance and reduce error propagation. So, we compare DDFE detectors with PR(1221)ML and PR(12321)ML on 16/17 maximum transition run (MTR) (3,11)-coded perpendicular magnetic recording channels and propose an extended DDFE that represents a dual version of the DDFE. Simulation results show that the DDFE has a bit-error-rate (BER) performance comparable to that for PR(12321)ML. Our extended DDFE in turn shows a performance gain over DDFE and PR(12321)ML at the normalized recording densities 3 and 4.

Pattern‐discrimination method for error correction of 16/17 MTR code on a high‐density magnetic recording channel

AbstractA pattern discrimination method for error correction of 16/17 MTR code is described for a high‐density magnetic recording channel. It is based on the characteristics of bit‐error patterns of the 16/17 MTR code, where frequent bit errors are restricted to several patterns. The difference between a playback signal and an estimated signal is compared to the waveform patterns caused by the frequent error events. When the difference in the patterns is close to the error waveform, a corresponding decoding error is thought to have occurred and this error is corrected. Simulation results showed that the use of this method improves performance by about 1.2 dB at a user recording density (iDU) of 3. © 2001 Scripta Technica, Electron Comm Jpn Pt 2, 84(6): 60–68, 2001

Iterative MAP detection using interleaved EPR4 equalizer for magnetic recording

In this paper, we propose an iterative MAP detection method using two interleaved EPR4 linear equalizer outputs for high-density magnetic recording channels. The iterative detection is performed using two EPR4 MAP decoders that are separated by an interleaver. Simulation results show that the proposed method outperforms the conventional EPR4ML detection 7 dB when the density is S=2.5. When S=3.0, the difference in performance is more evident.

Iterative decoding for partial response (PR), equalized, magneto-optical (MO) data storage channels

Turbo codes and low-density parity check (LDPC) codes with iterative decoding have received significant research attention because of their remarkable near-capacity performance for additive white Gaussian noise (AWGN) channels. Previously, turbo code and LDPC code variants are being investigated as potential candidates for high-density magnetic recording channels suffering from low signal-to-noise ratios (SNR). We address the application of turbo codes and LDPC codes to magneto-optical (MO) recording channels. Our results focus on a variety of practical MO storage channel aspects, including storage density, partial response targets, the type of precoder used, and mark edge jitter. Instead of focusing just on bit error rates (BER), we also study the block error statistics. Our results for MO storage channels indicate that turbo codes of rate 16/17 can achieve coding gains of 3-5 dB over partial response maximum likelihood (PRML) methods for a 10/sup -4/ target BER. Simulations also show that the performance of LDPC codes for MO channels is comparable to that of turbo codes, while requiring less computational complexity. Both LDPC codes and turbo codes with iterative decoding are seen to be robust to mark edge jitter.

A decision-feedback equalizer with pattern-dependent feedback for magnetic recording channels

A new nonlinear equalizer for high-density magnetic recording channels is presented. It has a structure of the decision-feedback equalizer (DFE) with a nonlinear model at the feedback section and a dynamic threshold detector. The feedback nonlinear model is a sequence of look-up tables (LUTs) indexed by time, and each table is addressed by a transition pattern formed by one future and /spl nu/ past transitions. We call this new nonlinear equalizer the pattern-dependent DFE (PDFE). The feedback nonlinear model cancels the trailing nonlinear intersymbol interference (ISI), and then the data decision is made by considering the precursor nonlinear ISI caused by one future symbol. We propose a tap optimization criterion SNR/sub d/ for the PDFE which in effect tries to maximize the output signal to noise ratio, and derive a closed-form solution for the tap values. We compare the detection performance of PDFE with that of the DFE and the RAM-DFE on experimental channels. The RAM-DFE is a DFE with one large LUT at its feedback section. The results show that the PDFE yields a significant performance improvement over the DFE and the RAM-DFE. Also the PDFE derived in this paper achieves a superior performance compared with the PDFE derived by the minimum mean-square-error criterion.

Reduced complexity maximum likelihood sequence estimation for multitrack high-density magnetic recording channels

In this paper we investigate the problem of designing reduced complexity detectors for multitrack high-density magnetic recording systems. The detectors derived in this work operate on superstate sets and carry several survivors for each set. We show that such a reduced state increased survivor approach provides near optimal performance to the maximum likelihood method, namely the Viterbi Algorithm (VA), but operate at a fractional complexity of the VA.

Noise-predictive maximum-likelihood method combined with infinite impulse response equalization

An infinite impulse response (IIR) can closely approximate the high density magnetic recording channel response with only a single pole and a small number of zeros. As a consequence, a near-optimal performance can be achieved with the Viterbi algorithm (VA) incorporating a single-tap noise predictor. The number of states in the VA trellis is determined by the number of zeros used in the IIR modeling of the channel response. The single noise-predictor tap corresponds to the single pole in the IIR model. The overall complexity for a given level of performance is smaller with this approach than with the noise-predictive maximum-likelihood (NPML) method based on conventional partial response equalization.

A new target response with parity coding for high density magnetic recording channels

In this paper, a modified equalization target is proposed for the high density magnetic recording channel. This target is a closer match to the channel than the EEPR4 response and hence has better detection performance. Based on the dominant error events for this target, a parity-based coding scheme is also proposed to achieve a coding gain with the modified target. The use of the parity code detects the occurrence of the dominant error events while achieving a high code rate. The detection system consists of a Viterbi detector matched to the channel response and a post processor to handle the code constraints. This system is shown to perform well compared to other proposed detection systems through analysis and simulation on a Lorentzian based channel model.

A new nonlinear multi-filter detection concept for the high density magnetic recording channel

In this work, a new approach to detection in high density magnetic recording is presented. The basic detector structure is a bank of parallel sub-detectors which are specialized in different channel states. The individual adaptation of the sub-detectors to the channel properties is done by a learning algorithm so that no explicit channel model is required. On both simulated and experimental data it is shown that the proposed detection scheme has excellent performance in the presence of strong nonlinear distortion and signal dependent noise. At user densities of 3.5 and 4.0 using RLL(1,7) encoding the new scheme outperforms multi-level decision feedback equalization (MDFE) detection by a factor of up to 500 in error rate. The structure is well suited for hardware implementation.

An estimation technique for nonlinear distortion in high-density magnetic recording channels

Nonlinear distortions, which limit detector performance at high recording densities, are known as the nonlinear transition shift and partial erasure. The nonlinear transition shift is known to be reduced substantially by the precompensation technique, while the partial erasure requires sophisticated nonlinear equalization techniques. In this paper, a new calculation intensive adaptive technique is presented that uses stochastic gradient method to minimize the mean squared error between actual playback signal samples and modeled signal samples. The effectiveness of the proposed adaptive approach to separately estimate these two nonlinear parameters uniquely is demonstrated by computer simulation.