Digital Magnetic Recording Channel Research Articles

Use of raised cosine interpolator filter for timing recovery

In this article the interpolation filter using truncated raised cosine pulse for timing recovery is investigated. The results reveal that with similar computational complexity, the raised cosine interpolator is superior to other interpolators such as the sinc, polynomial, and MMSE interpolators. The superiority of the raised cosine interpolator is also demonstrated on digital magnetic recording channel. Simulation results show that the raised cosine interpolator is superior in error performance to other interpolators. The main advantage of raised cosine interpolator is that it is potentially simpler and can lead to a fully digital implementation.

Raised Cosine Interpolator Filter for Digital Magnetic Recording Channel

Interpolators have found widespread applications in communication systems such as multimedia. In this paper, the interpolated timing recovery employing raised cosine pulse for digital magnetic recording channel is investigated. This study indicates that the raised cosine interpolator with rolloff factor β between 0.4 and 0.6 is shown to have less aliasing effect and achieve better MSE performance than other interpolators such as the sinc, polynomial, and MMSE interpolators with similar computational complexity. The superiority of the raised cosine interpolator over other interpolators is also demonstrated on the ME2PRIV recording channel through computer simulations. The main advantage of the raised cosine interpolator is that it is potentially simpler and can be fully digitally implemented.

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

Offset invariance in maximum-likelihood decoding for a class of partial response channels

In this letter we show that for a class of partial response channels with discrete-time pulse response of the form (1-D)P(D) whose output samples are corrupted by independent samples of additive white Gaussian noise with mean m, a maximum likelihood sequence detector designed for the case of m=0 is also the maximum likelihood sequence detector for an arbitrary value of m. The studied class of partial response channels is widely used for the characterization of digital magnetic recording channels where the DC offset is frequently an issue.

A quadratic sigmoid neural equalizer for nonlinear digital magnetic recording channels

A new neural equalizer is proposed in order to compensate for intersymbol interference and to mitigate nonlinear distortions in digital magnetic recording systems. The proposed equalizer uses the quadratic sigmoid function as the activation function. The performance of the proposed equalizer is compared to those of a decision-feedback equalizer (DFE) and a neural decision feedback equalizer (NDFE) in terms of bit-error rate in nonlinear digital magnetic recording channels. Simulation results demonstrate that the proposed equalizer outperforms both DFE and NDFE.

Noise-predictive maximum likelihood (NPML) detection

Sequence detectors for the digital magnetic recording channel that are based on noise-predictive partial-response equalization are described. Called Noise-Predictive Maximum Likelihood (NPML) detectors, they arise by imbedding a noise prediction/whitening process into the branch metric computation of a Viterbi detector. NPML detectors can be realized in a form that allows RAM table look-up implementation of the imbedded feedback. Alternatively, the noise prediction/whitening mechanism can be implemented as an infinite impulse response (IIR) filter. For a Lorentzian channel with operating points in the range 0.5<PW50/T<3.5, IIR predictors with at most two zeros and two poles offer the best possible performance. Simulation results obtained for Lorentzian channels show that a judicious tradeoff between performance and state complexity leads to practical schemes offering substantial performance gains over both PRML and extended PRML detectors. An important practical advantage of the family of NPML detectors is that they can be conveniently integrated into existing PRML architectures.

Model order reduction for optimal bounding ellipsoid channel models

This paper presents a new algorithm for performing model order reduction for Volterra series channel models of high-density digital magnetic recording channels. We employ a set-membership approach to the problem in which a set of consistent modeling solutions bounded by an optimal ellipsoid is first developed for the channel. We then present a new algorithm for finding the minimum number of coefficients in the Volterra series expansion which preserves the accuracy, in a least-squares sense, of the reduced order model in comparison with the original model.

Decision feedback equalizer with pattern dependent dynamic threshold

A new detector based on a practical nonlinear model for digital magnetic recording channels is described. The nonlinear model is easy to construct from simple measurements of the isolated transition response and dipulse responses. The new detector has a structure similar to that of the decision feedback equalizer (DFE) except that an add-on nonlinear canceller is used to cancel the trailing nonlinear intersymbol interference (ISI), and a pattern dependent dynamic threshold is employed to handle the precursor nonlinear ISI. We compare the detection performance of this new detector, which we call DFE with dynamic threshold (DFE-DT), to that of the DFE and the DFE with a trailing nonlinear canceller only (DFE-NC) on several experimental channels. The results show that the DFE-DT yields significant performance improvement over the DFE and the DFE-NC as measured by the detection signal-to-noise ratio (SNR).

Improving performance of PRML/EPRML through noise prediction

Sequence estimation detectors for the digital magnetic recording channel based on noise-predictive partial-response equalization are described. Called noise-predictive maximum-likelihood (NPML) detectors, they imbed a noise prediction/whitening process into the branch metric computation of a Viterbi detector. Simulation results show that a judicious tradeoff between system parameters leads to substantial performance gains over both PRML and EPRML systems. A programmable 8-state NPML detector without decision feedback is presented.

Comparison of different detection techniques for digital magnetic recording channels

A methodology for comparing different detection schemes for digital magnetic recording channels is presented. This methodology builds on previous work to improve the estimates of the bit error rates and to expand the scope of the results presented. The authors compare PRML/VA, DFE, and FDTS/DF detectors under different circumstances.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Methods for characterizing the replay pulse asymmetry for a digital magnetic recording channel

Two methods are examined for characterizing the asymmetric replay pulse from the digital magnetic recording channel. A time domain method based on the Taylor series expansion of a mixed longitudinal/perpendicular pulse model is used to obtain simple relationships between the replay pulse asymmetry and model parameters. A frequency domain method based on modelling the channel phase is used to characterize a simple longitudinal pulse model with linear displacement of the transition through the recording depth.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Effect of Non-Linear MR Read-back Distortion on a PRML Channel

The effect of the nonlinear readback process of an MR head on a PRML digital magnetic recording channel was studied. Although the combination of a highly sensitive MR read head and a PRML channel is promising for high areal-density recording, nonlinearity in the MR readback process is a critical issue in the case of a channel in which linearity is assumed. We theoretically analyzed the characteristics of SHD (second harmonic distortion) as an index of the nonlinearity. Then, the effect of nonlinearity on the error rate was studied by computer simulation and in experiments. The results show that an SHD of less than -25 dB is required in order for the channel to be free of nonlinear distortion.

Source-channel coding of analog data for digital magnetic recording

It is hypothesized that more data can be stored by increasing the density with which bits are placed on the media and using source-channel coding to both compress the data and protect it from the resulting increased bit error rate. This paper estimates the gains achievable with this approach. Central to this work is a model for the digital magnetic recording channel that contains a linear filter representing the Lorentzian step response and additive Gaussian processes representing electronic and media noises. The model differs from previous ones in that lineal bit density, as well as track density, are parameters that may be varied. Parameters for this model that typify disk storage systems are identified and the gains in data density for the proposed approach are estimated in two ways: by estimating the capacity of the channel model and by simulating a family of source-channel codes. From capacity bounds developed in a companion paper, it is estimated that data density may ultimately be increased by a factor of 20 or more. To assess the gains achievable with a practical system, a tree-structured family of source-channel codes is proposed and analyzed. It is found that these are much simpler than optimal unstructured source-channel codes, yet have comparable performance. By simulating them on a Gaussian source and the given channel model, it is estimated that gains on the order of 3 to 4 in data density are achievable with peak detection demodulation and gains of 2 to 3 are achievable with 1-D/sup 2/ partial response maximum likelihood demodulation, each with moderate increases in bit density. Comparable gains are anticipated for speech and images.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Partial response equalizer performance in digital magnetic recording channels

The performance of partial response linear and decision-feedback equalizers is evaluated for a digital magnetic recording channel having a symmetric pulse response, and a magnetic recording channel having an asymmetric pulse response. Both linear and decision-feedback equalizers are considered based on the zero-forcing criterion. Symbol-by-symbol detection and maximum-likelihood sequence estimation are investigated. The performance of the detection methods is evaluated both analytically and by Monte Carlo simulation. >

Nonlinear channel models for digital magnetic recording

Methods for identifying the digital magnetic recording channel in which data dependent nonlinear effects are present are described. The models used include the finite state machine (FSM), Volterra series, and channel state dependent transition shifting. Procedures to compute the model parameters are described, and the models are compared with a view to their accuracy and use for studying receiver performance. Results are included from prototype channels with various recording densities with significant nonlinear distortion. >

Upper bounds on the capacity of the digital magnetic recording channel

Upper bounds are derived for the channel capacity of a model for a digital magnetic disk storage device. The model is similar to that of C.A. French and J.K. Wolf (1988) in that it contains a linear filter to represent the Lorentzian step response and two additive Gaussian noise processes to represent the electronic and media noises. It differs in that both the lineal bit density and the track density are parameters that may be varied, as opposed to just track density. Using typical media parameters, it is estimated that, for this model, the channel capacity (in bits per unit area) may be increased up to a factor of approximately 20 by appropriately increasing the lineal and track densities. >

Timing sensitivity of (MMSE) linear and DF equalisation for digital magnetic recording channels

The performance of symbol-spaced linear and decision feedback (DF) equalisers for a magnetic recording channel with low-pass and matched filter front-ends is investigated. The optimum sampling phases for these two cases is derived analytically, and the timing sensitivity of the equaliser performance is characterised as a function of the recording density. The robustness of receiver performance with respect to target responses belonging to the class of partialresponse channels, as well as the front-end filter shapes, is obtained.

Comparative performance between drop-out detection and Viterbi reliability metric erasure flagging

It is known that reliable symbol erasure flags can significantly enhance the decoded performance of an interleaved Reed-Solomon code on a digital magnetic recording channel. The author compares the improvement afforded by a drop-out detector erasure flagger to the improvement provided by an erasure flagger based on a class IV partial response Viterbi detector. It is shown that, in addition to being less complex, the drop-out detector is the superior erasure flagger when decoded performance is burst-error-limited and burst errors are a result of signal level drops. Although the proposed Viterbi erasure flagger is derived heuristically, it performs as well as the previously considered optimum method and, hence, the drop-out detector can be claimed to be superior to all such Viterbi flaggers under the assumptions of the present work.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Representation of a digital magnetic recording channel

A representation or model of a digital magnetic recording channel which has value both as an expression of the transfer characteristics of the channel and as a tool for use in the design and development of digital coding techniques for that channel is presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Code merit in digital magnetic recording channels

Measures of the performance of channel codes for digital magnetic recording systems are derived and discussed.