Analytical modelling of perpendicular recording

An analytical model for perpendicular magnetic recording is presented which is capable of calculating 'ab-initio' the magnetisation distributions written by an 'arbitrary' head field into both single and double layer recording media. Magnetisations are shown to follow the head field distribution existing at the medium's top surface. Application of the theory allows prediction of many of the fundamental features of the perpendicular write/read cycle, e.g. transition widths, replay pulse shapes, D50values etc.     

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     

Comparison Between Viterbi Detectors for Magnetic Recording Channels Based on Regressive and Autoregressive Noise Models

A recent work presents a regressive noise model for the data-dependent correlated noise, at the output of a magnetic recording channel detector. We have generalized this channel model, considering digital equalization and a more efficient correlation matrix, in order to make a comparison with the usual detector in a more realistic environment. Simulation results show that the regressive detector performs better when the number of trellis states is lower than needed, while both approaches are comparable when the number of states matches the channel memory.     

A theory of digital magnetic recording on metallic films

A theory is presented predicting the performance of thin magnetic tape as a digital storage medium. The NRZ recording properties are discussed with reference to the properties of both the tape and the replay head. Expressions are derived relating the isolated pulse width, the output voltage, and the packing density to the coercivity and thickness of the tape, the head gap length, and the head-to-tape separation. The theoretical predictions are then compared with experimental results measured over a wide range of head and tape properties. The agreement obtained is excellent.     

An investigation of the effects of media characteristics on read channel performance for patterned media storage

Many view data storage on patterned magnetic media as one way of attaining storage densities in excess of 1 Tb/in/sup 2/ and thus overcoming the problems associated with recording at ultrahigh densities on conventional continuous media. In this paper we investigate, through the use of a replay simulation developed to take into account the three-dimensional nature of the patterned media, the effects that the shape-constrained media have on the bit-error-rate performance of the read channel in 1-Tb/in/sup 2/ perpendicular recording. In particular, we analyze how media configurations with varying island shape, size, and distribution affect the channel performance.     

An experimental, multilevel, high density disk recording system

Communication technology has been applied to a magnetic disk recording channel to achieve up to a fourfold increase in linear bit density as compared to conventional binary recording. Among the techniques incorporated were digital data transmission by Class IV Partial-Response signaling (Interleaved NRZI), recording channel pre-emphasis, equalization and filtering, and periodic amplitude sampling of the data signal. The magnetic recording channel was linearized using very high frequency a.c. bias, which also served simultaneously to erase old data. This enabled multilevel recording and the addition of a pilot tone for timing recovery. System block diagrams are presented together with a discussion of the optimization procedure and attained system performance.     

Transition shape analysis from medium noise measurements

We present a technique to determine the transition shape in digital magnetic recording. The method involves analyzing both temporal and spectral transition noise measurements. This combined method simultaneously determines the transition parameter and the cross-track correlation width along with the transition shape.     

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     

Diffraction Efficiency and Angular Selectivity of Volume Phase Holograms Recorded in Photorefractive Materials

The recording and replay of volume phase gratings in photorefractive crystals is investigated for both transmission and reflection geometries. Differential equations are derived and solved for a range of parameters including the length of the crystal, the magnitude, spatial distribution and phase angle of the refractive index modulation, the beam ratio at recording, and the angular range at replay. The recording process is assumed to reach a steady-state limit before replay with a weak probe beam. Solution of the repaly equations is mainly by numerical integration, although analytic solutions are derived for special cases. It is found that in certain cases the diffraction efficiency can be greatly increased by replaying the hologram at an angle different from the recording angle.     

Effect of island geometry on the replay signal in patterned media storage

In a move to extend the storage capabilities of magnetic storage systems beyond 1 Tb/in/sup 2/, the use of patterned media has often been cited. Here, recorded domains are constrained by the geometry of the magnetic island and not the geometry of the recording head. Conventional two-dimensional readout modeling techniques, using the reciprocity integral, rely on the assumption that the across-track medium magnetization is uniform under the giant magnetoresistive replay head. However, in the case of a geometrically constrained medium this is not the case. This work investigates the effect that the island geometry has on the characteristics of the replay signal in perpendicular patterned magnetic media storage through the extension of the reciprocity integral to three dimensions. The paper describes replay pulses that offer different characteristics from those obtained by conventional two-dimensional techniques. The origins of these differences are explained by the variation in medium magnetization across the track.     

Magnetoresistive read/write channel models

We studied the magnetic read/write channel with a magnetoresistive (MR) read head at a normalized channel density range of 2.5-3.0, observing and modeling partial erasure and nonlinear transition shift. The asymmetry of the MR head had a significant effect on the channel. We applied the transition-width-reduction model, the partial-erasure-plus-transition-shift model, and the Volterra model to the MR read/write channel, and evaluated the accuracy of these models on the basis of parameters obtained from experimental data. In order to consider the asymmetry of the MR head, we introduced a nonlinear MR head model into the read/write channel. These modified models achieved higher accuracy. Of all the models considered, the Volterra model provides the largest improvement over the linear model     

Statistical study of zig-zag transition boundaries in longitudinaldigital magnetic recording

In this paper, we study the statistics of zig-zag transition walls in digital magnetic recording and their relationship to transition noise defining quantities. We provide analytic results that link the statistics of zig-zag transitions to media/recording parameters. The basis of our study is the triangle zig-zag transition (TZ-ZT) model due to its well-defined triangle zig-zag shape and its cross-track stability. The results we derive here, however, are of a general nature, and given the right interpretation, apply to other zig-zag models as well, as we show in the paper. We also provide an interpretation of the cross-track correlation width, linking this quantity to the statistics of magnetized clusters in thin-film magnetic media. The paper concludes by showing how these results can be used in media noise modeling     

Power spectra of channel codes for digital magnetic recording

The power spectral density (PSD) is the average power per unit frequency of encoded random data transmitted over a perfect channel. The one-sided PSDs of a number of channel codes of recent interest in digital magnetic recording are calculated from codeword dictionaries and state diagrams. Given here are:     

Bounds on the capacity of a peak power constrained Gaussian channel

The authors present an upper bound and conjecture a lower bound on the information theoretic capacity of a digital magnetic recording channel. The channel is modeled as a linear time-invariant filter with a peak constrained input, and with additive non-white Gaussian noise at the output. The bounds are evaluated numerically using typical head and media parameters. The effects of write current, track width, media noise, and electronics noise on the channel capacity are examined     

Optimal code rates for concatenated codes on a PR4-equalizedmagnetic recording channel

At some nominal recording density, the read signal in digital magnetic recording resembles a Class IV partial response (PR4) signal and, hence, may be equalized to the PR4 shape with relatively little noise enhancement. When coding is added, for a fixed user density, the recording density must increase as a result of coding overhead, and the read signal will resemble PR4 to a lesser extent. Equalization to PR4 in this case will produce excessive noise enhancement. Thus, coding overhead (or rate) must be selected for optimum tradeoff between code strength and noise enhancement. Toward this end, we provide results for high-rate concatenated codes, assuming a Lorentzian recording channel model. In addition to examining optimal code rates, we compare parallel and serial concatenated code performance on the PR4 channel     

Effect of bitshift distribution on error rate in magnetic recording

A formalism is presented which relates the intrinsic error rate of a digital recording channel to measurable channel parameters: interpulse interactions and signal-to-noise ratio. Experimental data is provided to support the theoretical model. Implementation of the formalism allows clear identification of recording channel limitations and provides a method for determining the most reliable use of the channel.     

The helical-scan magnetic tape recorder as a digital communication channel

The properties of a magnetic tape recorder are viewed in terms of a digital magnetic recording/playback channel which exhibits fading (reduction of playback-signal level) and nonlinear behavior. A method is presented whereby channel nonlinearity may be quantified in a format useful for signal and receiver design. Measurements show this nonlinearity to be relatively small for symmetric two-level signals. Deep fades (dropouts) are the most significant source of errors in digital tape recordings. Fading is considered as multiplicative noise on an essentially linear channel, and measurements are made of the fade probability distribution and an associated additional time dispersion. While the fading process appears to occur relatively slowly (compared with the bit period), neither its probability distribution nor its associated dispersion encourage the use of a receiver which is able to adapt to the changing channel characteristics. Finally an attempt is made to ascribe the fading process to repeatable variations in head-tape separation, and a corresponding probability distribution for this separation is obtained. A helical-scan video recorder was used throughout the measurements because of its low cost and its potential as a high-density storage facility.     

Analytic determination of overwrite capability in magnetic recording systems

Analytic design criteria are provided to determine if a digital magnetic recording system can overwrite under worst-case conditions. The worst-case condition is taken to be a bubble of reversed magnetization in an otherwise saturated medium, written by applying current to a stationary recording head. A leading and a trailing transition are formed, creating a large demagnetizing field opposing the head field. Although the leading transition is commonly thought to be unimportant in saturation writing, its demagnetizing field can significantly hamper the writing of the trailing transition. First, self-consistent numerical calculation shows the characteristics of the bubble and its associated fields. Then the bubble is approximated analytically by a biquadratic form, and the demagnetizing field at the bubble center is compared with the field necessary to saturate the medium. A rapid loss of overwrite ability with decreasing gap-length is demonstrated. The importance of including image fields for thin-film heads is discussed. Graphical representations are given for the minimum gap-length necessary for overwrite. A relation between media parameters, bit density, and magnetic energy/bit in commercial disk drives is discussed.     

Selection of modulation code parameters for maximum lineal density

The relative performance capabilities for many known run-length-limited binary modulation codes useful in digital magnetic recording are placed in perspective. The criteria for grading is relative maximum achievable lineal recording density under conditions of quasi-optimal spectral shaping. The results are based upon a linear system analysis in which superposition is applicable in modeling saturation recording systems where the media is indeed fully saturated at the termination of each transition. The maximum relative achievable lineal density is shown in terms of code parameters for maximum theoretical information rate with run constraints. The results show which binary modulation code to select for maximal lineal density and how its performance compares with the maximum theoretically achievable for any binary modulation code.     

Off-axis Holographic Zone Plates Recorded and Reconstructed by Cylindrical Wavefronts

Theoretical aspects of off-axis holographic zone plate recording using two cylindrical waves, with arbitrary angled focal lines, and replay of such holograms with a cylindrical or spherical wave are discussed in the narrow-beam approximation. Expressions for the distances and orientations of focal lines of generally reconstructed astigmatic beams are given, and conditions for obtaining spherical waves are analysed. The results have been verified by experiments using photographic emulsion (Agfa-Gevaert Holotest 10E56 plates) as the recording material. In particular, experimentally obtained parameters of the reconstructed astigmatic beam and the spherical wave are found to be in good agreement with theoretical results.