A simple statistical model of partial erasure in thin film disk recording systems

Abstract

Absmcr-A simple statistical model of the partial erasure effect in metallic thin film recording is given. Experimental data is shown and was used to determine a fundamental parameter of the micro-magnetic structure of the medium. This single parameter determines the extent of erasure at any transition separation. Since it has no (rust order) dependence on the rate of the zigzags, it is anticipated that it will be relatively independent of the transition noise amplitude of the medium. INTRODUCTlONThe goal of achieving higher information densities in saturation recording invariably requires reducing the minimum spacing between magnetic transitions. As this spacing is reduced, linear superposition ceases to accurately predict the shape of the output waveform. In the case of thin film media, as used in virtually all current fixed disk data storage devices, the nonlinear behavior (for initially erased media) is predominately of two types: a transition shift and an anomalous amplitude reduction or partial erasure effect.The transition shift phenomenon is well known and documented [l], and can be compensated by appropriate time shifting of the write current reversals [2]. The partial erasure effect, on the other hand, shares neither of these aspects. It has only seen limited investigation, [3.4] for example, and no quantitative analysis has been done.However, an understanding of this thin film phenomena is critical to achieving extremely high density recording. Here dibit measurements at high densities will be analyzed utilizing a simple statistical model.A magnetic transition will be modelled by a random process across the track width which defines the location of a domain wall (i.e. a zigzag wall) separating mnes of opposite magnetization. A typical zigzag transition might look as shown in Fig. 1. If the recorded mck is very wide compared to the (average) width of the zigzags, then the cross track average is a good approximation to the actual average transition, and hence the output pulses look very similar to those which would be produced from an average transition. The average transition, Fig. 2, is often modelled as being a linear combination of an error function and an arctangent transition [ 11 characterized by two parameters: the percentage error function, and U, the transition width parameter.There is a second interpretation of this average transition profile that is used extensibly throughout this paper. Consider any point z located somewhere across the track. We would like to know the probability density that the domain wall at point z is located at some position x (in the recording direction), when the transition center is located at the position q. We will make the reasonable assumption that this probability density function (pdf) is independent of the value of z. Thus the average (normalized)

Applications of a new simulation model for media noise limited magnetic recording channels

“…91 as well as noise, and is completely specified by a few parameters. The model presented here expands a microtrack model for medium noise [3] to include partial erasure [4]. Among other uses, this model can be the basis of simulations to determine the error rate performance of various detector circuits such as PRML in the presence of media noise and partial erasure.…”

“…Next, partial erasure is incorporated into the microtrack model by using a simple model which was first proposed in [4]. If two magnetization flips on a microtrack occur closer together than some threshold L, then they eradicate each other.…”

Statistical study of zig-zag transition boundaries in longitudinal digital magnetic recording

“…This paper is focused on the presentation of theoretical results for isolated transitions. Coupling these results for isolated transitions with models for bit shift, transition position variance increase [15], [17], and percolation thresholds [16], [18], we can easily extend our TZ-ZT model to include the nonlinear effects of interacting transitions [19].…”

On the capacity of data dependent autoregressive noise channels

“…This model is similar to [9], with the only difference being that we assume a perpendicular channel impulse response rather than a longitudinal transition response. The recording track is modeled to consist of N parallel microtracks.…”

“…Gaussian random distance whose mean is zero and variance is σ 2 j . Two adjacent transitions in a microtrack cancel each other if the distance between them is less than a threshold T min , as modeled in [9]. The random jitters are assumed to be independent for different microtrack subchannels.…”