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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)

The presence of error floor in low density parity check (LDPC) codes is of great concern for potential applications of LDPC codes to data storage channels, which require the error correcting code (ECC) to maintain the near-capacity error correcting performance at frame error rate as low as 10 −12 . In order to investigate the error floor of LDPC codes under partial response channels used in data storage systems, we propose a new estimation method combining analytical tools and simulation, based on the concept of trapping sets. The definition of trapping sets is based on the dominant error patterns observed in the decoding process. The goal is to accurately estimate the error rate in the error floor region for certain types of LDPC codes under the partial response channel and further extend the frame error rate down to 10 −14 or lower. Towards this goal, we first use field programmable gate array (FPGA) hardware simulation to find the trapping sets that cause the decoding failure in the error floor region. For each trapping set, we extract the parameters which are key to the decoding failure rate caused by this trapping set. Then we use a much simpler in situ hardware simulation with these parameters to obtain the conditional decoding failure rate. By considering all the trapping sets we find, we obtain the overall frame error rate in the error floor region. The estimation results for a length-4623 QC-LDPC code under the EPR4 channel are within 0.3 dB of the direct simulation results. In addition, this method allows us to estimate the frame error rate of a LDPC code down to 10 −14 or lower.

The implementation of high density partial response channels in disk drives has been hampered by nonlinear interactions between -transitions occurring in the write process. It is shown that the degree of nonlinearity is not characterized by the density relative to the isolated transition pulse width, rather by the transition spacing in relation to the transition width. Factors that determine the transition width are examined. In particular, the potential gains from using low moment media are investigated. A nonlinear model of the disk channel is discussed. The dependence of partial response signaling on linear superposition is discussed. Eye patterns are shown revealing the effects of nonlinearites on a partial response system.

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