Optimal detection for perpendicular recording channels with transition noise

Cheng (Doctoral Dissertation, CIT, Pasadena, California, 1997) introduced a class of linear codes called low-density generator matrix (LDGM) codes and studied its performance on a memoryless additive white Gaussian noise (AWGN) channel. In this paper, we study its performance on perpendicular magnetic recording channels. The results shown in this paper indicate that the bit-error rate (BER) performance of some LDGM-codes is comparable to that of low-density parity check (LDPC) codes of the same rate.

We examine the performance of a rate-0.9 structured irregular repeat-accumulate (S-IRA) code on a perpendicular magnetic recording (PMR) channel with media noise. To account for the presence of data-dependent media noise, a pattern-dependent-noise-predictive (PDNP) channel detector is employed, in which the prediction filters are trained using the LMS algorithm. We compare the error rate performance of the S-IRA code with that of a Reed-Solomon (RS) code of the same length and rate, with the PDNP detector present in both cases. Our results show that the S-IRA code achieves a gain of over 1 dB relative to the RS code for sector error rates down past 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> , but only if the columns of its H-matrix are properly permuted. We have also estimated that the linear density gain attainable by the S-IRA code relative to the RS code is about 8% for the operating point we have chosen.

Due to the ongoing miniaturization of digital camera sensors and the steady increase of the “number of megapixels”, individual sensor elements of the camera become more sensitive to noise, even deteriorating the final image quality. To go around this problem, sophisticated processing algorithms in the devices, can help to maximally exploit the knowledge on the sensor characteristics (e.g., in terms of noise), and offer a better image reconstruction. Although a lot of research focuses on rather simplistic noise models, such as stationary additive white Gaussian noise, only limited attention has gone to more realistic digital camera noise models. In this article, we first present a digital camera noise model that takes several processing steps in the camera into account, such as sensor signal amplification, clipping, post-processing,.. We then apply this noise model to the reconstruction problem of high dynamic range (HDR) images from a small set of low dynamic range (LDR) exposures of a static scene. In literature, HDR reconstruction is mostly performed by computing a weighted average, in which the weights are directly related to the observer pixel intensities of the LDR image. In this work, we derive a Bayesian probabilistic formulation of a weighting function that is near-optimal in the MSE sense (or SNR sense) of the reconstructed HDR image, by assuming exponentially distributed irradiance values. We define the weighting function as the probability that the observed pixel intensity is approximately unbiased. The weighting function can be directly computed based on the noise model parameters, which gives rise to different symmetric and asymmetric shapes when electronic noise or photon noise is dominant. We also explain how to deal with the case that some of the noise model parameters are unknown and explain how the camera response function can be estimated using the presented noise model. Finally, experimental results are provided to support our findings.

The application of low-density parity-check (LDPC) codes for use in high-density magnetic recording channels is considered. A first order position jitter model is assumed in order to include the effect of signal dependent transition noise present in high density longitudinal thin film recording. Coding gains using pattern dependent noise-predictive soft detection to account for the transition noise are also determined via simulation. Results show that LDPC code performance degrades in equalized (colored) additive noise, but exhibits remarkable performance in the presence of signal dependent transition noise, especially when used in conjunction with an appropriately optimized detector.

Power Line Communication (PLC) channel is a very challenging environment, this is due to the fact that severe impairments adhering this medium. A more realistic and accurate noise model based symmetric alpha-stable distribution (SαS) is considered in this paper to better fit the properties of real noise inherent in power grid system. In this paper we study the impact of the degree of impulsiveness based SαS model on the performance of MIMO over PLC channel. Results show the improvement reached in PLC by using MIMO-OFDM, and reveal the effectiveness of considering a more realistic noise model.

Magnetization reversal is a crucial issue to reduce a medium noise in high-density perpendicular magnetic recording. The magnetization reversal behaviors govern the writing process, zigzag transition boundary, transition jitter, and thermal stability. However, up to now, few works have been devoted to reveal magnetization behaviors by in situ MFM observation under magnetic fields, which is an extremely important issue to improvement of recording media. In this work, in-situ MFM observations were performed under various magnetic fields to make clear the magnetization reversal process microscopically. The activation volume in media was estimated by the magnetization reversal field map (MRF-map) technique, and the magnetization processes was discussed.

In perpendicular magnetic recording, medium noise characterization is necessary to improve head and disk performance, and to establish the signal processing strategy. We examined the medium noise of CoPtCrSiO2 perpendicular recording media with various SiO2 concentrations deposited by separating noise into transition jitter, pulse width breathing, and reversed domain noise. Since the reversed domain noise magnitude was small near transitions, the noise power decreased in proportion to linear density, and disappeared at densities higher than 200 kFCI. Thus, the signal–to–noise ratios at high linear densities were determined by jitter noise and pulse width breathing. Although the reversed domain noise increased for disks with higher SiO2 concentrations, error rate performance was improved. Therefore, the significant parameter was the transition jitter, and the influence of reversed domain noise was small.

In this paper, a physical model of readback signals from a hybrid magneto-optical (MO) recording using magnetic flux detection is presented. The minimum mean-square error (MMSE) technique has been used to design generalized partial response (GPR) targets in order to facilitate the application of the trellis based channel detector. A PR target with integer coefficients is proposed as a good approximation to the GPR target. We also address the application of turbo codes and LDPC codes with iterative soft decoding structure to the hybrid magneto-optical (MO) recording channel. The effects of bloom, transition noise and giant magneto-resistive (GMR) sensor nonlinearity on the bit error rate (BER) performance are investigated both for uncoded partial response maximum likelihood (PRML) and iterative soft decoded recording channels. Our results for the hybrid recording channels indicate that turbo/LDPC codes of rate 16/17 can achieve coding gains of about 5 dB over PRML methods for a 10/sup -5/ target BER at the normalized density S=1.5. Turbo codes with iterative soft decoding are seen to be robust to transition noise.

The influence of thermal relaxation on the readback waveforms from perpendicular magnetic recording media was experimentally investigated in time-domain measurements. The signal decay rate at the magnetization transition was smaller than that in between the transitions, reflecting the demagnetization field distribution. The time dependence of the noise in the waveform was characterized as pulsewidth, transition jitter, and pulsewidth fluctuations. While the transition width decreased with elapsed time, the jitter and pulsewidth fluctuations were stable. These time-dependant results could be interpreted by considering the demagnetizing field distribution near the transitions and in between the transitions, which govern the random magnetization domain reversals.

Medium noise characteristics and transition jitter in perpendicular magnetic recording are explored using micromagnetic simulation. A noise plateau for intermediate recording densities is observed for a recording layer of typical magnetization. The plateau is replaced by a normal linear dependence of noise on recording density for a low magnetization recording layer. We show analytically that a source of the plateau is similar to that producing the non-linear transition shift of signal. In particular, magnetostatic effects are predicted to produce positive correlation of jitter and thus negative correlation of noise at the densities associated with the plateau.

In perpendicular magnetic recording, track edge noise, write fringing, and transition curvature are crucial issues that need to be addressed in order to increase track density. In particular, it is thought that the transition curvature at the written track edges broadens readback pulse width through the azimuth loss effect, but quantitative discussion of this phenomenon has not been sufficient. In this paper we extract transition lines observed in MFM images, and examine the influence of the transition curvature on the readback pulse width and transition jitter. Our findings show that this influence is not very large, and that deterioration of the writing resolution or broadening of the transition width at the track edges is more significant.

Actual examples are given to show that low head impedance is extremely important in narrow track-width heads for high-density perpendicular magnetic video recording and reproduction, and that it strongly affects the wideband frequency characteristics and the noise level of the head. A main pole excitation probe-type head (MPD), with 7 μm track width, was fabricated to compare the dependence of frequency band and noise characteristics on head impedance. With high sensitivity and low impedance, the MPD head had a very favorable CN ratio of 54.5 dB, suggesting that in the future it will provide significant advantages for widebanddigital recording.

The long-term bit error rate (BER) performance of partial response maximum likelihood (PRML) system in a perpendicular magnetic recording (PMR) channel with thermal decay is studied. A thermal decay model based on the experimental data for three CoPtCr-SiO2 PMR media with different thermal stability is obtained. Then, the performance of PR1ML channel for the 16/17(0,6/6) and 128/130(0,16/8) codes as a run-length-limited (RLL) code is evaluated by computer simulation using the model. Moreover, the relationships between the elapsed time and the BER are obtained for the combinations of two RLL codes and three PMR media and their performances are compared. The results show that for the combination of the 128/130(0,16/8) code and the medium with the poorest thermal stability, the degradation with the elapsed time is noticeable compared with the other combinations

In this work, we consider a perpendicular magnetic recording channel where the data is stored perpendicular to the plane of magnetic media. The perpendicular magnetic recording provides significant aerial density gain compared to the conventional longitudinal magnetic recording. This gain comes at the cost of adding a baseline wander noise which degrades the system performance and affects the data integrity. In this article, we propose a model for the baseline wander noise. The parameters of the proposed model are computed by posing the problem as minimizing the mean square error. We demonstrate that this problem can be appropriately simplified and posed as finding a least squares problem. The proposed model on the baseline wander noise requires the knowledge of information bits to estimate the noise but this information is unavailable at the time of decoding. We propose a novel technique to cancel the baseline wander effect on the Viterbi trellis. This cancellation is done on the fly in the trellis and obviates the need of the information bits yet provides the performance gain close to the genie performance. Simulation and experimental results corroborate the analysis of the proposed algorithm and demonstrate that the proposed algorithm provides the performance gain.

We address joint design of optimum generalized partial response (GPR) target and equalizer for perpendicular recording channels with jitter noise. We develop a new cost function which accounts for the data-dependent nature of jitter noise based on the minimum mean square error (MMSE) criterion. Using the step-response-based channel model, we derive expressions for the statistics required to compute the optimum equalizer and target in the presence of jitter noise. We also derive a bit-response-based model for the jitter noise channel. We present an approach for doing simulations as well as analytical computations for the jitter noise channel without resorting to the widely used Taylor series approximations. Our computational and simulation results show that, while the targets designed without accounting for the jitter lead to error-floor effect in the bit-error-rate performance, the targets designed by our approach give significant performance improvement under high jitter conditions, with no sign of error-floor effect for the range of signal-to-noise ratios considered.