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Media noise is inevitable in bit-patterned media (BPM) due to fabrication imperfections, and degrades the bit error rate (BER) performance of channel. In this paper, a new channel model is proposed to characterize the media noise in BPM fabricated with cost-effective self-assembled technology, which exhibits long-range island orientation fluctuations in addition to the usual local island position and size fluctuations. To alleviate the effects of the significant media noise and write errors for such BPM at 4 Tera-islands/in2 density, we have proposed a recording scheme that uses multiple islands (2 by 2 islands) for 1-bit information in contrast to the conventional recording scheme of recording 1 bit on one island. For both recording schemes using low-density parity check code at the same user areal density (0.9 Tb/in2), when the island orientation fluctuation is large (i.e., ${\ge} 10$ °), the proposed 4 islands/bit scheme outperforms 1 island/bit scheme. This BER improvement is because the write error and media noise become increasingly dominant compared to the readback error caused by the inter-track interference and additive white Gaussian noise when the island orientation fluctuation is large. Although the proposed multiple islands recording scheme decreases the user density significantly, the proposed model can be helpful in developing more advanced signal processing and coding techniques that can alleviate the long-range island orientation fluctuations without such a sacrifice in user density. [ABSTRACT FROM AUTHOR]

Heat-assisted magnetic recording (HAMR) is the leading candidate for the next generation of magnetic recording. In HAMR, the thermal profile (with circular contours produced by the near-field transducer) combined with the current writer structures results in recording transitions with noticeable curvature, which causes edge erasure at high linear density and increased transition noise. This transition curvature affects the bit error rate (BER) and is thus important to the model. As the micromagnetic simulations are computationally demanding, in this paper we investigate a fast and simplified write model to capture the transition curvature of HAMR. As the transition curvature causes signal degradation in normally oriented read head array (NHA) having straight gaps, we propose a V-shaped read head array (VHA) by rotating the side readers at appropriate angles to follow the curvature shapes and improve the readback signal. Simulations indicate that, with 2-D signal processing, VHA can provide improved BER performance compared to the NHA in the presence of readback transition curvature on HAMR media. Also this paper indicates that the Curie temperature variance affects BER performance more severely than the anisotropy field variance. [ABSTRACT FROM AUTHOR]

The increased track density in bit patterned media recording (BPMR) causes increased inter-track interference (ITI), which degrades the bit error rate (BER) performance. In order to mitigate the effect of the ITI, signals from multiple tracks can be equalized by a 2D equalizer with 1D target. Usually, the 2D fixed equalizer coefficients are obtained by using a pseudo-random bit sequence (PRBS) for training. In this study, a2Dvariable equalizer is proposed, where various sets of 2D equalizer coefficients are predetermined and stored for different ITI patterns besides the usual PRBS training. For data detection, as the ITI patterns are unknownin the first global iteration, the main and adjacent tracks are equalized with the conventional 2D fixed equalizer, detected with Bahl- Cocke-Jelinek-Raviv (BCJR) detector and decoded with low-density parity-check (LDPC) decoder. Then using the estimated bit information from main and adjacent tracks, the ITI pattern for each island of the main track can be estimated and the corresponding 2D variable equalizers are used to better equalize the bits on the main track. This process is executed iteratively by feeding back the main track information. Simulation results indicate that for both single-track and two-track detection, the proposed 2D variable equalizer can achieve better BER and frame error rate (FER) compared to that with the 2D fixed equalizer. [ABSTRACT FROM AUTHOR]

Shingled writing on bit patterned media (BPM) is a promising technology to further increase the areal density beyond 1 Tbit/in2 without drastic changes in writer design. In this paper, a shingled writer is modeled for writing a 2-D sector on BPM, and in particular, we investigate the potential benefit of leaving the last track in the 2-D sector untrimmed, making it fatter than the other tracks in that 2-D sector. During detection, the more reliable information from the last untrimmed (i.e., the fat) track is used as a priori information for detecting the data in the other tracks in that 2-D sector. The simulation results indicate that for 2-D sector with ten tracks (at 3.64 Tbits/in2 channel bit density) and 5% media noise and at a target bit error rate of 10^\mathrm -3 , using the fat track information, 2-D equalizer +2-D target + symbol-based pattern-dependent noise-predictive detector detecting a single track can provide about 2.9 dB SNR gain compared with that with the same joint detection method using uniform tracks at the same areal density. However, the latency increases due to the decision feedback detection. We can reduce this latency penalty by detecting three tracks at a time, but the SNR gain then reduces to 0.9 dB. [ABSTRACT FROM PUBLISHER]

We report the results of an investigation of bit-patterned media recording (BPMR) channels containing insertion/deletion errors that may be introduced because of the write synchronization problem. We first describe a simple channel model for insertion/deletion errors in BPM, as a result of write clock frequency offset. Based on this channel model, we propose a new error correction coding (ECC) scheme to correct insertion/deletion errors--picket shift. Simulation results show that picket shift performs significantly better than a no-ECC scheme in the presence of insertion/deletion errors. [ABSTRACT FROM AUTHOR]

In bit-patterned media (BPM), media noise is expected to be dominated by fabrication imperfections and to manifest as island size and spacing fluctuations. Previous work has shown that media noise has a significant impact on the error rates of BPM channels. Thus, having a realistic model of media noise is essential to evaluate the performance of the BPM channels. In this work, we apply image processing techniques to a scanning electron microscope image of a candidate BPM nano-mask, produced by a self-assembly technique, to estimate likely size and location fluctuations of the islands. These statistics may also be useful to characterize the samples of candidate BPM masks. We assume that these observed fluctuations are representative of patterning noise that might result from such a mask. The results indicate that these fluctuations are correlated and can be modeled by Gaussian random processes. Using estimated characteristics of islands size and location fluctuations, we model the correlated media noise and investigate the performance of BPM channels in the presence of such correlated media noise. [ABSTRACT FROM AUTHOR]

In high density bit-patterned media (BPM), bits or magnetic islands are very close leading to significant inter-track interference (IT!) in addition to inter-symbol interference (IS!). Also, in BPM, major sources of media noise are the fluctuations in the location of the magnetic islands and fluctuations in the sizes of the magnetic islands. The location fluctuations can happen in both along-the-track and in cross-track directions. The size fluctuations affect both IS! and IT!. In order to obtain a more realistic channel model that includes the 2-D interference and the 2-D impact of media noise, we have developed a 2-D pulse response simulator for BPM. Utilizing the 2-D pulse response, we model the IT! and the media noise. Simulation results show that to achieve an acceptable bit error rate (BER), the location and size fluctuations should be smaller than 8% of the bit period at a density of 1.5 Tb/in². [ABSTRACT FROM AUTHOR]

When occasional dropouts occur in magnetic tape recording systems because of defects and debris, the readback signal exhibits amplitude loss, pulse widening, and peak shifts, and the corresponding entire data block may be lost. In this paper, we develop a dropout compensation method that works in conjunction with the interpolated timing recovery method. In this method, we estimate the readback signal envelope and use it as a measure of the depth of a dropout. On the basis of the estimated envelope, an equalizer can be selected from a pretrained filter bank to transform the distorted transition response in a dropout to the desired partial response target. In addition, a Kalman filter-based scheme can be used to determine the phase and the frequency update gains in the timing recovery loop. We show that, by using Kalman filter-based timing recovery, more dropouts can be compensated. [ABSTRACT FROM AUTHOR]

Correlation filtering methods are becoming increasingly popular for image recognition and location. The recent introduction of optimal tradeoff circular harmonic function filters allowed the user to specify the response of a correlation filter to in-plane rotation distortion. In this paper we introduce a new correlation filter design that can provide a user-specified response to in-plane scale distortion. The design is based on the Mellin radial harmonic (MRH) transform and incorporates multiple harmonics into the correlation filter for improved discrimination capability. Additionally, the filter design minimizes the average correlation energy in order to achieve sharp correlation peaks, and thus we refer to these filters as minimum average correlation energy Mellin radial harmonic (MACE-MRH) filters. We present underlying theory, a MACE-MRH filter design method, and numerical simulation results. [ABSTRACT FROM AUTHOR]

This paper addresses a new scheme by Vasic and Pedagani to combine low-density parity-check (LDPC) codes with run length limited (RLL) constraints. In this method, the RLL constraints are embedded into the LDPC codewords by deliberately flipping the bits of LDPC codewords that violate the RLL constraints. It is important to keep the number of flipped bits small in order to not overburden the LDPC decoder. In this paper, we introduce a method to control the number of flipped bits by using pseudorandom sequences. We present a new low-complexity iterative decoding and detection scheme to correct both the flipped bits and channel errors in a partial response channel. Analyses and simulation results show that the proposed method has good performance and reasonable complexity for (0, k) RLL constraints. [ABSTRACT FROM AUTHOR]

Baseline wander (BLW) is one of major sources of bit errors in perpendicular recording. In this paper, we present a method to compensate for BLW by per-survivor processing (PSP), i.e., along each surviving path in the Viterbi algorithm (VA). We apply the PSP method in VA in timing recovery loop and SOVA for iterative decoding. Simulation results show that the cycle slip rate and bit error rate are lowered and approach ideal case where there is no BLW. [ABSTRACT FROM AUTHOR]

Low-density parity check (LDPC) codes have shown near-capacity performance in additive white Gaussian noise (AWGN) channels. However, in magnetic recording systems, the readback signals suffer from various impairments (namely, transition noise, nonlinear transition shift, and partial erasure) in addition to AWGN. In this paper, we describe an FPGA-based advanced magnetic recording channel simulator (that includes these impairments) and an LDPC coding system. The error correcting performances of LDPC codes in the presence of such realistic impairments are investigated down to bit error rate (BER) of 10-11 and frame error rate (FER) of 10-8. [ABSTRACT FROM AUTHOR]

Focuses on a study which presented a time-domain model to characterize the noise from particulate recording media. Autocorrelation function of the media noise; Inadequacy of power spectrum measurements; Information on the stationary stochastic processes used to model the nonstationary media noise in the time domain.

A 2-D write/read channel model, which can accurately capture the media, writer, and reader characteristics, is proposed and investigated for very-high-density bit-patterned media recording (BPMR) system with large media noise. For the write process, a 2-D data-dependent write channel combined with a micromagnetic model of the writer is investigated for BPMR. In order to better understand the proposed channel model, several 2-D patterns are investigated, and the corresponding write failure events are studied. It is observed that the write error rates (WERs) are different for different 2-D patterns due to the 2-D data-dependent nature of the write-in errors, even though the write failure rates are the same for these different 2-D patterns. For the readback process, a read channel, including media noise, is combined with the write channel, and the bit error rates (BERs) are studied for various 2-D patterns as a function of media jitter and write clock phase drift. It is observed that the 2-D pattern corresponding to four identical bits in a square pattern provides the best performance at a target BER of 10^\mathrm -2 , because it can provide adequate tolerance to media noise and interference in down-track and cross-track (CT) directions. The difference between the WER and the BER after readback is studied for various 2-D patterns, and the pattern corresponding to 4 bits with transitions in the CT direction is found to exhibit the largest difference among the studied patterns due to the fact that inter-track interference is more severe than the inter-symbol interference. These results motivate possible inclusion of 2-D modulation codes in BPMR channel to avoid certain bit patterns. [ABSTRACT FROM PUBLISHER]

This paper investigates 2-D media noise in shingled magnetic recording (SMR) systems. The media noises caused by the overwriting of the next track and the residual information from the previous track are asymmetric in the cross-track (CT) direction and are found to vary with the linear density. The media noise after equalization is found to be 2-D data dependent, with its mean and variance affected by the nonlinear transition shift in the CT and down-track directions, respectively. Also the effect of media noise on the bit error rate (BER) is studied for increased track densities during the writing process. The effect of jitter on the BER is always significant with increased track density in SMR systems, while the effect of overwriting and inter-track interference on the BER performance are quite different for readback with rotated and normally oriented readers, even though the same writer is used during the writing process. [ABSTRACT FROM AUTHOR]

Support vector machine (SVM) classifiers are popular in many computer vision tasks. In most of them, the SVM classifier assumes that the object to be classified is centered in the query image, which might not always be valid, e.g., when locating and classifying a particular class of vehicles in a large scene. In this paper, we introduce a new classifier called Maximum Margin Correlation Filter (MMCF), which, while exhibiting the good generalization capabilities of SVM classifiers, is also capable of localizing objects of interest, thereby avoiding the need for image centering as is usually required in SVM classifiers. In other words, MMCF can simultaneously localize and classify objects of interest. We test the efficacy of the proposed classifier on three different tasks: vehicle recognition, eye localization, and face classification. We demonstrate that MMCF outperforms SVM classifiers as well as well known correlation filters. [ABSTRACT FROM PUBLISHER]

In this paper, we first present a recording physics based analytical channel model for bit-patterned media recording (BPMR) systems with staggered islands configuration. We further propose an analytical approach to jointly design the equalizer with partial response (PR) target for BPMR systems, by using the minimum mean-squared error (MMSE) criterion with monic constraint, taking into account inter-track interference (ITI) and media noise. Simulation results show that the proposed approach performs better than the system designed without considering ITI and media noise. We further investigate the performance of staggered array against regular array islands with bit-aspect ratios (BAR) of 1 and 2, and with different amount of media noise, inter-symbol interference (ISI), and ITI. We found that staggered array islands with BAR of 2 offer better bit error rate (BER) performance and better tolerance to media noise. [ABSTRACT FROM PUBLISHER]

The feasibility of two-dimensional magnetic recording (TDMR) at 4 Tb/in^2 customer areal-density is investigated via numerical simulations. In addition to the coding overhead needed to correct possible errors in a TDMR channel, the overhead required to obtain accurate position and timing estimates is taken into account in determining achievable customer density. The TDMR channel model used for this investigation is based on a random Voronoi granular medium, a two-dimensional (2-D) Gaussian read sensitivity function with random position and timing offsets and additive white Gaussian noise (AWGN). Read channel signal processing consists of a 2-D linear minimum mean square error (LMMSE) equalizer, a Gaussian mixture model (GMM) based log likelihood ratio (LLR) extractor and a low-density parity-check (LDPC) decoder. This work suggests that reliable performance may be achieved on media with 14 \times 10^12 grains/in^2 by TDMR at a net customer areal-density of 0.29 bits per grain, including the overhead required for the LDPC code and the position and the timing fields. [ABSTRACT FROM AUTHOR]

Two-dimensional magnetic recording (TDMR) is a new magnetic recording paradigm that aims to record one bit of information in one or a few grains, with the goal of achieving a recording density of nearly 10 Tbit/in². In addition to the usual noise, a TDMR channel experiences the problem that some bits are never recorded because of the randomness of grain size and location. Thus, it is believed that a key component of a TDMR channel is two-dimensional (2-D) signal processing along with a strong error correction code. In this study, the TDMR channel is investigated based on a random Voronoi grain model and a signal processing architecture is proposed. Here, a 2-D linear minimum mean squared error (LMMSE) equalizer and a low-density parity-check (LDPC) code are employed and the effects of unwritten bits are modeled by a Gaussian mixture model. In numerical simulations, the proposed architecture shows the feasibility of user bit densities near 10 Tbit/in² for media with a 20 Tgrains/in² grain density. [ABSTRACT FROM AUTHOR]

In this paper, we first propose a simple but general analytical channel model for bit-patterned media (8PM) systems. It facilitates the generation of accurate readback signals with a large amount of media noise, as well as the analytical design of equalizer and channel partial response (PR) target. We further propose an analytical approach to jointly design the two-dimensional (2-D) equalizer with one-dimensional (1-D) channel PR target for BPM systems with media noise, according to the minimum mean square error (MMSE) criterion with monic constraint. Simulation results show that the proposed 2-D equalizer with 1-D target based approach achieves significant performance gain over the system designed without considering media noise. [ABSTRACT FROM AUTHOR]

In read channels in magnetic recording systems, a finite impulse response (FIR) filter is often used as an equalizer, and the filter coefficients are adapted via a least mean squares (LMS) algorithm. This equalizer adaptation loop can interfere with the timing recovery (TR) loop and the automatic gain control (AGC) loop that are also present in such channels. In a previous paper by L. Du et al., a linear constraint is proposed for the LMS loop so that it is decoupled from the TR and the AGC loops. In this paper, we generalize that constraint, and propose a new constraint that offers the advantage of easier implementation. [ABSTRACT FROM AUTHOR]

We describe a general probabilistic framework for matching patterns that experience in-plane nonlinear deformations, such as iris patterns. Given a pair of images, we derive a maximum a posteriori probability (MAP) estimate of the parameters of the relative deformation between them. Our estimation process accomplishes two things simultaneously: It normalizes for pattern warping and it returns a distortion-tolerant similarity metric which can be used for matching two nonlinearly deformed image patterns. The prior probability of the deformation parameters is specific to the pattern-type and, therefore, should result in more accurate matching than an arbitrary general distribution. We show that the proposed method is very well suited for handling iris biometrics, applying it to two databases of iris images which contain real instances of warped patterns. We demonstrate a significant improvement in matching accuracy using the proposed deformed Bayesian matching methodology. We also show that the additional computation required to estimate the deformation is relatively inexpensive, making it suitable for real-time applications. [ABSTRACT FROM AUTHOR]

We propose an improved bit-flipping scheme that combines error-correcting codes such as low-density parity check codes with run length limit (RLL) constraints. In addition to its compatibility with soft decision decoding, the proposed scheme has the advantages of no error propagation and fixed block length. Testing with simulated data and real data show good performance. The loss in performance due to the introduction of RLL constraint is less than 0.1 dB at bit-error rate 10-6 and block-error rate 10-4. [ABSTRACT FROM AUTHOR]

Good performance of iterative detection and decoding using low-density parity check (LDPC) codes has stimulated great interest in the data storage industry. One major concern in using LDPC codes in the read channel is their error floor, which is still an open question. To investigate the performance of LDPC codes in low bit-error rates (BER ∼ 10-10), we developed a high-throughput fully reconfigurable simulator using a field programmable gate array. Using this simulator, we are able to observe the performance of LDPC codes at low BER within a reasonably short time (10-10 within 1.5 h). We show the evaluation results for two types of LDPC codes. [ABSTRACT FROM AUTHOR]

In this paper, we present a general approach for constructing high-rate cycle codes having girth 12 which achieve the lower bound on the block length. An efficient encoding algorithm is also proposed for this class of codes. We estimate the word error rate of the cycle codes for additive white Gaussian noise (AWGN) channels under maximum likelihood decoding, using the minimum distance and its multiplicity. These estimates are compared to simulation results with iterative soft decoding. The performance of these codes for partial response channels is studied under iterative soft decoding using computer simulations. [ABSTRACT FROM AUTHOR]

A high throughput, reconfigurable field programmable gate array (FPGA) implementation of the soft output Viterbi algorithm (SOVA) is described. Such a SOVA module provides the soft information needed by an iterative soft decoder used with Turbo codes and low density parity check (LDPC) codes. The implementation of the SOVA algorithm runs at 100 Mb/s on Xilinx Virtex II 2000 FPGA. Using a higher capacity FPGA and repeating the circuit doubles the throughput. The design can be reconfigured for different partial response (PR) targets. The design requires about 5 kb of memory for the EPR4 channel and may be integrated on a single chip with serially implemented LDPC decoder. [ABSTRACT FROM AUTHOR]

Correlation filters (CFs) are a class of classifiers that are attractive for object localization and tracking applications. Traditionally, CFs have been designed in the frequency domain using the discrete Fourier transform (DFT), where correlation is efficiently implemented. However, existing CF designs do not account for the fact that the multiplication of two DFTs in the frequency domain corresponds to a circular correlation in the time/spatial domain. Because this was previously unaccounted for, prior CF designs are not truly optimal, as their optimization criteria do not accurately quantify their optimization intention. In this paper, we introduce new zero-aliasing constraints that completely eliminate this aliasing problem by ensuring that the optimization criterion for a given CF corresponds to a linear correlation rather than a circular correlation. This means that previous CF designs can be significantly improved by this reformulation. We demonstrate the benefits of this new CF design approach with several important CFs. We present experimental results on diverse data sets and present solutions to the computational challenges associated with computing these CFs. Code for the CFs described in this paper and their respective zero-aliasing versions is available at http://vishnu.boddeti.net/projects/correlation-filters.html [ABSTRACT FROM PUBLISHER]

Low-density parity-check (LDPC) codes offer a promising error correction approach for high-density magnetic recording systems due to their near-Shannon limit error-correcting performance. However, evaluation of LDPC codes at the extremely low bit error rates (BER) required by hard disk drive systems, typically around 10-12 to 10-15, cannot be carried out on high-performance workstation using conventional Monte Carlo techniques in a tractable amount of time. Even field-programmable gate array (FPGA) emulation pla forms take a few weeks to reach BER between 10-11 and 10-12. Thus, we implemented a highly parallel FPGA processing clust to emulate a perpendicular magnetic recording channel, which enabled us to accelerate the emulation by > 100x over the fastest n ported emulation. This increased throughput enabled us to characterize the performance of LDPC code BER down to near 10-14 an investigate its error floor. [ABSTRACT FROM AUTHOR]

Iterative codes such as low density parity check (LDPC) codes and turbo product codes (TPC) are of interest for data storage appli- çations. To apply these codes to digital recording systems, two possible schemes are considered in this paper. In the first scheme, a single LDPC code of column weight j > 2 is used to replace the Reed-Solomon (RS) code of the conventional channel. In the second scheme, an iterative code is used as the inner code and is concatenated with an outer RS code. Single parity check TPC code is considered for this scheme. We developed a high-throughput field programmable gate array (FPGA) platform to evaluate the error floor performance of LDPC codes and the error statistics of TPC codes in partial response (PR) channel with turbo equalization. High rate codes (rate 8/9 for LDPC code and rate 0.935 for TPC code) are evaluated for magnetic recoding application. The bit error rate (BER) performance of LDPC code down to 1010can be reached within 2 h using the FPGA platform. The TPC code error statistics are evaluated using about 1011 bits at different signal-to-noise (SNR) levels. For practical implementation complexity and power consumption, 2 channel iterations and 2 TPC decoder iterations are employed. The results show that the gain by applying TPC code under 2 channel iterations and 2 TPC decoder iterations is marginal. [ABSTRACT FROM AUTHOR]