An iterative ITI cancellation method for multi-head multi-track bit-patterned magnetic recording systems

One of the major problems in bit-patterned magnetic recording (BPMR) systems is an inter-track interference (ITI) that can significantly degenerate the system performance, especially at high areal densities (ADs). Generally, the BPMR system with staggered islands experiences less ITI effect than that with regular islands. Therefore, we propose an iterative two-head two-track detection method for a staggered BPMR system to further reduce the ITI effect, which employs two read heads to read two adjacent tracks and decodes them simultaneously. To lessen the ITI, the weighted readback signal of one track, serving as an ITI signal, is subtracted from the readback signal of the other track, and vice versa, before passing the refined readback signal to an iterative decoding process. Hence, the decoded data will be utilized to estimate the ITI signal for the next global iteration, $N_{\mathrm{ G}}$ . Supposing that the refined readback signal has only one-side ITI effect. We also present the design of the $2{\times }3$ target and its compatible equalizer that will be employed in the proposed system. Results demonstrate that the proposed system not only is superior to the conventional system but also has low complexity. Specifically, the proposed system can perform close to the conventional system whose readback signal encounters only one-side ITI effect when $N_{\mathrm{ G}} = 2$ , 3 and 5 iterations for $\text {AD} = 2$ , 2.5, and 3 Tb/in2, respectively.

To increase an areal density (AD) of an ultra-high density bit-patterned magnetic recording (BPMR) system [1], we have proposed track mis-regristration (TMR) correction method combined with the soft information adjustor (SIA) to cope with the effects of TMR and two-dimensional (2D) interference [2]. However, we found that soft information or log-likelihood ratio (LLR) can be improved to earn better bit-error rate (BER) performances. Therefore, we propose to use two deep neural networks (DNNs), e.g., multi-layer perceptron (MLP) [3] and long short-term memory (LSTM) network [4] that are operated together with an early SIA on a two-head/two-track (2H2T) BPMR system as shown in Fig. 1.The user sequences, xl,k ∈ {±1} of the l-th track and k-th bit, are recorded onto the medium. All readback signals are produced using two readers, which are then sent to TMR predictor [2]; meanwhile, they are equalized by the consistent 2D equalizers. Then, the equalized sequences, zl,k, are fed into the 2D detectors to output LLRs. The SIA is used to first improve the reliability of each LLR sequence before passing them to our proposed schemes based on DNNs to decide the estimated recorded bits, x'l,k.. The LLR that is obtained from SIA under various TMR effects is given as an input dataset, while the recorded sequence is fixed as an output dataset of DNNs. All of readback signals that relate to considered datasets are interrupted with several electronic noise levels. Here, we set all input and output datasets as 5,200 files, each file consists of 2×32,768 bits, which are directly mapped to be as a pair of input and output datasets.Fig. 2 shows BER performances between the proposed and conventional SIA systems [2]. It is clear that the proposed systems yield better BER performances over the conventional system at all TMR levels with and without position jitter. At BER = 10-5, the proposed LSTM gains for about 4.0 and 4.4 dBs over the conventional SIA system for both cases at TMR 0%. We found that LSTM network slightly provides better performance.  A 2H2T BPMR channel with the DNNs based soft-information improvement.  BER performances of the conventional SIA [2] and proposed systems.

In bit-patterned media (BPM) aimed at magnetic recording densities of 1 Tbit/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and higher, adjacent tracks may become very close leading to significant inter-track interference (ITI). Read-head offset or track mis-registration (TMR) can further degrade the performance of the channel. To investigate the effects of ITI and TMR on the performance of the channel, we have developed a two-dimensional (2D) pulse response simulator for BPM. Simulation results using these pulse responses suggest that equalizers and detectors optimized for zero TMR may not perform well in the presence of TMR. To mitigate the effects of TMR, we propose a modified trellis for the Viterbi algorithm (VA). The modified VA (MVA) takes into account the ITI while computing branch metrics. Simulation results show that the MVA can improve the bit error rate in the presence of TMR.

Inter-track interference (ITI) cancelation is one of the considerable challenges for high areal density (AD) magnetic recording such as in bit-patterned media recording (BPMR) systems. In literature, the two-dimensional (2D) modulation codes have been proposed to cancel the ITI effect [1, 2] which can efficiently improve the overall system performance, e.g., a rate-5/6 2D modulation code [2]. Although the rate-5/6 modulation code ensures that the readback signal of the center track will not be corrupted by severe ITI; however, both the upper and lower tracks can still be interfered by their sidetracks. To improve this shortcoming; therefore, we propose the bit-flipping technique that performs together with the rate5/6 2D modulation code. Here, the relationship between the data encoding condition and soft-information obtained from the soft output Viterbi algorithm (SOVA) detector is utilized to be a criterion for flipping the ambiguous data bits. Simulation results indicate that the proposed system is better than the conventional coded system under with/without media noise and track mis-registration.

The use of bit-patterned media is one of the approaches being investigated to extend magnetic recording densities to 1 Tbit/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and beyond. In patterned media, track pitch may be small causing adjacent tracks to have significant interference on the replay waveform from the main data track. To mitigate the effect of such inter-track interference (ITI), we propose the use of a two-dimensional (2D) generalized partial response (GPR) equalizer. We select both the equalizer and the partial response target using the minimum mean squared error (MMSE) criterion. However, we avoid the need for a 2D Viterbi algorithm by imposing a constraint on the 2D target that forces the adjacent track contributions (in the ideal case) to zero. Simulation results show that this 2D equalizer significantly improves the bit error rate (BER). In this work, the effect of a 2D GPR equalizer on the performance of a patterned media system in the presence of track misregistration (TMR) is also investigated. Based on the simulation results, the 2D equalization method appears to be more tolerant to TMR than the conventional GPR The main drawback of the proposed method is the need for simultaneously acquiring the signals from three adjacent tracks.

To meet the growing demand for higher storage capacities, bit-patterned magnetic recording (BPMR) has emerged as a leading solution for achieving ultra-high user densities (UDs). However, BPMR systems are significantly impacted by two-dimensional (2D) interferences, specifically inter-symbol interference (ISI) and inter-track interference (ITI), which can degrade the quality of the readback signal. This paper introduces a rate-4/5 constructive ITI (CITI) modulation scheme, combined with a Tabu search (TS)-based error correction algorithm, to address the limitations of conventional CITI modulation codes. In the original encoding scheme, some codewords still contain forbidden patterns within their borders. The TS algorithm enhances the performance of the outermost tracks by refining unreliable bits identified through a distance-based reliability metric, which differs from earlier TS-based detectors that were directly used for multi-track detection. A proposed soft-information adjuster is then used to correct the poor reliability of soft information, resulting in improved soft-information reliability and decoding performance. A modified TS detector is also proposed, where the single-bit criterion for selecting the number of input bits is adopted, to improve neighbor selection and better align with the signal characteristics of the inner tracks. Simulation results show that the proposed system can achieve up to 2.7 dB and 4.0 dB improvements in bit error rate (BER) at a user density (UD) of 2.4 Terabits per square inch, compared to conventional uncoded and coded systems, respectively, while also reducing computational complexity. Furthermore, the results also imply that when the recording systems must operate under fluctuations in the size and position of the bit-island, our proposed system can provide superior performance.

Bit-patterned media recording (BPMR) is a promising technology for ultra-high density media, however, there are some challenges that need to be addressed including two-dimensional (2D) interference, and track mis-registration (TMR). The system can experience TMR due to misalignment of the head and the track center. Conventionally, TMR is tackled using a servo system in which the head position offset is estimated by processing the overhead servo sequences before reading the data sequences. However, TMR impairment can also occur when the head is reading data sequences that are beyond the servo mechanism. To address this problem, we proposed TMR detection and correction techniques based on our previous work involving a single-track equalization method for a BPMR system using cross-correlation functions between the single readback signal and each of the training sequences from three adjacent tracks. In this proposed technique, the presence and level of TMR is detected and estimated based on the changes in the value of mean square error (MSE) between the equalized and feedback signals from the detectors after passing through a one-dimensional (1D) target for each sequence. Then, the estimated TMR levels are used in selecting the appropriate equalizer and the generalized partial response (GPR) target pair to tackle the TMR from the readback signal. The simulation results show improvement in the data recovery of a BPMR system using the proposed method when the system is experiencing 2D interference and TMR impairment.

The escalating demand for high-density storage of hard disk drives has prompted the innovation of advanced technologies to significantly boost an areal density (AD). Among these, three-dimensional magnetic recording systems incorporating double recording layers and bit-patterned magnetic recording (BPMR) have currently emerged as one promising solution. Therefore, this article investigates the integration of double-layer magnetic recording and BPMR technologies which is called double-layer BPMR, aiming for a substantial increase in AD. The primary focus lies on minimizing inter-layer interference and mitigating two-dimensional interferences by optimizing bit-island sizes for both upper and lower layers under the incorporation of staggered-like recording media arrangement and an array of magneto-resistive readers. Moreover, we also employ a rate-5/6 modulation code for compensating these effects. Detailed examinations reveal that our proposed system has a superior bit-error rate performance compared with conventional single-layer BPMR system.

Recent magnetic recording technologies have opened the possibility of reaching densities of 10 Tb/in2. A 2-D magnetic recording (TDMR) scheme has pointed out one of the key technologies for increasing areal density. From the viewpoint of signal processing for TDMR, a recording system is desirable or preferable to be capable of allowing to get readback signals from a group of adjacent parallel tracks and detect recorded data written in these tracks simultaneously. This paper proposes a novel signal processing scheme with coding and detection for bit-patterned media recording (BPMR) which is considered to be TDMR using bit-patterned media. Actually, the proposed signal processing scheme for BPMR gets mixed readback signal sequences from the parallel tracks using a single reading head and these readback signal sequences are equalized to a frequency response given by a desired 2-D generalized partial response system. In decoding process, a single maximum likelihood sequence detector is capable of detecting the equalized signal sequence, and it leads to an increase in the effective transfer rate because the recorded data on the parallel tracks are decoded for each time slot.

Track misregistration (TMR) in ultra-high density bit-patterned media recording (BPMR) is one of the crucial problems, because it can severely degrade the overall system performance. In practical, TMR can be detected and adjusted by a servo control loop system. However, this paper proposes to utilize multiple readback signals obtained from the optimized positioning of the two side read head closer to the main read head to improve the TMR prediction process in a multitrack multi-head BPMR system with position jitter noise. In addition, we also propose the soft-information exchange and the bit-flipping techniques for the multitrack data detection, so as to improve the bit-error rate (BER) performance of all three data tracks simultaneously. Simulation results indicate that the proposed system is superior to the conventional system, especially, when the amount of TMR and position jitter is high. Furthermore, we also found that the upper and lower read heads, which are moved closer to the center track by 25% of a track pitch, will provide the best BER performance with and without position jitter noise.

The performance of a rate-4/5 modulation code is evaluated in two-dimensional magnetic recording (TDMR) channels, where a magnetic medium is described by a discrete Voronoi model, and the two-dimensional sensitivity function of the reader is adopted to generate the TDMR readback signal. Since the read-head sensitivity function covers many tracks, it causes intertrack interference (ITI) that can deteriorate the system performance. Therefore, this letter proposes an ITI subtraction scheme in conjunction with the rate-4/5 modulation code in a coded TDMR channel to mitigate the ITI effect embedded in the readback signals before performing an iterative decoding process. We also investigate the data-dependent readback amplitude distributions and evaluate the TDMR system performance via computer simulation. Results show that the proposed scheme helps improve the TDMR system performance, especially when the areal density is high.

The track misregistration (TMR) required to achieve gigabit areal densities is calculated for a set of components based on the average bit error rate for a file. The average error rate is a statistical average, based on the TMR of the file, of the on-track and off-track error rate. The on-track and off-track error rates are dependent on squeeze from adjacent tracks. In this analysis, the average error rate is calculated using measured error rate profiles of the center track. For a file average soft error rate of 1*10/sup -6/, the results show, for a particular head/disk combination designed for gigabit recording and operating at a linear density of 158 kbpi, that a track pitch of 4.0 mu m (3.35 ktpi) can be achieved with a TMR of 0.635 mu m. Obtaining this TMR value in a file is one of the challenges to recording of 1 Gb/in/sup 2/ in magnetic storage products. >

비트 패턴 미디어 (BPM) 저장장치는 기존 자기 기록장치의 한계를 극복하기 위한 기술 중 하나로 주목 받고 있다. 하지만 고밀도의 BPM 저장창치에서는 트랙간의 간섭 (ITI), 심벌간의 간섭 (ISI), 잡음이 비트 오율 (BER)을 심각하게 저하시키는 문제가 있다. 본 논문에서는 ITI와 ISI의 악영향을 경감시키기 위해 축약사상 기반의 단순 반복적 2차원 등화기를 제안한다. 또한 제안한 2차원 등화기에 대한 BPM 저장장치의 채널 특성이 수렴 조건을 만족함을 살펴보았다. 모의실험에서 1차원 등화기와 2차원 등화기의 비트 분리 특성 차이를 보였고, 제안한 등화기의 BER 성능을 다른 등화 방법과 비교하여 평가하였다. 실험결과에 의하면 본 논문에서 제안한 등화기는 적당한 복잡도를 유지하면서 고밀도 BPM 저장장치를 위한 훌륭한 등화기라 할 수 있다.

With the development of 5G technology, programs are gradually moving to cloud services. This leads to an increasing demand for storage. In the field of high-density data storage, bit-pattern media recording (BPMR) is considered a promising approach, as it can expand the data density to 4 Tb/in2. However, in high-density BPMR, bits or magnetic islands are very close to each other, leading to significant intertrack interference (ITI) from the cross-track direction and intersymbol interference (ISI) from the down-track direction. To minimize two-dimensional interference, including ITI and ISI, the serial detector method has been highly effective. However, in this method, the signal at the output of the first decoder is still a hard output. Therefore, we suggest methods to convert the output of the first detector into a soft output. Additionally, we have developed a new form of generalized partial response target to overcome the track mis-registration. The results show that our proposed methods apparently improve bit error rate performance.

Shingled bit-patterned media (BPM) recording is a promising candidate to improve the magnetic recording density above 1 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> while keeping the conventional writer design. However, shingled magnetic recording (SMR) leads to a narrower track pitch, and thus increased inter-track interference motivating the investigation of array readers and 2-D sectors. In this paper, we investigate SMR on BPM with 2-D sectors at the channel density of 3.71 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Use of 2-D sectors allows the possibility of using either hard or soft information from already detected tracks in that 2-D sector to improve the detection performance on the current track. An important question in this context is whether all tracks in a 2-D sector should be of the same nominal width or if there is a potential benefit to using different widths for adjacent tracks. Based on our investigation, we show that alternating track widths [i.e., one less-trimmed (fat) track followed by one more-trimmed (narrow) track] are beneficial to a bit error rate (BER) perspective. In particular, we propose and investigate the use of a bidirectional decision feedback modified Viterbi (BD-DFMV) detector to improve the BER performance. Our simulations indicate that for a hypothetical 2-D sector with 13 tracks and 5% media noise and at the target BER of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> , using alternating track widths and readback with a single reader, the BD-DFMV algorithm can provide about 1.6 dB signal-to-noise ratio (SNR) gain, compared with using the same detection algorithm but on a 2-D sector with uniform track widths. When using a reader array instead of a single reader, this SNR gain improves to about 2.0 dB. The alternating track width structure also appears to provide more robustness to track mis-registration compared with the 2-D uniform track width case.