Two-dimensional Magnetic Recording Research Articles

Deep Neural Network Detection With an ITI Subtraction for Non-Uniform Track-Width Two-Dimensional Magnetic Recording

Deep Neural Network Detection With an ITI Subtraction for Non-Uniform Track-Width Two-Dimensional Magnetic Recording

Non-Linear CNN-Based Read Channel for Hard Disk Drive With 30% Error Rate Reduction and Sequential 200-Mbits/s Throughput in 28-nm CMOS

In this work, we present the world first ASIC implementation of a machine learning (ML)-based data detection channel for hard disk drives (HDDs) using a customized convolutional neural network (CNN). The chip demonstrates a 30.3% error rate reduction over the state-of-the-art HDD detection channel with two-dimensional magnetic recording (TDMR) setting. The work incorporates a full-scale co-optimization flow between the ML algorithms and the customized hardware design for achieving: 1) superior detection accuracy; 2) high-throughput sequential detections; and 3) improved power efficiency at the same time. This work also demonstrates for the first time the non-linear detection capability being embedded into the HDD reading channels. The key features of our chip include: 1) a fully unrolled CNN with dedicated silicon and hardware implementation for each convolutional layer to produce fast sequential time-series data detection at 200-Mbits/s; 2) in total six depthwise-separable convolutional layers implemented with two types of systolic arrays and 100% PE utilization for continuous data flow and high pipelining; 3) integer-only convolutions with reduced-precision weights (8 bit) and internal data (6 bit) for detection at an improved detection power efficiency at 0.86 nJ/bit and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sim $ </tex-math></inline-formula> 4TOPS/W; and 4) customized quantized ReLU (QReLU) units designed to maintain low-precision feature maps and recovery accuracy loss from the model quantization.

Convolutional Neural Network-Based Media Noise Prediction and Equalization for TDMR Turbo-Detection With Write/Read TMR

This article considers a turbo-detection system that includes a convolutional neural network (CNN)-based equalizer, a Bahl-Cocke-Jelinek-Raviv (BCJR) trellis detector, a CNN-based media noise predictor (MNP), and a low-density parity-check (LDPC) channel decoder for two-dimensional magnetic recording (TDMR) in the presence of track misregistration (TMR). The input readings are passed to a 2-D partial response (PR) equalizer, which is either linear or CNN-based. The equalized waveforms are inputs to a 2-D BCJR detector, which generates log-likelihood-ratio (LLR) outputs. The CNN MNP is provided with BCJR LLRs to estimate signal-dependent media noise samples and feed them back to the BCJR. A second pass through the BCJR produces LLRs, which are decoded by an LDPC decoder; achieved areal density (AD) is computed from the LDPC code rate. Spatially varying read- and write-TMR models are developed. We investigate the performance of the proposed system on simulated TDMR readback waveforms generated by grain-switching probabilistic (GSP) simulations. We have two types of GSP datasets. Dataset #1 includes two 10 nm bit length (BL) datasets with 18 and 24 nm track pitch (TP). Dataset #2 has 11 nm BL and 15 nm TP. The comparison baseline is a 1-D BCJR detector with pattern-dependent noise prediction (PDNP) and soft intertrack interference (ITI) subtraction, referred to as 1-D PDNP with LLR exchange. The write-TMR and read-TMR are modeled as cross-track-independent downtrack-correlated random processes. In the presence of joint write- and read-TMR, the proposed turbo-detection system achieves 8.34% and 0.70% AD gain over 1-D PDNP with LLR exchange for TP 18 and 24 nm dataset #1, respectively, and is more robust to TMR compared to the baseline.

ASIC Implementation of Nonlinear CNN-Based Data Detector for TDMR System in 28 nm CMOS at 200 Mbits/s Throughput

In this work, we present the first application-specific integrated circuit (ASIC) implementation of a convolutional neural network (CNN)-based data detection channel for the two-dimensional magnetic recording (TDMR) system in hard disk drive (HDD). This chip is fabricated in TSMC 28 nm complementary metal–oxide–semiconductor (CMOS). TDMR signals captured from a real HDD are used to train and test the network, and the chip is designed to make inferences only. This work presents a systematic pipeline to codesign the neural network structure and the corresponding hardware implementation. To meet the high-throughput requirement, the CNN is fully unrolled with dedicated silicon for each convolution layer using systolic arrays. Quantization-aware training algorithms are used to help improve power efficiency without comprising accuracy. Overall, our chip achieves 200 Mbits/s throughput at 0.9 V supply voltage. In addition, it achieves improved detection accuracy compared to the physical-model-based conventional channel. Our chip consumes 173–219 mW power at 200 M3 clock rate for supply voltage 0.8–0.9 V, respectively.

Reduced Complexity Neural Network Equalizers for Two-Dimensional Magnetic Recording

This article investigates the reduced complexity neural network (NN)-based architectures for equalization over the two-dimensional magnetic recording (TDMR) digital communication channel for data storage. We use realistic waveforms measured from a hard disk drive (HDD) with TDMR technology. We show that the multilayer perceptron (MLP) nonlinear equalizer achieves a 10.91% reduction in bit error rate (BER) over the linear equalizer with cross-entropy (CE)-based optimization. However, the MLP equalizer’s complexity is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$6.6\times $ </tex-math></inline-formula> the linear equalizer’s complexity. Thus, we propose the reduced complexity MLP (RC-MLP) equalizers. Each RC-MLP variant consists of finite-impulse response (FIR) filters, a nonlinear activation, and a hidden delay line. A proposed RC-MLP variant entails only <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.59\times $ </tex-math></inline-formula> the linear equalizer’s complexity while achieving a 8.23% reduction in BER over the linear equalizer.

Multilayer perceptron-based detection for a coded two-dimensional magnetic recording

Recently, magnetic recording technology has been on the verge of reaching its recording density limit. Two-dimensional (2-D) magnetic recording (TDMR) is expected to be a candidate for next-generation magnetic recording because it provides powerful 2-D signal processing tools that are seamlessly compatible with the current technology. However, the degradation in signal quality due to 2-D interference when increasing the recording density far beyond the limit is inevitable even advanced signal processing tools cannot thoroughly handle such interference. In this work, we introduce two architectures of the multilayer perceptron (MLP)-based detection capable of producing soft information in the form of a log-likelihood ratio (LLR) for a coded TDMR system. This also enables turbo decoding capability to take place in the system, which further enhances the system performance. Such an architecture has two structures explicitly designed to execute before and during turbo decoding with a low-density parity-check code. In the first architecture, we employ triple MLP-based detection to process three readback sequences individually. For another architecture, it is designed to collectively process three readback sequences using just single MLP-based detection. The results show that both architectures of proposed detections outperform the systems using the conventional detection based on the Viterbi algorithm and single MLP-based detection achieves slightly better performance than triple MLP-based detection despite having much less complexity.

The Secret Arithmetic of Patterns: A General Method for Designing Constrained Codes Based on Lexicographic Indexing

Constrained codes are used to prevent errors from occurring in various data storage and data transmission systems. They can help in increasing the storage density of magnetic storage devices, in managing the lifetime of electronic storage devices, and in increasing the reliability of data transmission over wires. We recently introduced families of lexicographically-ordered constrained (LOCO) codes. These codes achieve capacity with simple encoding and decoding, and they are easy to reconfigure. In this paper, we generalize our work on LOCO codes by presenting a systematic method that guides the code designer to build any constrained code based on lexicographic indexing once the finite set of data patterns to forbid is known. In particular, we connect the set of forbidden patterns directly to the cardinality of the code and to the rule that uncovers the index associated with a codeword. By doing that, we reveal the secret arithmetic of patterns, and make the code design significantly easier. We design optimal (rate-wise) constrained codes for the new two-dimensional magnetic recording (TDMR) technology. We show notable performance gains as a result of solely applying the new codes. Moreover, we show how near-optimal constrained codes be designed and used to further reduce complexity.

Shingled Magnetic Recording (SMR) and Two-Dimensional Magnetic Recording (TDMR)

Data areal-density has always been a key metric in magnetic recording. An increase in ‘bits per square inch’ allows a higher capacity product to be developed at similar cost. Areal densities have grown at rates as high as 100% per year, but by 2010 these rates had dropped to more like 10%. In response to this slowdown, numerous other avenues were explored including increasing the number of disks in the form factor - an opportunity enabled by the advent of helium-filled drives. Alongside such mechanical improvements, two important innovations were made in the physical recording processes. These innovations were Shingled Magnetic Recording (SMR) and Two Dimensional Magnetic Recording (TDMR). SMR was developed as a response to the difficulty of maintaining fields while writing very narrow tracks with a conventional magnetic head. By keeping the head relatively wide, the field could be kept strong and by overlapping the written tracks, the final track pitch could be reduced. Two Dimensional Magnetic Recording (TDMR) was developed recognizing that increases in track density were also limited by the interference between tracks. By reading back the wanted track(s) with several closely-spaced sensors, the effects of the interference could be greatly mitigated. Both SMR and TDMR are now widely deployed in modern hard disk drives although neither realized the gains originally anticipated.

CNN-Based Machine Learning Channel on TDMR Drive Data

In this article, we demonstrate a convolutional neural network (CNN)-based data detection channel on real data from a commercial hard disk drive (HDD) employed with two-dimensional magnetic recording (TDMR) dual-reader technology. The neural network has two sets of input neurons and is trained using 485 4-kB sectors from the drive. Data detection is performed using the trained network and a one-to-one comparison of bit-error-rate (BER) performance with the HDD channel is systematically conducted. The trained neural network demonstrates comparable or slightly better performance than the state-of-the-art HDD channel. In addition, comparing to detection with a single reader, CNN-machine learning (ML) channel autonomously enables ~6% recording density gain when the second reader is available, and there is no physical modeling needed to manually combine or “fuse” signals from the multiple readers. We believe that the understanding elucidated in this article is crucial for developing more capable, robust, and effective ML-based data detection channels with the potential to realize even greater areal density gain in TDMR systems and higher capacity HDD.

TDMR With Machine Learning Data Detection Channel

In this article, we present a systematic study of using a machine learning (ML) data detection channel consisting of a convolutional neural network (CNN) for data recovery in a two-dimensional magnetic recording (TDMR) setting with two displaced readers. To mimic the actual head skew angle change over the entire disk platter, data recovery over a wide range of inter-track interference (ITI) has been investigated. During training, the CNN-based ML channel only “learns” to detect the main track data although the sampled input signals from both readers are taken as input. It is found that with reasonable training, the ML channel can almost completely eliminate the ITI-caused degradation of bit error rate (BER). Moreover, it is also found that the training processes are only needed at very few head skewing angles, adding to the viability of the possible practical implementation. We believe the understanding elucidated in this article could serve the basis for developing viable and robust ML-based data detection channels leading to significant areal density gain for TDMR technology.

Efficient Parallel Decoding Architecture for Cluster Erasure Correcting 2-D LDPC Codes for 2-D Data Storage

Native 2-D low-density parity-check (LDPC) codes provide 2-D burst erasure correction capability and have promising applications in two-dimensional magnetic recording (TDMR) technology. Though carefully constructed rastered 1-D LDPC codes can provide 2-D burst erasure correction, they are not as efficient as 2-D native codes constructed for handling the 2-D span of burst erasures. Our contributions are twofold. First, we propose a new 2-D LDPC code with girth greater than 4 by generating a parity-check tensor through stacking permutation tensors of size $p\times p\times p$ along with the $i,j,k$ -axes. The permutations are achieved through circular shifts on an identity tensor along different coordinate axes in such a way that it provides a burst erasure correction capability of at least $p\times p$ . Second, we propose a fast, efficient, and scalable hardware architecture for a parallel 2-D LDPC decoder based on the proposed code construction for data storage applications. Through efficient indexing of the received messages in an RAM, we propose novel routing mechanisms for messages between the check nodes and variable nodes through a set of two barrel shifters, producing shifts along two axes. Through simulations, we show that the performance of the proposed 2-D LDPC codes matches a 1-D QC-LDPC code, with a sharp waterfall drop of three to four orders of magnitude over ~0.3 dB, for random errors over code sizes of ~32 kbits or equivalently ~ $180\times 180 2$ -D arrays. Furthermore, we prove that the proposed native 2-D LDPC codes outperform their 1-D counterparts in terms of 2-D cluster erasure correction ability. For $p=16$ and code arrays of size $48\times 48$ , we implemented the proposed design architecture on a Kintex-7 KC-705 field-programmable gate array (FPGA) kit, achieving a significantly high worst case throughput of 12.52 Gb/s at a clock frequency of 163 MHz.

Convolutional Neural Network Based Symbol Detector for Two-Dimensional Magnetic Recording

Data detection in magnetic recording (MR) channels can be viewed as an image processing problem, proceeding from the 2-D image of readback bits, to higher level abstractions of features using convolutional layers that finally allow classification of individual bits. In this work, convolutional neural networks (ConvNets) are employed in place of the typical partial response equalizer and maximum-likelihood detector with noise prediction to directly process the un-equalized readback signals and output soft estimates. Several variations of ConvNets are compared in terms of network complexity and performance. The best performing ConvNet detector with two convolutional layers provides a data storage density of up to 3.7489 Terabits/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> on a low track pitch two-dimensional MR channel simulated with a grain-flipping-probability (GFP) model. An alternate ConvNet architecture reduces the network complexity by about 74%, yet results in only a 2.09% decrease in density compared to the best performing detector.

Non-Binary Constrained Codes for Two-Dimensional Magnetic Recording

The two-dimensional magnetic recording (TDMR) technology promises storage densities of $10$ terabits per square inch. However, when tracks are squeezed together, a bit stored in the two-dimensional (TD) grid suffers inter-symbol interference (ISI) from adjacent bits in the same track, and inter-track interference (ITI) from nearby bits in the adjacent tracks. A bit is highly likely to be read incorrectly if it is isolated in the middle of a $3 \times3$ square; surrounded by its complements, horizontally and vertically. We improve the reliability of TDMR systems by designing two-dimensional constrained codes that prevent these square isolation patterns. We exploit the way TD read heads operate to design our codes, and we focus on TD read heads that collect signals from three adjacent tracks. We represent the two-dimensional square isolation constraint as a one-dimensional constraint on an alphabet of eight non-binary symbols. We use this new representation to construct a non-binary lexicographically-ordered constrained code where one third of the information bits are unconstrained. Our TD constraint codes are capacity-achieving, and the data protection is achieved with redundancy less than $3\%$ and at modest complexity.

A Multiple-Input Multiple-Output Extension of the Mueller and Müller Timing Error Detector

We present a multiple-input multiple-output (MIMO) extension of the timing error detector (TED) that was originally developed by Mueller and Müller for synchronization on pulse-amplitude modulation over 1-D channels. This MIMO extension applies to the joint detection of multiple asynchronous tracks from one or more readback waveforms in a two-dimensional magnetic recording (TDMR) channel. We provide accurate theoretical expressions of the performance of the proposed scheme and verify its applicability on a modern MIMO TDMR channel. Performance results show that the proposed TED outperforms the conventional 1-D TED that completely ignores the presence of crosstalk interference in MIMO channels.

Automatically Resolving Intertrack Interference With Convolution Neural Network Detection Channel in TDMR

Convolution neural network (CNN) is used as the data detection channel for two-dimensional magnetic recording (TDMR). We demonstrate that by only feeding interfered multireader signals as well as the target binary data at supervised learning, it is possible for CNN to automatically resolve the intertrack interference (ITI) in a noisy environment without any physical modeling. It is worth mentioning that throughout the entire training/learning process, CNN never receives ITI-free waveforms as target nor is explicitly “instructed” to resolve ITI. We illustrate that the nonlinear detection capability plays the most important role for CNN to effectively “learn” the right correlation between multiple read channels under heavy noise. Therefore, ITI can be completely eliminated as long as the noise exhibits similar correlation, while the white electronic noise completely disturbs this correlation and “decorrelates” the channels, hence posing most serious limitations toward ITI mitigation capability for CNN.

Deep Neural Network a Posteriori Probability Detector for Two-Dimensional Magnetic Recording

In two-dimensional magnetic recording (TDMR) channels, intersymbol interference (within and between tracks) and pattern-dependent media noise are impediments to reaching higher areal density. We propose a novel deep neural network (DNN)-based a posteriori probability (APP) detection system with parallel multi-track detection for TDMR channels. The proposed DNN-based APP detector replaces the trellis-based Bahl–Cocke–Jelinek–Raviv (BCJR) or Viterbi algorithm and pattern-dependent noise prediction (PDNP) in a typical TDMR scenario, in which it directly outputs log-likelihood ratios of the coded bits and iteratively exchanges them with a subsequent channel decoder to minimize bit error rate (BER). We investigate three DNN architectures—fully connected DNN, convolutional neural network (CNN), and long short-term memory (LSTM) network. The DNN’s complexity is limited by employing linear partial response (PR) equalizer pre-processing. The best performing DNN architecture, CNN, is selected for iterative decoding with a channel decoder. Simulation results on a grain-flipping-probability (GFP) media model show that all three DNN architectures yield significant BER reductions over a recently proposed 2D-PDNP system and a previously proposed local area influence probabilistic (LAIP)-BCJR system. On a GFP model with 18 nm track pitch and 11.4 Teragrains/in2, the CNN detection system achieves an information areal density of 3.08 Terabits/in2, i.e., a 21.72% density gain over a standard BCJR-based 1D-PDNP; the CNN-based system also has $3\times $ the throughput of 1D-PDNP, yet requires only 1/10th the computer run time.

Performance Analysis and Optimization of Spatially Coupled Protograph-Based Low-Density Parity-Check Codes for Two-Dimensional Magnetic Recording Systems

As a class of convolutional-based low-density parity-check (LDPC) codes, spatially coupled protograph (SC-P) codes not only can exhibit outstanding error performance but also can realize low-complexity implementation. Motivated by the prominent superiorities, SC-P codes have been intensively investigated in various communication environments. However, no research works regarding SC-P codes in the magnetic recording (MR) scenarios have been done so far. To explore such an issue mentioned previously, this article carries out a comprehensive study on the SC-P codes in the two-dimensional magnetic recording (TDMR) systems. Specifically, a turbo-like extrinsic information transfer (EXIT) algorithm is conceived for the SC-P-coded TDMR systems. With the help of such an algorithm, we evaluate the convergence performance (i.e., decoding thresholds) for conventional SC-P codes over TDMR channels with turbo equalization and illustrate that such codes should be re-constructed to attain better performance. Therefore, we develop an optimization scheme to generate a novel class of SC-P codes, called enhanced SC-P codes, which can exhibit promising decoding thresholds without losing the linear-minimum-distance superiority. The convergence-performance analyses and simulated results reveal that such enhanced SC-P codes can obtain more desirable coding gains in contrast to the conventional SC-P codes and the state-of-the-art protograph codes for the whole signal-to-noise-ratio (SNR) range under study. The excellent performance and simple implementation make the enhanced SC-P codes a very competitive error-correction solution for the next-generation TDMR devices.

Read Channel Modeling and Neural Network Block Predictor for Two-Dimensional Magnetic Recording

Various schemes have been investigated to study the modeling of recording media, the writing/reading process, and the information recovery in magnetic recording systems, such as two-dimensional magnetic recording (TDMR) and bit-patterned media recording (BPMR). As the bit scales down to the size of the media particles, the channel modeling and simulation become more complicated because of the increasing media noise. Meanwhile, it relies on more powerful 2-D signal-processing algorithms error control codes. The contributions of this article are three-fold: 1) we improve the read process in terms of our proposed reliability for read response that captures the effects of inter-track interference (ITI), inter-symbol interference (ISI), and the randomness of grains; 2) we present a neural network block predictor (NNBP) and a logistic regression method to provide heuristic methods in studying data recovery; and 3) we investigate the most possible harmful transitions and patterns. Results show the NNBP achieves good performance and is good at detecting those totally isolated bits that are thought to be bad patterns from an intuitive point of view.

Joint Four-Reader Array Equalization and Detection for a Single Track in TDMR

Two-dimensional magnetic recording (TDMR) by shingled magnetic recording (SMR) is one of the promising technologies to achieve a magnetic recording areal density (AD) of 10 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The readback signal of TDMR suffers severe 2-D inter-symbol interference (2-D ISI). At ultra-high AD, reader array is proposed to process the signals from the 2-D ISI channel because it can acquire multiple interfered signal streams simultaneously from the adjacent tracks. In this article, we propose a novel architecture for signal detection, which uses a four-reader array to recover the recording data. The auxiliary reader of the four-reader array can offer additional soft information of bits on the detected track, and this information can be used to improve the bit error rate (BER) performance. We consider three approaches to utilize the auxiliary reader and investigate the position of the auxiliary reader. Simulation results show that the proposed approach outperforms both the conventional single-reader detection and three-reader array detection. The auxiliary reader is set with an offset of 10% track pitch and can obtain a significant improvement of BER performance when the signal-to-noise rates (SNRs) of all the four readers are the same.

Data Recovery for Multilayer Magnetic Recording

Multilayer magnetic recording (MLMR) is a next-generation technology that has the potential to enhance the longevity of magnetic recording technology by storing data on multiple layers that are stacked on top of one another. The challenges associated with the development of MLMR fall into two main categories: the challenges of writing to multiple layers and the challenges of reading back from multiple layers. As there is already a fair amount of existing work addressing the former, in this article we target the latter by building and testing detection schemes that are able to separate the signals from multiple layers that are mixed together during the readback. In this initial work, we consider a two-layer system. The resolution of the bottom layer is worse than that of the top due to the increased separation of the bottom layer from the reader. We assume a geometry of two single-width tracks on the top-layer straddling a double-width track on the bottom layer and with intersymbol interference (ISI) response on the bottom layer having half the amplitude and double the length of that on the top-layer. We examine the performance of two candidate detection algorithms, a Viterbi-based algorithm operating on a trellis, and a least-squared (LS) algorithm that attempts to invert the effect of the channel’s interference. We evaluate the error rate performance of these detection schemes using a common channel model that sums the ISI and intertrack interference (ITI) components from each of the layers. The main result from this work is that 14.5% density gains over the conventional perpendicular magnetic recording (PMR) and 7.6% gains over two-dimensional magnetic recording (TDMR) could be possible for the novel MLMR system.