Two-dimensional Magnetic Recording Channel Research Articles

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.

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.

Signal Processing and Coding Techniques for 2-D Magnetic Recording: An Overview

Two-dimensional magnetic recording (TDMR) is an emerging storage technology that aims to achieve areal densities on the order of 10 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , mainly driven by innovative channels engineering with minimal changes to existing head/media designs within a systems framework. Significant additive areal density gains can be achieved by using TDMR over bit patterned media (BPM) and energy-assisted magnetic recording (EAMR). In TDMR, the sectors are inherently 2-D with reduced track pitch and bit widths, leading to severe 2-D intersymbol interference (ISI). This necessitates the development of powerful 2-D signal processing and coding algorithms for mitigating 2-D ISI, timing artifacts, jitter, and electronics noise resulting from irregular media grain positions and read-head electronics. The algorithms have to be eventually realized within a read/write channel architecture as a part of a system-on-chip (SoC) within the disk controller system. In this work, we provide a wide overview of TDMR technology, channel models and capacity, signal processing algorithms (detection and timing recovery), and error-correcting codes attuned to 2-D channels. The innovations and advances described not only make TDMR a promising future technology, but may serve a broader engineering audience as well.

2-D LDPC Codes and Joint Detection and Decoding for Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording (TDMR) is a promising technology for boosting areal densities (ADs) using sophisticated signal processing algorithms within a systems framework. The read/write channel architectures have to effectively tackle 2-D inter-symbol interference (ISI), 2-D synchronization errors, media and electronic noise sources, as well as thermal asperities resulting in burst erasures. The 1-D low-density parity check (LDPC) codes are well studied to correct large 1-D burst errors/erasures. However, such 1-D LDPC codes are not suitable for correcting 2-D burst errors/erasures due to the 2-D span of errors. In this paper, we propose construction of a native 2-D LDPC code to effectively correct 2-D burst erasures. We also propose a joint detection and decoding engine based on the generalized belief propagation algorithm to simultaneously handle 2-D ISI, as well as correct bit/burst errors for TDMR channels. This paper is novel in two aspects: 1) we propose the construction of native 2-D LDPC codes to correct large 2-D burst erasures and 2) we develop a 2-D joint signal detection-decoder engine that incorporates 2-D ISI constraints, and modulation code constrains along with LDPC decoding. The native 2-D LDPC code can correct >20% more burst erasures compared with the 1-D LDPC code over a 128 $\times $ 256 2-D page of detected bits. Also, the proposed algorithm is observed to achieve a signal-to-noise ratio gain of >0.5 dB in bit error rate performance (translating to 10% increase in ADs around the 1.8 Tb/in2 regime with grain sizes of 9 nm) as compared with a decoupled detector-decoder system configuration over a small 2-D LDPC code of size 16 $\times $ 16. The efficacy of our proposed algorithm and system architecture is evaluated by assessing AD gains via simulations for a TDMR configuration comprising of a 2-D generalized partial response over the Voronoi media model assuming perfect 2-D synchronization.

Joint Timing Recovery and Signal Detection for Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording (TDMR) is a promising technology for boosting areal densities using sophisticated signal processing algorithms within a systems framework. The channel impairments comprise of 2-D intersymbol interference (ISI), 2-D synchronization errors along with media, and electronic noise sources, making it challenging for designing optimum algorithms and architectures for read/write channels. In this paper, we propose a novel iterative joint timing and signal detection algorithm to handle synchronization errors along with the 2-D ISI for TDMR channels. Our work is novel in two aspects: 1) we develop a discrete timing error model using 2-D random walk by incorporating correlated timing drifts due to phase and frequency offsets and 2) we develop a 2-D joint timing and signal detection engine for handling 2-D ISI constraints along with timing errors toward near maximum likelihood detection. The proposed 2-D joint timing-detection algorithm can be iteratively configured and observed to achieve a significant signal-to-noise ratio gain of > 1.2 dB in bit error rate performance (translating to similar to 10% increase in areal densities around the 1 Tb/in(2) regime with the grain sizes of 10 nm and the bit sizes of 25x25 nm) at the output of 2-D soft-output Viterbi algorithm (SOVA) as compared with a standalone timing loop coupled to a 2-D detector in an open-loop configuration. The efficacy of our proposed algorithm and system architecture is evaluated via simulations for TDMR configurations comprising of a 2-D generalized partial response equalization along the 2-D SOVA with data-dependent noise prediction capability over the Voronoi media model.

Exploring Two-Dimensional Magnetic Recording Gain Constraints

Two-dimensional magnetic recording (TDMR) offers the opportunity to provide areal density (AD) gain, but questions were unanswered as to how the gain is achieved and what can be done to maximize the gain from this new technology. In this paper, we offer some reasons why different investigators might report different AD gain opportunities. We present data collected on a spin stand with two reader heads and processed with a commercially available field programmable gate array TDMR channel. The implications of this paper should provide guidelines on reader geometries, placement, and performance.

An Intertrack Interference Subtraction Scheme for a Rate-4/5 Modulation Code for Two-Dimensional Magnetic Recording

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.

Novel Joint Detection and Decoding Schemes for TDMR Channels

Two-dimensional magnetic recording (TDMR) relies on advanced signal processing and coding techniques to enable storage of data at higher densities. Various detection and decoding schemes have been proposed in the literature. In this paper, a recently proposed joint detection and decoding scheme known as the joint Viterbi detector decoder (JVDD) is presented for TDMR channels. The JVDD operates on a trellis and attempts to find a sequence in the trellis that belongs to a legal codeword with minimum metric. It does so by using a metric thresholding and parity checking technique over the same trellis structure. The iterative detector/decoder consisting of a soft-output Viterbi algorithm detector and low-density parity check decoder is used as a performance benchmark for the JVDD. In this paper, we perform the comparison with various equalization/detection techniques consisting of: 1) a 1-D general partial response equalization scheme followed by a 1-D-detector as used in today’s Partial Response Maximum Likelihood Detection (PRML) channels; 2) a 2-D equalization scheme that equalizes to a 1-D target [fully equalizing away the intertrack interference (ITI)], followed by a series of parallel 1-D-detectors to handle the intersymbol interference (ISI); and 3) a 2-D-equalization scheme followed by 2-D detector to combat both ITI and ISI.

Investigation of Two-Dimensional Magnetic Recording (TDMR) With Position and Timing Uncertainty at 4 Tb/in$^{2}$

The feasibility of two-dimensional magnetic recording (TDMR) at 4 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> 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 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">12</sup> grains/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> 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.

Signal Processing for Near 10 Tbit/in$^{2}$ Density in Two-Dimensional Magnetic Recording (TDMR)

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> 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/in<formula formulatype="inline"><tex Notation="TeX">$^{2}$</tex></formula>. 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/in<formula formulatype="inline"><tex Notation="TeX">$^{2}$</tex> </formula> for media with a 20 <formula formulatype="inline"><tex Notation="TeX">${\rm Tgrains/in}^{2}$</tex></formula> grain density. </para>

Channel Modeling and Capacity Bounds for Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording (TDMR) differs from traditional track recording in that the bit-size-to-grain-size ratio is drastically reduced so that the channel bits are roughly of the same sizes as those of the magnetic media grains. This is envisioned to be achieved by shingled writing, a write-process in which the corner-writer partially overwrites the previously written adjacent track, effectively writing very closely spaced narrow tracks with no guard bands. Since the tracks are very narrow, they can be read by an array of read-elements whose spacing is equal to the narrow track pitch, creating a two-dimensional (2-D) array of readback signals (the two dimensions being the cross-track and the down-track dimensions). In the absence of an array of read elements, the same 2-D readback can be obtained by progressive scans of a single read element that reads one narrow track at a time and stores the readback signal in a 2-D array. In this paper, we present simple magnetic grain media models and shingled-write process models that capture the essence of TDMR. We assume that the granular recording medium consists of randomly shaped tiles (each tile represents a grain), randomly covering the medium plane. We then derive a suitable 2-D read/write process model. Using proper information-theoretic inequalities and bounding techniques, we derive methods to bound the capacities of TDMR channels. The results reveal that information capacities in excess of 0.6 user bits per grain are possible to attain over TDMR channels.

Channel Models and Detectors for Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording (TDMR) is a novel recording architecture intended to support densities beyond those of conventional recording systems. The gains from TDMR come primarily from more powerful coding and signal processing algorithms that allow the bits to be packed more tightly on the disk, and yet be retrieved with acceptable error rates. In this paper, we present some preliminary results for an advanced channel model based on micromagnetic simulations, coined the Grain Flipping Probability model. This model requires a one-time computationally complex characterization phase, but subsequently provides fast and accurate two-dimensional (2-D) readback waveforms that include effects captured from micromagnetic simulations and the statistical effects derived from the granularity of the recording medium. We also show the performance of several detectors over a pre-existing TDMR channel model directly as a function of channel density rather than the signal-to-noise ratio (SNR).

Read Channel Modeling for Detection in Two-Dimensional Magnetic Recording Systems

In this paper, we describe a read channel model for detector design for two-dimensional magnetic recording (TDMR) system, a novel strategy for recording at upto 10 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . We describe a scheme for (1) modeling of the recording medium, (2) modeling of the write/readback process, and (3) an experimental method for the characterization of noise in the TDMR channel, occurring due to irregularities in the bit-boundaries in the recording medium, that can be used for detection purposes.