Partial Response Maximum Likelihood Research Articles

Track Misregistration Mitigation Using CNN-Based Method on Single-Reader/Two-Track Reading BPMR Systems

One of the problems that cause a decrease in the performance of the ultra-high bit-patterned magnetic recording (BPMR) system is track misregistration (TMR). Since the gap between data tracks is extremely narrow, it easily affects keeping the reader in the desired position. Therefore, this paper proposes the track misregistration mitigation included the estimation and correction techniques on single-reader/two-track reading (SRTR) BPMR using only a readback signal. The TMR estimation technique uses the convolutional neural network (CNN) to estimate the TMR level by the histograms of the readback signal enabling minimization of the complexity of the CNN structure and amount of training time. The estimated TMR levels obtained from the proposed CNN-histogram-based method will then be utilized to detect the estimated recorded bit by the CNN-based data detector. The simulation shows that our proposed system provides better TMR prediction accuracy even though the system has to face higher media noise. Furthermore, the CNN-based data detectors perform superior to the partial response maximum likelihood (PRML) based data detector, especially in strong electronic noise situations and the severe imperfection of recording media.

A Study of Three-Dimensional Equalization for Reproducing a Double-Layer Magnetic Recording Medium

To increase the recording density of hard disk drives (HDD), three-dimensional (3-D) magnetic recording with multiple recording layers is attracting much attention as a next-generation recording method. We have reported that the two-dimensional (2-D) partial response maximum likelihood (PRML) can achieve a good BER performance using the PR channel obtained from the differential-phase bit response in the 3-D magnetic recording system with a double recording layer. In this study, we realize the 3-D equalization by the 2-D finite impulse response (FIR) (2-D FIR) filter and 2-D PRML system over two layers and evaluate the 3-D equalization to further increase the recording density. The transfer function of the 2-D PR channels is determined by the response for the in-phase or differential-phase bits in a double-layer magnetic recording medium. The results show that the 2-D PRML channels with 3-D equalization based on the differential-phase transfer function achieve a good bit error rate (BER) performance for system noise.

A Study of Channel Time-Domain Response on Equalization for Reproducing a Double-Layer Magnetic Recording Medium

To increase the recording density of hard disk drives (HDD), 3-D magnetic recording using microwave-assisted magnetic recording (MAMR) with multiple recording layers is attracting much attention as a next-generation recording method. Developing a signal processing method for 3-D magnetic recording using the multiple conventional recording layers and an magnetoresistive (MR) head reading system is desired. In this article, we evaluate 2-D partial response maximum likelihood (PRML) channels by the bit error rate (BER) performance, where the transfer function of the PR channel is determined by the response of the in-phase or differential-phase bits between layers in a double-layer magnetic recording medium. The results show that a BER of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10^{-4}$ </tex-math></inline-formula> can be achieved by the PRML channel determined by the differential-phase response with the signal-to-noise ratio (SNR) greater than 26.0 dB for system noise.

Asynchronous Multitrack Detection With a Generalized Partial-Response Maximum-Likelihood Strategy

Asynchronous Multitrack Detection With a Generalized Partial-Response Maximum-Likelihood Strategy

Iterative Multihead Multitrack Detection Scheme for Bit-Patterned Media Recording

An iterative multi-head multi-track detection scheme for bit patterned media recording is proposed in this paper. The proposed scheme employs two iterative strategies with the multi-head multi-track detection where three tracks are simultaneously processed to accurately estimate the channel with TMR and effectively detect the data by using inter-track interference (ITI) information with high reliability. The first outer iteration aims to compensate for the track misregistration (TMR) effect, and the second inner iteration aims to improve the reliability of the data. In outer iteration, the TMR effect is compensated by modifying the generalized partial response (GPR) target to a channel that reflects the TMR estimated by a TMR estimator using expectation and maximization algorithm. In inner iteration, iterative equalization and decoding (IED) is conducted between the two-dimensional partial response maximum likelihood detector and the low-density parity check decoder based on the revised GPR target. Since each track has different channel performance according to the amount of ITI information in the multi-track detection, we design the GPR target and the code rate separately for each track to maximize the overall channel performance. The bit error rate performances of the proposed IED scheme are compared with the conventional IED scheme when areal density is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2 Tb/in^{2}$</tex-math></inline-formula> . Simulation results show that the proposed IED scheme has more than 2dB gains compared with the conventional IED scheme for 30 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\%$</tex-math></inline-formula> TMR.

Signal Detection Using Extrinsic Information From Neural Networks for Bit-Patterned Media Recording

To meet the demand for storing large amounts of data, there has been a stronger focus on increasing the recording density of a hard disk drive (HDD). While conventional HDD suffers from thermal effect and superparamagnetic limit, bit-patterned media recording (BPMR) has the potential to resolve these problems and is capable of increasing areal density (AD) beyond 1 terabit per square inch. To increase the AD of BPMR, the distance between islands in both the down- and cross-track directions must be reduced. Consequently, the decreased bit period and track pitch induce more intersymbol interference (ISI) and intertrack interference (ITI), which degrade the bit error rate (BER) performance. In this study, extrinsic information obtained from a multilayer perceptron (MLP) equalizer is used as a priori information in a partial response maximum-likelihood (PRML) detector to improve the detection performance of BPMR. The proposed detection scheme shows better performance compared to both the MLP equalizer and conventional PRML alone. In addition, it was found that the proposed detector provides improved performance when track misregistration (TMR) occurs.

Design of high throughput asynchronous FIR filter using gate level pipelined multipliers and adders

SummaryThis work presents the design of an asynchronous digital finite impulse response (FIR) filter suitable for high‐performance partial response maximum likelihood (PRML) read channel ICs. A high throughput, low latency FIR filter is the basic requirement for the equalization process in read channels. To achieve the enhancement in speed and reduction in latency of the FIR filter, its computational units are deeply pipelined using high‐capacity hybrid (HC‐hybrid) logic pipeline method. The designed FIR filter has been simulated using UMC‐180 nm and UMC‐65 nm technologies. Simulation results show that the asynchronous digital FIR filter can operate up to a throughput of 1.17 Giga items/s in 180 nm and 2.3 Giga items/s in 65 nm technology yet with the latency in the order of ns.

Decision feedback equalizer for holographic data storage.

Holographic data storage (HDS) has attracted much attention as a next-generation storage medium. Because HDS suffers from two-dimensional (2D) inter-symbol interference (ISI), the partial-response maximum-likelihood (PRML) method has been studied to reduce 2D ISI. However, the PRML method has various drawbacks. To solve the problems, we propose a modified decision feedback equalizer (DFE) for HDS. To prevent the error propagation problem, which is a typical problem in DFEs, we also propose a reliability factor for HDS. Various simulations were executed to analyze the performance of the proposed methods. The proposed methods showed fast processing speed after training, superior bit error rate performance, and consistency.

High Symbol Rate Signal Generation and Detection With Linear and Nonlinear Signal Processing

Digital signal processing is the core functional block in beyond-100G transmission systems with a high symbol rate and/or high spectral efficiency. We review recent progress on high symbol rate signal generation and detection, and corresponding advanced algorithms for signal equalization and compensation at the transmitters (Tx) and the receivers (Rx), respectively. Thanks to the joint Tx-side optical pre-equalization (pre-EQ) and Rx-side partial response maximum likelihood sequence estimation, significant performance improvement can be achieved by reducing the penalty caused by bandwidth limitations of the optical and electronic components. A joint pre-EQ and look-up table predistortion technique is also reviewed in this paper, which is demonstrated to be an effective method for mitigating devices' nonlinearity impairment. We exemplify how these advanced algorithms enable high symbol rate beyond-100G transmission systems with signal generation based on either electronic time-division multiplexing or digital-to-analog converters.

Performance of the hybrid MLPNN based VE (hMLPNN-VE) for the nonlinear PMR channels

This paper proposes a hybrid of multilayer perceptron neural network (MLPNN) and Volterra equalizer (VE) denoted hMLPNN-VE in nonlinear perpendicular magnetic recording (PMR) channels. The proposed detector integrates the nonlinear product terms of the delayed readback signals generated from the VE into the nonlinear processing of the MLPNN. The detection performance comparison is evaluated in terms of the tradeoff between the bit error rate (BER), complexity and reliability for a nonlinear Volterra channel at high normalized recording density. The proposed hMLPNN-VE outperforms MLPNN based equalizer (MLPNNE), VE and the conventional partial response maximum likelihood (PRML) detector.

A two-dimensional partial response maximum likelihood detection scheme for misalignment compensation in holographic data storage systems

A two-dimensional (2D) partial response maximum likelihood (PRML) detection scheme for misalignment compensation for holographic data storage systems is proposed. In the proposed detection scheme, a misalignment estimator and a predetermined table are added to the conventional 2D PRML scheme to estimate and reflect the effect of misalignment in the vertical and horizontal directions, respectively. In the vertical detection, the misalignment estimator located behind the vertical 2D equalizer and one-dimensional PRML detector estimates the misalignment by the adaptive least-mean-square algorithm (LMS). To improve the estimation accuracy, the misalignment is estimated iteratively by modifying the vertical equalizer coefficients reflecting the estimated misalignment. By considering the estimated misalignment, the vertical 2D equalizer coefficients, horizontal 2D equalizer coefficients, and 2D partial response (PR) target are selected among the predetermined table. In the predetermined table, the vertical and horizontal 2D equalizer coefficients for various misalignments were previously computed on the basis of the misalignment and 2D PR target by the LMS. By employing the horizontal 2D equalizer coefficients and 2D PR target reflecting the misalignment in the horizontal detection, the effect of misalignment is effectively mitigated. Simulation results show that the proposed scheme has more than 3 dB gains than the conventional scheme in the 10% misalignment in the horizontal and vertical directions.

Two-Track Reading With a Wide-Track Reader for Shingled Track Recording

In order to avoid the requirement for a narrow track reader in high track density shingled recording, decoding schemes for two-track simultaneous reading, which allows a wide-track reader to be used, are investigated. The strong intertrack interference (ITI) is a major difficulty to be overcome. To avoid ITI, the recorded magnetization in the two tracks should be staggered. Two possible 2-D decoding techniques are provided: 1) recursive decoding by oversampling and 2) Partial Response Maximum Likelihood (PRML) detection. Because data in two track are read simultaneously, the data transfer rate is two times higher than in regular single-track reading. Despite the high data rate, the requirement on the reader for high readback resolution, such as a small shield gap length, magnetic spacing, can be mitigated.

Generalized Partial Response Equalization and Data-Dependent Noise Predictive Signal Detection Over Media Models for TDMR

Two-dimensional magnetic recording (2-D TDMR) is an emerging technology that aims to achieve areal densities as high as 10 Tb/in2 using sophisticated 2-D signal-processing algorithms. High areal densities are achieved by reducing the size of a bit to the order of the size of magnetic grains, resulting in severe 2-D intersymbol interference (ISI). Jitter noise due to irregular grain positions on the magnetic medium is more pronounced at these areal densities. Therefore, a viable read-channel architecture for TDMR requires 2-D signal-detection algorithms that can mitigate 2-D ISI and combat noise comprising jitter and electronic components. Partial response maximum likelihood (PRML) detection scheme allows controlled ISI as seen by the detector. With the controlled and reduced span of 2-D ISI, the PRML scheme overcomes practical difficulties such as Nyquist rate signaling required for full response 2-D equalization. As in the case of 1-D magnetic recording, jitter noise can be handled using a data-dependent noise-prediction (DDNP) filter bank within a 2-D signal-detection engine. The contributions of this paper are threefold: 1) we empirically study the jitter noise characteristics in TDMR as a function of grain density using a Voronoi-based granular media model; 2) we develop a 2-D DDNP algorithm to handle the media noise seen in TDMR; and 3) we also develop techniques to design 2-D separable and nonseparable targets for generalized partial response equalization for TDMR. This can be used along with a 2-D signal-detection algorithm. The DDNP algorithm is observed to give a 2.5 dB gain in SNR over uncoded data compared with the noise predictive maximum likelihood detection for the same choice of channel model parameters to achieve a channel bit density of 1.3 Tb/in2 with media grain center-to-center distance of 10 nm. The DDNP algorithm is observed to give $\sim$ 10% gain in areal density near 5 grains/bit. The proposed signal-processing framework can broadly scale to various TDMR realizations and areal density points.

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.

Performance evaluation of signal dependent noise predictive maximum likelihood detector for two-dimensional magnetic recording read/write channel

Two-dimensional magnetic recording is affected by the inter-track interference (ITI) from the adjacent tracks. We investigate the improvement of partial response maximum likelihood (PRML) systems with signal dependent noise predictor (SDNP) in the bit error rate performance. The systems reduce the influence of ITI by two dimensional finite impulse response filter using the waveforms reproduced by triple readers from the adjacent tracks. The results show that the SDNP provides larger improvement to PR(2,6,1)ML system compare with PR1ML system.

Data page reconstruction method based on two-dimensional soft output Viterbi algorithm with self reference for holographic data storage

This study introduces a two-dimensional (2D) partial response maximum likelihood (PRML) method to reconstruct a degraded data page having 2D inter-symbol interference for holographic data storage. The proposed 2D PRML method consists of 2D partial response (PR) target, 2D equalizer using least mean square algorithm, and 2D soft output Viterbi algorithm (SOVA) having just two one-dimensional (1D) SOVAs in horizontal and vertical directions. To accurately organize a trellis diagram of the 1D SOVA in structural accordance with the 2D PR target, this study proposes the self-reference process for the extrinsic information in the 1D SOVA. Finally, simulation results show that the proposed method has bit error rate performance similar to that of modified 2D SOVA having four 1D SOVAs despite the relatively low computational complexity. Moreover, parallel processing is possible in the two 1D SOVAs through the self-reference process.

Recording characteristics of high-density thin optical disk using near-field optical recording

We report on the recording characteristics of a near-field optical recording thin optical disk (NFR-TOD). We proposed a new cooling-less-type write strategy for recording, applied it to the NFR-TOD experimental system, and also applied a partial response maximum likelihood (PRML) signal processing, which was evaluated and optimized the PR coefficient for playback signals of the prototype NFR-TOD. The NFR-TOD has a track pitch of 160 nm and improved recording characteristics. The experimental results of the prototype NFR-TOD and the system indicate sufficiently low bit error rates (bERs) for recorded data at a fourfold higher recording density than the current Blu-ray disk.

Improved partial response maximum likelihood method combining modulation code for signal waveform modulation multi-level disc

In this paper, we describe an improved adaptive partial response maximum likelihood (PRML) method combining modulation code for signal waveform modulation multi-level disc. This improved adaptive PRML method employs partial response equalizer and adaptive viterbi detector combining modulation code. Compared with the traditional adaptive PRML detector, the improved PRML detector additionally employs illogical sequence detector and corrector. Illogical sequence detector and corrector can avoid the appearance of illogical sequences effectively, which do not follow the law of modulation code for signal waveform modulation multi-level disc, and obtain the correct sequences. We implement the improved PRML detector using a DSP and an FPGA chip. The experimental results show good performance. The higher efficient and lower complexity can be obtained by using the improved PRML method than by using the previous PRML method. Meanwhile, resource utilization of the improved PRML detector is not changed, but the bit error rate (BER) is reduced by more than 20%.

A 6/9 Four-Ary Modulation Code for Four-Level Holographic Data Storage

A holographic data storage (HDS) system can provide high storage capacity, faster transmission, and shorter access time. However, there are two major concerns with such systems: two-dimensional (2D) inter-symbol interference (ISI) and inter-page interference (IPI). The use of existing partial response maximum likelihood (PRML) detection can somewhat mitigate the problem of ISI. However, if the channel is subject to misalignment, the performance of PRML detection can be degraded. This problem can be remedied by a modulation code. Thus, this paper proposes a 6/9 modulation code, which mitigates ISI, and a modulation/demodulation scheme.

Two-Dimensional Soft Output Viterbi Algorithm with a Variable Reliability Factor for Holographic Data Storage

In a practical holographic data storage system, the reconstruction process for a data page should account for the processing time as well as the bit error rate (BER) performance. To improve both aspects, we introduce two-dimensional (2D) partial response maximum likelihood composed of a 2D partial response (PR) target including diagonal elements and a 2D soft output Viterbi algorithm (SOVA) with a variable reliability factor. The 2D SOVA performs two one-dimensional (1D) SOVAs in structural accordance with the 2D PR target where extrinsic information uses the expected value calculated on a synchronization pattern. Finally, the 2D SOVA exports a weighted average using the reliability factor that is updated similarly as the optimization scheme for each page. The simulation results show that the proposed method has superior BER performance, despite using only two 1D SOVAs as compared with the modified 2D SOVA composed of four 1D SOVAs.