Bahl-Cocke-Jelinek-Raviv Detector Research Articles

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.

Improved Recording Performance With Writer Design and Joint Learning-Based Neural Network for Heat-Assisted Interlaced Magnetic Recording

Heat-assisted interlaced magnetic recording (HIMR) further increases the areal density with the interlaced track layout architecture compared to conventional heat-assisted magnetic recording. However, besides the 2-D inter-symbol interference (ISI) and thermal jitters, the transition curvatures due to the circular thermal profile cause severe erasures after write and obvious nonlinear distortions of readback signals. This deteriorates the recording performance severely. Especially the degrees of transition curvatures for the low temperature written track (LT) and high temperature written track (HT) are distinct, which makes the correction of transition curvature with only the writer design impossible. Correspondingly, a comprehensive method consisting of writer design and multitrack detection algorithm with joint learning-based neural network (JLNN) is proposed to mitigate the effects of transition curvature and 2-D ISI for both LT and HT of HIMR. First, a designed writer with splitting main poles produces the spatially nonuniform write field along the crosstrack direction to correct the transition curvature of LT. Then the multitrack detection with JLNN and improved Bahl–Cocke–Jelinek–Raviv (BCJR) detector (JLNN-IB) algorithm is studied to further mitigate the effects of residual transition curvatures, thermal jitters, and 2-D ISI for both HT and LT. Specifically, the readback signals of read head array and decoded log-likelihood ratio (LLR) outputted by the low-density parity check (LDPC) decoder are fed into JLNN to obtain the equalized signal and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$a$ </tex-math></inline-formula> <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">priori</i> probability (AP) of three tracks. Then the equalized signal as well as AP of current track and corresponding soft bit estimations of adjacent tracks are embedded into the branch metrics of improved BCJR detector for data detection, and the LDPC decoder is cascaded for the error correction. The simulation indicates that at the recording density of 2.11 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , the proposed comprehensive writer design and JLNN-IB algorithm provide 9.2 and 9.7 dB signal to noise ratio (SNR) gains compared to the conventional 2-D neural network equalizer and 2-D linear equalizer under the uniform write field and circular thermal profile, respectively.

Detection Scheme With Joint Intertrack Interference and Media Noise Mitigations for Heat Assisted Interlaced Magnetic Recording

Heat assisted interlaced magnetic recording (HIMR) is a promising candidate for the next-generation of magnetic recording technology to further increase the area density beyond 1Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Specifically, the high temperature and low temperature tracks are written in an interlaced order to improve the recording performance. However, the inter-track interference (ITI), inter-symbol interference (ISI) and thermal jitters brought by the increased recording density and Curie temperature variations are severe in HIMR, which degrade the bit error rate (BER) performance obviously. In this study, we propose a multitrack detection scheme with joint intertrack interference and media noise mitigations. Here a multi-task neural network (MTNN) is designed to simultaneously predict ITI pattern and residual media noise, then the 2D variable equalizers corresponding to different ITI patterns are implemented and predicted residual media noises are embedded into the branch metrics of modified Bahl-Cocke-Jelinek-Raviv (BCJR) detector to mitigate ITI and whiten media noise. The simulation demonstrates that the proposed MTNN with variable equalizer and modified BCJR detector (MTNN+VE+MB) algorithm mitigates the ITI and media noise effectively. At the channel bit density of 3.10 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , it provides 2.6 dB signal-to-noise ratio (SNR) gain compared to that of conventional 2D fixed equalizer with pattern dependent noise prediction detector (FE+PDNP) for the low temperature (LT) tracks with 4% Curie temperature variance.

Multitrack Detection With a Two-Dimensional Soft-Transition Assisted Multitask Neural Network for Heat-Assisted Interlaced Magnetic Recording

Heat-assisted interlaced magnetic recording (HIMR) further increases recording density compared to heat-assisted magnetic recording due to the interlaced track layout. However, the smaller circular thermal profile of the top low-temperature-written tracks results in severe transition curvatures, which causes nonlinear distortions of the readback signal and degrades the bit error rate (BER) performance. Moreover, the increased recording density causes severe two-dimensional (2-D) intersymbol interference (ISI) along both down track and cross track directions. To mitigate the effect of nonlinear distortion and 2-D ISI in an HIMR system, we model a 2-D soft-transition, information-assisted, multitask neural network and modified Bahl–Cocke–Jelinek–Raviv (BCJR) detector (2DST-MTNN-MB) algorithm to detect three tracks simultaneously. The readback signal and 2-D soft-transition information are fed into the multitask neural network to obtain equalized signals and soft bit estimates of three tracks simultaneously. Then, the signal of the current track and soft estimates of the side tracks are embedded into the branch metrics of the modified BCJR detector for data detection, and the low-density parity check decoder is cascaded for error correction. The simulation results show that the 2DST-MTNN-MB algorithm provides 5.0 dB signal-to-noise ratio gains with reduced computation complexity compared with a single-track, single-task neural network and one-dimensional BCJR detector algorithm for the low-temperature-written track at channel bit density of 3.51 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , thereby narrowing the gap of BER performance between high- and low-temperature-written tracks.

Deep Neural Network Based Media Noise Predictors for Use in High-Density Magnetic Recording Turbo-Detectors

This article presents a combined Bahl–Cocke–Jelinek–Raviv (BCJR) and deep neural network (DNN) turbo-detection architecture for 1-D hard disk drive (HDD) magnetic recording. Simulated HDD readings based on a grain flipping probabilistic (GFP) model are input to a linear filter equalizer with a 1-D partial response (PR) target. The equalizer output is provided to the BCJR detector in order to minimize the intersymbol interference (ISI) due to the PR mask. The BCJR detector’s log-likelihood-ratio (LLR) outputs (along with the linear equalizer outputs) are then input to the DNN detector, which estimates the signal-dependent media noise. The media noise estimate is then fed back to the BCJR detector in an iterative manner. Several DNN media noise estimation architectures based on fully connected (FC) and convolutional neural networks (CNNs) are investigated. For GFP data at 48 nm track pitch and 11 nm bit length, the CNN-based BCJR-DNN turbo detector reduces the detector bit error rate (BER) by $0.334\times $ and the per bit computational time by $0.731\times $ compared to a BCJR detector that incorporates 1-D pattern-dependent noise prediction (PDNP). The proposed BCJR-DNN turbo detection architecture can be generalized for two-dimensional magnetic recording (TDMR).

ISI/ITI Turbo Equalizer for TDMR Using Trained Local Area Influence Probabilistic Model

In this paper, a local area influence probabilistic (LAIP) detector for estimating magnetic grain interactions with coded data bits in two-dimensional magnetic recording is combined with a 2-D Bahl-Cocke-Jelinek-Raviv (BCJR)-based detector for joint removal of intertrack interference (ITI) and intersymbol interference (ISI). The LAIP detector sends log-likelihood ratio estimates of coded bits and an estimate of the local ISI/ITI convolution mask to a BCJR-based ISI/ITI detector followed by an irregular-repeat-accumulate decoder. Simulation results on a random Voronoi grain media model with ISI and ITI show that the concatenated LAIP/BCJR system, which detects three tracks simultaneously, achieves user information bit areal densities competitive or higher than results reported in a previous paper that employed the LAIP detector alone on a Voronoi grain channel without ISI/ITI. Simulation results on a grain-flipping probability media model based on micromagnetic simulations show that the proposed detector achieves an 11.3% bit error rate reduction compared to a recently proposed system with a 2-D linear equalizer followed by a two-track BCJR detector with 2-D pattern-dependent noise prediction.

Design of a Capacity-Approaching Chaos-Based Multiaccess Transmission System

As an enhanced version of Walsh-code-based multiaccess differential chaos shift keying (DCSK-WC), the differentially DCSK-WC (DDCSK-WC) benefits from better error performance and stronger robustness against inter-symbol interference in multipath fading channels. In this paper, the Bahl–Cocke–Jelinek–Raviv (BCJR) decoding algorithm is applied in the detection of DDCSK-WC to form DDCSK-WC-BCJR. Theoretical analyses and simulation results demonstrate that the BCJR detector achieves a significant performance gain with respect to the conventional generalized-maximum-likelihood detector, while retaining the hardware complexity almost unchanged. To further improve the performance, protograph-based low-density-parity-check channel codes are incorporated into the DDCSK-WC-BCJR system so as to construct a serial concatenated coding scheme. However, the capacity-approaching protograph code in additive white Gaussian noise (AWGN) channels performs poorly in the DDCSK-WC-BCJR system over multipath fading channels. To tackle this problem, a new protograph code is designed with the help of a modified extrinsic information transfer analysis. The proposed code has decoding thresholds gap within 1.0 dB way from to the system capacity limits. Besides, the performance superiority of the protograph-coded DDCSK-WC-BCJR architecture is illustrated over a practical UWB channel. More importantly, the proposed scheme does not require channel state information as in uncoded-DCSK schemes, which makes it extremely promising for low-cost and low-complexity wireless communication applications.

Micromagnetics-Based Analysis of Multi-Track Detection With Simplified 2-D Write Precompensation on Shingled Magnetic Recording

In shingled magnetic recording systems, a shingled writer is used to write narrow tracks by overlapping the previous tracks, which also leads to severe inter-track interference, jitter, and nonlinear transition shift (NLTS) in the cross-track direction. To deal with these challenges, we propose a simplified 2-D write precompensation (WPC) scheme that adjusts the write current magnitude instead of the timing, to mitigate the 2-D NLTS in the writing process. In the proposed WPC scheme, the WPC is only implemented for the few specific patterns that seem to cause large media noise mean and variance. During the training period, the optimum write field for current transition being written is obtained by subtracting demagnetizing field from the previous neighboring bits in the current and nearest previous tracks from a fixed write field, and the optimum writing current is determined by minimizing the mean-squared error between the needed field and the available fields within a writer field library. Then, the specific bits producing the dominant demagnetizing field and the obtained optimum writing current are stored in a lookup table during the training period. During the writing process, we can obtain the optimum writing current by matching the specific previous written bits against the bit patterns in the lookup table, avoiding the need for computing the demagnetizing field and optimum writing current for every written bit. Here, two simplified WPC schemes are investigated corresponding to precompensating two sets of data patterns. For readback, a joint pattern-dependent noise-predictive (PDNP) detector is investigated to further whiten the 2-D media noise. Simulations indicate that at the target bit error rate of $10^{-2}$ , the proposed simplified WPC schemes combined with the joint PDNP detector can provide the density gains of as high as 22% compared with the system without WPC and detected with a joint Bahl–Cocke–Jelinek–Raviv detector.

Improved BER Performance With Rotated Head Array and 2-D Detector in Two-Dimensional Magnetic Recording

Two-dimensional magnetic recording is a promising candidate to further extend the areal density above 1 Tb/in2 density while using a conventional writer and media. During the writing process, a shingled writer is usually used to write narrow tracks by overlapping previous tracks, which brings severe intertrack interference (ITI), fewer grains per channel bit and corresponding lower signal-to-noise ratio (SNR). As a consequence, for the current shingled magnetic recording system, a normally oriented head array (NHA) is usually implemented to detect a single track by using 2-D signal processing to mitigate the ITI and media noise. Then, a rotated head array (RHA) has been found to effectively avoid the ITI and regain the lost down-track resolution using signal processing. Correspondingly, in this paper, the RHA is investigated to simultaneously detect three tracks with 1-D and joint pattern-dependent noise-predictive (PDNP) Bahl–Cocke–Jelinek–Raviv (BCJR) detectors. Simulation indicates that, for the perfect writing at the 6 nm Voronoi grains, if the 1-D PDNP BCJR detector is implemented, the RHA combined with a designed 2-D equalizer producing multiple equalized waveforms can provide 16% density gains compared with the NHA with a 2-D equalizer and 1-D target at the target bit error rate (BER) of $10 ^{\mathrm {-2}}$ . If the joint PDNP BCJR detector is implemented, the RHA can provide 25% density gain compared with that for the NHA with the same detection algorithm at the target BER of $10 ^{\mathrm {-2}}$ . With respect to error correction, a longer codeword length of binary low density parity check code can be used for decoding of the multi-track detection compared with that for the single-track detection, which provides an extra SNR gain.

Coding and Detection for Channels With Written-In Errors and Inter-Symbol Interference

Written-in errors (WIEs), which include written-in substitutions, insertions, and deletions, as well as 2-D inter-symbol interference (2-D-ISI), form one of the major challenges for the new emerging bit-patterned media recording technology. Coding and detection scheme with performance/complexity tradeoffs is expected to address such a challenge. In this paper, a new channel model with WIEs and ISI (WIE-ISI) is presented, and the embedded marker code scheme (EMCS) with Bahl-Cocke-Jelinek-Raviv (BCJR) detector is employed to perform channel detection. By investigating the effect of ISI on the WIE-ISI channel considering BCJR detector, a virtual written-in substitution probability is introduced and a new synchronization algorithm with written-in substitution detection (SA-WSD) is developed. The EMCS employing the proposed SA-WSD demonstrates better error correction performance than that of the original SA. Furthermore, the SA-WSD is found to be robust to small estimation errors in the written-in substitution probability.

Bidirectional Pattern-Dependent Noise Prediction With LDPC Codes for HAMR

As areal densities increase, substantial jitter noise is expected in heat-assisted magnetic recording (HAMR). To mitigate the effects of jitter noise, in an earlier work we proposed the bidirectional pattern-dependent noise prediction (BiPDNP) detector, which employs backward linear prediction as well as the conventional forward linear prediction. However, no error correction codes were used in this earlier work. In this paper, we implement BiPDNP in the Bahl-Cocke-Jelinek-Raviv (BCJR) detector, and investigate its performance with low-density parity check (LDPC) codes. For the LDPC coded channel, by combining the BCJR detector with BiPDNP, we observe that a SNR gain of 1 dB (at bit error rate 10 $^{-4}$ with 30% microtrack jitter) is achieved over the conventional BCJR detector. Further, in HAMR channel modeling we employ the thermal Williams-Comstock (TWC) model. Conventionally, a linear relationship for coercivity with temperature is used. In this paper, we update the TWC model by using a nonlinear relationship for coercivity with temperature.

Reduced-State Bahl–Cocke–Jalinek–Raviv Detector for Patterned Media Storage

Bit-patterned media (BPM) is a promising candidate for future high-capacity magnetic storage. The inter-track interference (ITI) in BPM has been taken into account by the “multiple islands per read head” model. However, the complexity of the symbol-based detection for this model is too high for practical use. To reduce complexity, we propose to use the reduced-state Bahl-Cocke-Jelinek-Raviv (BCJR) detection algorithm for such a two-dimensional model. We compare the computational complexity of the proposed reduced-state detector to that of the full-state BCJR detector. Simulation results show that the proposed reduced-state BCJR detector can approach the optimal performance by 0.5 dB while significantly reducing the detector complexity.

Reduced-complexity turbo equalization for high-density magnetic recording systems

This paper considers a decision-feedback-equalizer (DFE)-based soft decision detector as an alternative for the Bahl-Cocke-Jelinek-Raviv (BCJR) front-end for a coded magnetic recording channel. In previous work, a bidirectional-arbitrated DFE (BAD) was shown to perform in between a BCJR detector and a minimum mean-square error DFE. We propose a soft-output BAD (S-BAD) which takes advantage of the original structure and is suitable for iterative decoding when used with outer codes. We show that with a convolutional code as an outer code, S-BAD performs close to higher complexity detectors.