On Coding and Detection Techniques for Two-Dimensional Magnetic Recording

Edited version embargoed until 15.04.2020 Full version: Access restricted permanently due to 3rd party copyright restrictions. Restriction set on 15/04/2019 by AS, Doctoral CollegeThe areal density growth of magnetic recording systems is fast approaching the superparamagnetic limit for conventional magnetic disks. This is due to the increasing demand for high data storage capacity. Two-dimensional Magnetic Recording (TDMR) is a new technology aimed at increasing the areal density of magnetic recording systems beyond the limit of current disk technology using conventional disk media. However, it relies on advanced coding and signal processing techniques to achieve areal density gains. Current state of the art signal processing for TDMR channel employed iterative decoding with Low Density Parity Check (LDPC) codes, coupled with 2D equalisers and full 2D Maximum Likelihood (ML) detectors. The shortcoming of these algorithms is their computation complexity especially with regards to the ML detectors which is exponential with respect to the number of bits involved. Therefore, robust low-complexity coding, equalisation and detection algorithms are crucial for successful future deployment of the TDMR scheme. This present work is aimed at finding efficient and low-complexity coding, equalisation, detection and decoding techniques for improving the performance of TDMR channel and magnetic recording channel in general. A forward error correction (FEC) scheme of two concatenated single parity bit systems along track separated by an interleaver has been presented for channel with perpendicular magnetic recording (PMR) media. Joint detection decoding algorithm using constrained MAP detector for simultaneous detection and decoding of data with single parity bit system has been proposed. It is shown that using the proposed FEC scheme with the constrained MAP detector/decoder can achieve a gain of up to 3dB over un-coded MAP decoder for 1D interference channel. A further gain of 1.5 dB was achieved by concatenating two interleavers with extra parity bit when data density along track is high. The use of single bit parity code as a run length limited code as well as an error correction code is demonstrated to simplify detection complexity and improve system performance. A low-complexity 2D detection technique for TDMR system with Shingled Magnetic Recording Media (SMR) was also proposed. The technique used the concatenation of 2D MAP detector along track with regular MAP detector across tracks to reduce the complexity order of using full 2D detection from exponential to linear. It is shown that using this technique can improve track density with limited complexity. Two methods of FEC for TDMR channel using two single parity bit systems have been discussed. One using two concatenated single parity bits along track only, separated by a Dithered Relative Prime (DRP) interleaver and the other use the single parity bits in both directions without the DRP interleaver. Consequent to the FEC coding on the channel, a 2D multi-track MAP joint detector decoder has been proposed for simultaneous detection and decoding of the coded single parity bit data. A gain of up to 5dB was achieved using the FEC scheme with the 2D multi-track MAP joint detector decoder over un-coded 2D multi-track MAP detector in TDMR channel. In a situation with high density in both directions, it is shown that FEC coding using two concatenated single parity bits along track separated by DRP interleaver performed better than when the single parity bits are used in both directions without the DRP interleaver.9mobile Nigeri

Channel detection on two-dimensional magnetic recording

Two-dimensional magnetic recording (TDMR) coupled with shingled-magnetic recording (SMR) is one of next generation techniques for increasing the hard disk drive (HDD) capacity up to 10 Tbit/in2 in order to meet the growing demand of mass storage.We focus on solving the tough problems and challenges on the detection end of TDMR. Since the reader works on the overlapped tracks, which are even narrower than the read head, the channel detector works in an environment of low signal-to-noise ratio (SNR), two-dimensional (2-D) inter-symbol interference (ISI) and colored noise, therefore it requires sophisticated detection techniques to provide reliable data recovery. Given that the complexity of optimal 2-D symbol detection is exponential on the data width, we had to choose suboptimal solutions.To build our research environment, we use an innovative Voronoi grain based channel model which captures the important features of SMR, such as squeezed tracks, tilted bit cells, 2-D ISI, electronic and media noise, etc. Then we take an in-depth exploration of channel detection techniques on the TDMR channel model. Our approaches extend the conventional 1-D detection techniques, by using a joint-track equalizer to optimize the 2-D partial-response (PR) target followed by the multi-track detector (MTD) for joint detection, or using the inter-track interference (ITI) canceller to estimate and cancel the ITI from side tracks, followed by a standard BCJR detector. We used the single-track detector (STD) for pre-detecting the side tracks to lower the overall complexity. Then we use pattern-dependent noise prediction (PDNP) techniques to linearly predict the noise sample, so as to improve the detection performance under colored media noise, and especially the data dependent jitter noise. The results show that our 2-D detectors provide significant performance gains against the conventional detectors with manageable complexity

Coding and Probabilistic Inference Methods for Data-Dependent Two-Dimensional Channels

Recent advances in magnetic recording systems, optical recording devices and flash memory drives necessitate to study two-dimensional (2-D) coding techniques for reliable storage/retrieval of information. Most channels in such systems introduce errors in messages in response to certain data patterns, and messages containing these patterns are more prone to errors than others. For example, in a single-level cell flash memory channel, inter-cell interference (ICI) is at its maximum when 101 patterns are programmed over adjacent cells in either horizontal or vertical directions. As another example, in two-dimensional magnetic recording channels, 2-D isolated-bits patterns are shown empirically to be the dominant error event, and during the read-back process inter-symbol interference (ISI) and inter-track interference (ITI) arise when these patterns are recorded over the magnetic medium. Shannon in his seminal work, ``A Mathematical Theory of Communications," presented two techniques for reliable transmission of messages over noisy channels, namely error correction coding and constrained coding. In the first method, messages are protected via an error correction code (ECC) from random errors which are independent of input data. The theory of ECCs is well studied, and efficient code construction methods are developed for simple binary channels, additive white Gaussian noise (AWGN) channels and partial response channels. On the other hand, constrained coding reduces the likelihood of corruption by removing problematic patterns before transmission over data-dependent channels. Prominent examples of constraints include a family of binary one-dimensional (1-D) and 2-D $\left(d,k\right)$-run-length-limited (RLL) constraints which improves resilience to ISI timing recovery and synchronization for bandwidth limited partial response channels, where d and k represent the minimum and maximum number of admissible zeros between two successive ones in any direction of array. In principle, the ultimate coding approach for such data-dependent channels is to design a set of sufficiently distinct error correction codewords that also satisfy channel constraints. Designing channel codewords satisfying both ECC and channel constraints is important as it would achieve the channel capacity. However, in practice this is difficult, and we rely on sub-optimal methods such as forward concatenation method (standard concatenation), reverse concatenation method (modified concatenation), and combinations of these approaches. In this dissertation, we focus on the problem of reliable transmission of binary messages over data-dependent 2-D communication channels. Our work is concerned with several challenges in regard to the transmission of binary messages over data-dependent 2-D channels. Design of Two-Dimensional Magnetic Recording (TDMR) Detector and Decoder: TDMR achieves high areal densities by reducing the size of a bit comparable to the size of the magnetic grains resulting in 2-D ISI and very high media noise. Therefore, it is critical to handle the media noise along with the 2-D ISI detection. In this work, we tune the Generalized Belief Propagation (GBP) algorithm to handle the media noise seen in TDMR. We also provide an intuition into the nature of hard decisions provided by the GBP algorithm. Investigation into Harmful Patterns for TDMR channels: This work investigates into the Voronoi based media model to study the harmful patterns over multi-track shingled recording systems. Through realistic quasi micromagnetic simulations studies, we identify 2-D data patterns that contribute to high media noise. We look into the generic Voronoi model and present our analysis on multi-track detection with constrained coded data. We show that 2-D constraints imposed on input patterns result in an order of magnitude improvement in the bit error rate for TDMR systems. Understanding of Constraint Gain for TDMR Channels: We study performance gains of constrained codes in TDMR channels using the notion of constraint gain. We consider Voronoi based TDMR channels with realistic grain, bit, track and magnetic-head dimensions. Specifically, we investigate the constraint gain for 2-D no-isolated-bits constraint over Voronoi based TDMR channels. We focus on schemes that employ the GBP algorithm for obtaining information rate estimates for TDMR channels. Design of Novel Constrained Coding Methods: In this work, we present a deliberate bit flipping (DBF) coding scheme for binary 2-D channels, where specific patterns in channel inputs are the significant cause of errors. The idea is to eliminate a constrained encoder and, instead, embed a constraint into an error correction codeword that is arranged into a 2-D array by deliberately flipping the bits that violate the constraint. The DBF method relies on the error correction capability of the code being used so that it should be able to correct both deliberate errors and channel errors. Therefore, it is crucial to flip minimum number of bits in order not to overburden the error correction decoder. We devise a constrained combinatorial formulation for minimizing the number of flipped bits for a given set of harmful patterns. The GBP algorithm is used to find an approximate solution for the problem. Devising Reduced Complexity Probabilistic Inference Methods: We propose a reduced complexity GBP that propagates messages in Log-Likelihood Ratio (LLR) domain. The key novelties of the proposed LLR-GBP are: (i) reduced fixed point precision for messages instead of computational complex floating point format, (ii) operations performed in logarithm domain, thus eliminating the need for multiplications and divisions, (iii) usage of message ratios that leads to simple hard decision mechanisms

Multitrack Detection for Magnetic Recording

The thesis develops advanced signal processing algorithms for magnetic recording to increase areal density. The exploding demand for cloud storage is motivating a push for higher areal densities, with narrower track pitches and shorter bit lengths. The resulting increase in interference and media noise requires improvements in read channel signal processing to keep pace. This thesis proposes the multitrack pattern-dependent noise-prediction algorithm as a solution to the joint maximum-likelihood multitrack detection problem in the face of pattern-dependent autoregressive Gaussian noise. The magnetic recording read channel has numerous parameters that must be carefully tuned for best performance; these include not only the equalizer coefficients but also any parameters inside the detector. This thesis proposes two new tuning strategies: one is to minimize the bit-error rate after detection, and the other is to minimize the frame-error rate after error-control decoding. Furthermore, this thesis designs a neural network read channel architecture and compares the performance and complexity with these traditional signal processing techniques.Ph.D

Coding and Probabilistic Inference Methods for Data-Dependent Two-Dimensional Channels

Recent advances in magnetic recording systems, optical recording devices and flash memory drives necessitate to study two-dimensional (2-D) coding techniques for reliable storage/retrieval of information. Most channels in such systems introduce errors in messages in response to certain data patterns, and messages containing these patterns are more prone to errors than others. For example, in a single-level cell flash memory channel, inter-cell interference (ICI) is at its maximum when 101 patterns are programmed over adjacent cells in either horizontal or vertical directions. As another example, in two-dimensional magnetic recording channels, 2-D isolated-bits patterns are shown empirically to be the dominant error event, and during the read-back process inter-symbol interference (ISI) and inter-track interference (ITI) arise when these patterns are recorded over the magnetic medium. Shannon in his seminal work, ``A Mathematical Theory of Communications," presented two techniques for reliable transmission of messages over noisy channels, namely error correction coding and constrained coding. In the first method, messages are protected via an error correction code (ECC) from random errors which are independent of input data. The theory of ECCs is well studied, and efficient code construction methods are developed for simple binary channels, additive white Gaussian noise (AWGN) channels and partial response channels. On the other hand, constrained coding reduces the likelihood of corruption by removing problematic patterns before transmission over data-dependent channels. Prominent examples of constraints include a family of binary one-dimensional (1-D) and 2-D $\left(d,k\right)$-run-length-limited (RLL) constraints which improves resilience to ISI timing recovery and synchronization for bandwidth limited partial response channels, where d and k represent the minimum and maximum number of admissible zeros between two successive ones in any direction of array. In principle, the ultimate coding approach for such data-dependent channels is to design a set of sufficiently distinct error correction codewords that also satisfy channel constraints. Designing channel codewords satisfying both ECC and channel constraints is important as it would achieve the channel capacity. However, in practice this is difficult, and we rely on sub-optimal methods such as forward concatenation method (standard concatenation), reverse concatenation method (modified concatenation), and combinations of these approaches. In this dissertation, we focus on the problem of reliable transmission of binary messages over data-dependent 2-D communication channels. Our work is concerned with several challenges in regard to the transmission of binary messages over data-dependent 2-D channels. Design of Two-Dimensional Magnetic Recording (TDMR) Detector and Decoder: TDMR achieves high areal densities by reducing the size of a bit comparable to the size of the magnetic grains resulting in 2-D ISI and very high media noise. Therefore, it is critical to handle the media noise along with the 2-D ISI detection. In this work, we tune the Generalized Belief Propagation (GBP) algorithm to handle the media noise seen in TDMR. We also provide an intuition into the nature of hard decisions provided by the GBP algorithm. Investigation into Harmful Patterns for TDMR channels: This work investigates into the Voronoi based media model to study the harmful patterns over multi-track shingled recording systems. Through realistic quasi micromagnetic simulations studies, we identify 2-D data patterns that contribute to high media noise. We look into the generic Voronoi model and present our analysis on multi-track detection with constrained coded data. We show that 2-D constraints imposed on input patterns result in an order of magnitude improvement in the bit error rate for TDMR systems. Understanding of Constraint Gain for TDMR Channels: We study performance gains of constrained codes in TDMR channels using the notion of constraint gain. We consider Voronoi based TDMR channels with realistic grain, bit, track and magnetic-head dimensions. Specifically, we investigate the constraint gain for 2-D no-isolated-bits constraint over Voronoi based TDMR channels. We focus on schemes that employ the GBP algorithm for obtaining information rate estimates for TDMR channels. Design of Novel Constrained Coding Methods: In this work, we present a deliberate bit flipping (DBF) coding scheme for binary 2-D channels, where specific patterns in channel inputs are the significant cause of errors. The idea is to eliminate a constrained encoder and, instead, embed a constraint into an error correction codeword that is arranged into a 2-D array by deliberately flipping the bits that violate the constraint. The DBF method relies on the error correction capability of the code being used so that it should be able to correct both deliberate errors and channel errors. Therefore, it is crucial to flip minimum number of bits in order not to overburden the error correction decoder. We devise a constrained combinatorial formulation for minimizing the number of flipped bits for a given set of harmful patterns. The GBP algorithm is used to find an approximate solution for the problem. Devising Reduced Complexity Probabilistic Inference Methods: We propose a reduced complexity GBP that propagates messages in Log-Likelihood Ratio (LLR) domain. The key novelties of the proposed LLR-GBP are: (i) reduced fixed point precision for messages instead of computational complex floating point format, (ii) operations performed in logarithm domain, thus eliminating the need for multiplications and divisions, (iii) usage of message ratios that leads to simple hard decision mechanisms

Synchronization and detection for two-dimensional magnetic recording

This thesis develops efficient synchronization and detection algorithms for two-dimensional magnetic recording (TDMR) under a low latency constraint. TDMR is a new technology for increasing data density of hard disk drives up to 10 Tera bits per square inch of the medium. TDMR read channel suffers from two-dimensional interference, bit position (timing) uncertainty, and data dependent noise, to name a few. The problem of timing uncertainty is addressed with synchronization. This thesis focuses on the synchronization component of the read channel and develops synchronization solutions which effectively compensate for the asynchrony between the phase of the received readback waveforms and the phase of the sampling clocks. In particular, this thesis proposes solutions to reduce the computational cost of current generation of read channels, where only one data track is detected at a time. For future generations of TDMR read channels, where multiple tracks will be detected jointly, this thesis provides a first-time solution to the synchronization problem for joint detection of multiple asynchronous tracks.Ph.D

Reducing the Complexity of Equalisation and Decoding of Shingled Writing

Full version: Access restricted permanently due to 3rd party copyright restrictions. Restriction set on 24/05/2017 by SC, Graduate schoolShingled Magnetic Recording (SMR) technology is important in the immediate need for expansion of magnetic hard disk beyond the limit of current disk technology. SMR provides a solution with the least change from current technology among contending technologies. Robust easy to implement Digital Signal Processing (DSP) techniques are needed to achieve the potentials of SMR. Current DSP techniques proposed border on the usage of Two Dimensional Magnetic Recording (TDMR) techniques in equalisation and detection, coupled with iterative error correction codes such as Low Density Parity Check (LDPC). Currently, Maximum Likelihood (ML) algorithms are normally used in TDMR detection. The shortcomings of the ML detections used is the exponential complexities with respect to the number of bits. Because of that, reducing the complexity of the processes in SMR Media is very important in order to actualise the deployment of this technology to personal computers in the near future. This research investigated means of reducing the complexities of equalisation and detection techniques. Linear equalisers were found to be adequate for low density situations. Combining ML detector across-track with linear equaliser along-track was found to provide low complexity, better performing alternative as compared to use of linear equaliser across track with ML along track. This is achieved if density is relaxed along track and compressed more across track. A gain of up to 10dB was achieved. In a situation with high density in both dimensions, full two dimensional (2D) detectors provide better performance. Low complexity full 2D detector was formed by serially concatenating two ML detectors, one for each direction, instead of single 2D ML detector used in other literature. This reduces complexity with respect to side interference from exponential to linear. The use of a single bit parity as run length limited code at the same time error correction code is also presented with a small gain of about 1dB at BER of 10^-5 recorded for the situation of high density.Emerging Markets Telecommunication Services Limited (Etisalat Nigeria)