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

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

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

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

Advances in Modeling and Signal Processing for Bit-Patterned Magnetic Recording Channels with Written-In Errors

In the past perpendicular magnetic recording on continuous media has served as the storage mechanism for the hard-disk drive (HDD) industry, allowing for growth in areal densities approaching 0.5 Tb/in2. Under the current system design, further increases are limited by the superparamagnetic effect where the medium's thermal energy destabilizes the individual bit domains used for storage. In order to provide for future growth in the area of magnetic recording for disk drives, a number of various technology shifts have been proposed and are currently undergoing considerable research. One promising option involves switching to a discrete medium in the form of individual bit islands, termed bit-patterned magnetic recording (BPMR).When switching from a continuous to a discrete media, the problems encountered become substantial for every aspect of the hard-disk drive design. In this dissertation the complications in modeling and signal processing for bit-patterned magnetic recording are investigated where the write and read processes along with the channel characteristics present considerable challenges. For a target areal density of 4 Tb/in2, the storage process is hindered by media noise, two-dimensional (2D) intersymbol interference (ISI), electronics noise and written-in errors introduced during the write process. Thus there is a strong possibility that BPMR may prove intractable as a future HDD technology at high areal densities because the combined negative effects of the many error sources produces an environment where current signal processing techniques cannot accurately recover the stored data. The purpose here is to exploit advanced methods of detection and error correction to show that data can be effectively recovered from a BPMR channel in the presence of multiple error sources at high areal densities.First a practical model for the readback response of an individual island is established that is capable of representing its 2D nature with a Gaussian pulse. Various characteristics of the readback pulse are shown to emerge as it is subjected to the degradation of 2D media noise. The writing of the bits within a track is also investigated with an emphasis on the write process's ability to inject written-in errors in the data stream resulting from both a loss of synchronization of the write clock and the interaction of the local-scale magnetic fields under the influence of the applied write field.To facilitate data recovery in the presence of BPMR's major degradations, various detection and error-correction methods are utilized. For single-track equalization of the channel output, noise prediction is incorporated to assist detection with increased levels of media noise. With large detrimental amounts of 2D ISI and media noise present in the channel at high areal densities, a 2D approach known as multi-track detection is investigated where multiple tracks are sensed by the read heads and then used to extract information on the target track. For BPMR the output of the detector still possesses the uncorrected written-in errors. Powerful error-correction codes based on finite geometries are employed to help recover the original data stream. Increased error-correction is sought by utilizing two-fold EG codes in combination with a form of automorphism decoding known as auto-diversity. Modifications to the parity-check matrices of the error-correction codes are also investigated for the purpose of attempting more practical applications of the decoding algorithms based on belief propagation. Under the proposed techniques it is shown that effective data recovery is possible at an areal density of 4 Tb/in2 in the presence of all significant error sources except for insertions and deletions. Data recovery from the BPMR channel with insertions and deletions remains an open problem

ADVANCED SIGNAL PROCESSING FOR MAGNETIC RECORDING ON PERPENDICULARLY MAGNETIZED MEDIA

In magnetic recording channels (MRCs) the readback signal is corrupted by many kinds of impairments, such as electronic noise, media noise, intersymbol interference (ISI), inter-track interference (ITI) and different types of erasures. The growth in demand for the information storage, leads to the continuing pursuit of higher recording density, which enhances the impact of the noise contamination and makes the recovery of the user data from magnetic media more challenging. In this dissertation, we develop advanced signal processing techniques to mitigate these impairments in MRCs.We focus on magnetic recording on perpendicularly magnetized media, from the state-of-the art continuous media to bit-patterned media, which is a possible choice for the next generation of products. We propose novel techniques for soft-input soft-output channel detection, soft iterative decoding of low-density parity-check (LDPC) codes as well as LDPC code designs for MRCs.First we apply the optimal subblock-by-subblock detector (OBBD) to nonbinary LDPC coded perpendicular magnetic recording channels (PMRCs) and derive a symbol-based detector to do the turbo equalization exactly. Second, we propose improved belief-propagation (BP) decoders for both binary and nonbinary LDPC coded PMRCs, which provide significant gains over the standard BP decoder. Third, we introduce novel LDPC code design techniques to construct LDPC codes with fewer short cycles. Performance improvement is achieved by applying the new LDPC codes to PMRCs. Fourth, we do a substantial investigation on Reed-Solomon (RS) plus LDPC coded PMRCs. Finally, we continue our research on bit-patterned magnetic recording (BPMR) channels at extremely high recording densities. A multi-track detection technique is proposed to mitigate the severe ITI in BPMR channels. The multi-track detection with both joint-track and two-dimensional (2D) equalization provide significant performance improvement compared to conventional equalization and detection methods

Dependable Embedded Systems

This Open Access book introduces readers to many new techniques for enhancing and optimizing reliability in embedded systems, which have emerged particularly within the last five years. This book introduces the most prominent reliability concerns from today’s points of view and roughly recapitulates the progress in the community so far. Unlike other books that focus on a single abstraction level such circuit level or system level alone, the focus of this book is to deal with the different reliability challenges across different levels starting from the physical level all the way to the system level (cross-layer approaches). The book aims at demonstrating how new hardware/software co-design solution can be proposed to ef-fectively mitigate reliability degradation such as transistor aging, processor variation, temperature effects, soft errors, etc. Provides readers with latest insights into novel, cross-layer methods and models with respect to dependability of embedded systems; Describes cross-layer approaches that can leverage reliability through techniques that are pro-actively designed with respect to techniques at other layers; Explains run-time adaptation and concepts/means of self-organization, in order to achieve error resiliency in complex, future many core systems

The Logic of Random Pulses: Stochastic Computing.

Recent developments in the field of electronics have produced nano-scale devices whose operation can only be described in probabilistic terms. In contrast with the conventional deterministic computing that has dominated the digital world for decades, we investigate a fundamentally different technique that is probabilistic by nature, namely, stochastic computing (SC). In SC, numbers are represented by bit-streams of 0's and 1's, in which the probability of seeing a 1 denotes the value of the number. The main benefit of SC is that complicated arithmetic computation can be performed by simple logic circuits. For example, a single (logic) AND gate performs multiplication. The dissertation begins with a comprehensive survey of SC and its applications. We highlight its main challenges, which include long computation time and low accuracy, as well as the lack of general design methods. We then address some of the more important challenges. We introduce a new SC design method, called STRAUSS, that generates efficient SC circuits for arbitrary target functions. We then address the problems arising from correlation among stochastic numbers (SNs). In particular, we show that, contrary to general belief, correlation can sometimes serve as a resource in SC design. We also show that unlike conventional circuits, SC circuits can tolerate high error rates and are hence useful in some new applications that involve nondeterministic behavior in the underlying circuitry. Finally, we show how SC's properties can be exploited in the design of an efficient vision chip that is suitable for retinal implants. In particular, we show that SC circuits can directly operate on signals with neural encoding, which eliminates the need for data conversion.PhDComputer Science and EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113561/1/alaghi_1.pd

The HBP1 tumor suppressor is a negative epigenetic regulator of MYCN driven neuroblastoma through interaction with the PRC2 complex

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