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UNIVERSITY of CALIFORNIA, SAN DIEGO Channel Modeling, Signal UNIVERSITY OF CALIFORNIA, SAN DIEGO Channel Modeling, Signal Processing and Coding for Perpendicular Magnetic Recording A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Electrical Engineering (Communication Theory and Systems) by Zheng Wu Committee in charge: Professor Jack K. Wolf, Chair Professor Paul H. Siegel, Co-Chair Professor Vitaliy Lomakin Professor Lance W. Small Professor Alexander Vardy 2009 c Copyright Zheng Wu, 2009 All rights reserved. The dissertation of Zheng Wu is approved, and it is acceptable in quality and form for publication on mi- crofilm and electronically: Co-Chair Chair University of California, San Diego 2009 iii To my parents. iv CONTENTS SignaturePage............................. iii Dedication ............................... iv Contents ................................ v ListofFigures ............................. viii ListofTables.............................. x Acknowledgements .......................... xi Vita and Publications . xiii Abstract of the Dissertation . xiv Chapter 1 Introduction to the Magnetic Recording System . ...... 1 1.1 Perpendicular Recording Channels . 3 1.1.1 ReadandWriteProcess. 3 1.1.2 Noise and Distortions in Perpendicular Recording Sys- tems........................... 6 1.2 Signal Processing and Coding Techniques in Read Channel . 7 1.2.1 Advanced Techniques . 12 1.3 Summary of Dissertation . 14 Bibliography.............................. 14 Chapter 2 Design Curves and Information-Theoretic Limits for Perpendicular RecordingSystems .......................... 19 2.1 Design Curves for Perpendicular Recording Systems . 20 2.1.1 Perpendicular Recording System with Jitter-Noise and AWGN ......................... 20 2.1.2 Parameter Optimization and Design curves . 21 2.1.3 Design Curves of Different Coding and Equalization Schemes......................... 24 2.2 Information-Theoretic Limit of the Perpendicular Recording System.............................. 27 2.2.1 Monte-Carlo Estimation of Information Rate . 29 2.2.2 Reducing computation complexity . 32 2.3 Information-Theoretic Limit of the Design Curves . 33 v Bibliography.............................. 40 Chapter 3 Nonlinear Transition Shift and Write Precompensation in Perpendic- ularRecordingSystems . 42 3.1 Perpendicular Recording Channel with Nonlinear Transition Shift 43 3.1.1 Nonlinear Transition Shift Model . 43 3.1.2 Write Precompensation . 49 3.1.3 Channel Output and Approximations . 50 3.1.4 SystemDiagram. 51 3.2 PrecompensationSchemes. 52 3.2.1 Dibit Precompensation . 52 3.2.2 Two-level Precompensation . 53 3.2.3 Multilevel Precompensation . 53 3.3 SimulationResults. 54 3.3.1 Dibit Precompensation . 54 3.3.2 Two-level Precompensation . 57 3.3.3 Higher Density and Multilevel Precompensation . 61 3.4 OtherCriteria .......................... 64 Bibliography.............................. 68 Chapter 4 Analysis of the Bit-Error-Rate for Perpendicular Recording Channels withNLTS............................... 69 4.1 Pairwise Error Probability . 70 4.1.1 Order-1 channel Approximation . 72 4.1.2 Order-2 Channel Approximation . 73 4.2 Upper and Lower Bounds on Bit-Error-Rate . 75 4.3 SimulationResults. 77 4.4 Application of the Analysis . 80 Chapter 5 Mean-Adjusted Pattern-Dependent Noise Prediction Detector for Per- pendicular Systems with Nonlinear Transition Shift . 86 5.1 Channel Model and Notations . 88 5.2 Pattern-Dependent Noise Predictive Detector . 89 5.3 Mean-Adjusted Pattern-Dependent Noise Predictive Detector . 91 5.4 SimulationResults. 93 5.5 Conclusions ........................... 95 Bibliography.............................. 97 Chapter 6 Error-Locating Codes and Soft-Decision Decoding . ........ 99 6.1 Tensor-Product Parity Code and Soft-Decision Decoding . 100 6.1.1 Introduction to Error-Locating Codes . 100 vi 6.1.2 A Tensor-Product Parity Code with Soft-Decision De- coding for an ISI Channel . 105 6.1.3 Simulation Results . 110 6.2 Generalized Error-Locating Codes and List Decoding . 112 6.2.1 Introduction to Generalized Error-Locating Codes . 113 6.2.2 List Decoding Algorithm for GEL Code . 118 6.3 Conclusions ........................... 119 Bibliography.............................. 120 vii LIST OF FIGURES Figure 1.1 Illustration of the writing process in perpendicular recording sys- tems. ................................... 4 Figure 1.2 The approximations of the ideal transition response in perpen- dicularrecordingsystems. 5 Figure 1.3 The dipulse response using the error function approximation of the transition response. T50 = 20nm; B = 15nm. ............ 6 Figure 1.4 System diagram of the perpendicular recording system. ..... 8 Figure 2.1 The system diagram for design curve computation. ....... 22 Figure 2.2 An example of the user density optimization. ....... 23 Figure 2.3 Illustration of the normalized design curve and the design curve in the (T50, σJ )-plane. .......................... 24 Figure 2.4 Normalized design curves for MMSE equalizers with unit energy constraint and monic constraint. 25 Figure 2.5 The system with tensor product parity codes. ...... 27 Figure 2.6 Normalized design curves for tensor product parity check code combinedwithRScode. ......................... 28 Figure 2.7 SIR curves v.s. jitter noise for SNRW =17dB. 34 Figure 2.8 Normalized user density curves v.s. jitter noise for SNRW =17dB. 35 Figure 2.9 Normalized design curves for information-theoretic limit. 36 Figure 2.10 Comparison of the design curves for optimal RS code and SIR at SNRW =17dB, Buser=20nm. ....................... 37 Figure 3.1 The generation of the nonlinear transition shift. ......... 44 Figure 3.2 Illustration of the calculation of NLTS. ....... 45 Figure 3.3 The normalized absolute contributions of the past transitions. 47 Figure 3.4 The distribution of NLTS for a random sequence. ...... 49 Figure 3.5 The system diagram for NLTS and precompensation study. 52 Figure 3.6 Influence on BER of NLTS window length. 55 Figure 3.7 Comparison of BER for several channel approximations. 56 Figure 3.8 Best dibit precompensation levels for different jitter noise levels. 57 Figure 3.9 Best dibit precompensation levels for different AWGN levels. 58 Figure 3.10 Best dibit precompensation levels for different T50. ....... 59 Figure 3.11 Surface plot of BER for the two-level precompensation scheme. 60 Figure 3.12 Comparison of simulated BER for dibit precompensation and two-level precompensation with σJ = 0.08B. .............. 61 Figure 3.13 Comparison of simulated BER for dibit precompensation and two-level precompensation with σJ = 0.12B. .............. 62 viii Figure 3.14 Comparison of the Dibit, Two-level and multilevel precompen- sation schemes for B=16nm. ....................... 63 Figure 3.15 Comparison of the Dibit, Two-level and multilevel precompen- sation schemes for B=14nm. ....................... 65 Figure 3.16 Normalized MSE using the dibit precompensation for different T50values. ................................. 67 Figure 4.1 Illustration of error event ǫ =(ξ1 ξ2).............. 70 Figure 4.2 The lower bound estimation for order-1→ channel approximation with dibit precompensation scheme. 78 Figure 4.3 The lower bound estimation for order-2 channel approximation with dibit precompensation scheme. 79 Figure 4.4 Histogram of the pairwise error probability for a system with no NLTS and a system with optimal two-level precompensation. ..... 82 Figure 5.1 Comparison between Viterbi, PDNP, and MA-PDNP detectors. 94 Figure 5.2 Comparison between different Ly and Lx. ............ 95 Figure 5.3 MA-PDNP detector with dibit precompensation. ....... 96 Figure 6.1 A systematic encoding procedure for error-locating codes. 103 Figure 6.2 System diagrams using TPP code. (a) without interleaver; (b) withinterleaver. ............................. 107 Figure 6.3 Hard and soft decision decoder structures for TPP code for an ISIchannel. ................................ 108 Figure 6.4 Combination of the channel trellis and the accumulated parity bit trellis. ................................... 110 Figure 6.5 The graph structure of the MP-BCJR algorithm. 111 Figure 6.6 Performance comparison of several decoding algorithms for sys- tems with and without interleaver. 112 Figure 6.7 Encoding of the GEL codes. 115 Figure 6.8 Comparison between Farhner’s hard decision decoding and the list decoding of the GEL code in BSC channel. 120 Figure 6.9 Comparison between Farhner’s hard decision decoding and the list decoding of the GEL code in AWGN channel. 121 ix LIST OF TABLES Table 2.1 Comparing T50/Buser of the RS-coded system and SIR. 36 Table 2.2 Comparing code rate of the RS-coded system and SIR. 37 Table 3.1 The nonlinear transition shifts for different patterns. 48 Table 3.2 The precompensation levels corresponding to the preceding 3-bit patterns................................... 54 Table 3.3 Error-event counts for system with no NLTS and with optimal two-level precompensation . 60 Table 3.4 Optimal precompensation values for different criteria . 66 Table 4.1 Comparison of the optimal precompensation values obtained from the Monte-Carlo simulation and the lower bound estimate. 80 x ACKNOWLEDGEMENTS It is my fortune and pleasure to have two great professors – professor Jack Wolf and professor Paul Siegel – to be my advisors of the phD program in UCSD. I would like to express my great thanks to them for their guidance, encouragement and support during my work and stay in UCSD. They are superb in their areas of research, kind and patient to students. I am impressed by
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