2D Coding and Iterative Detection Schemes

Transcription

1 2D Coding and Iterative Detection Schemes J. A. O Sullivan, N. Singla, Y. Wu, and R. S. Indeck Washington University Magnetics and Information Science Center

2 Nanoimprinting and Switching of Patterned Media A Washington University Rowan University Collaboration s

3 Enabling Technology: Disk Drives ~10,000,000x increase in 45 years! Magnetic disk storage areal density vs. year of IBM product introduction (From D. A. Thompson)

4 Conflicting Demands on Media Medium noise is less in a medium with smaller grains actual location intended location Decrease volume to increase storage density Maintain volume for thermal stability

5 Patterned Media: 1 bit/ grain Increase magnetic region for stability and low noise increase intergranular exchange Create single domain regions switching (no wall motion) predefine placement

6 Motivation Need medium which can sustain smaller, stable magnetic regions 1. Continuous film with discrete grains ; echange ds-coupled; make grains smaller; create bits from 1000 grains 2. Discrete film; glue (via exchange) structure within region; 1 bit per region 2a. Smooth film, ion beam medification, create discrete regions, mag. w/in region exchange coupled Want a manufacturable process!

7 Viable Patterned Medium Fabrication Technique Grow magnetic material Spin on sacrificial polymer Nanoimprint polymer at room-temperature Ion beam modify material to produce islands of magnetic material Remove polymer

8 Challenges with the Patterning of Media Fine features Large area coverage Complicated, non-rectangular structures High substrate throughput... conventional processing inadequate

9 Imprint Lithography

10 Nanoimprint Lithography for patterning recording media bilayer resist (a) imprinter substrate (d) metal (b) (e) residual polymer (f) (c)

11 Nanoimprinting for patterning recording media

12 Room-Temperature Nanoimprint Lithography A hyperbranched perfluorinated polymer (HBFP) is the RT imprint resist The low glass transition temperature (T g =54 C) allows RT resist displacement Have demonstrated fine features (<20 nm) of imprinting using Alumina imprinter

13 Terris: IBM Ion Beam Modification

14 Nanoimprinting/Ion Modification Small-scale features (10 nm) Large-scale extensibility Smooth topography Suitable for irregular patterns non-rectangular, sector and servo...viable for patterning recording media, memory elements and sensors

15 Nanoimprinting 6 millionmillion bits/square inch!

16 Medium Microstructure and Noise Each microscopic region has uniaxial anisotropy Randomness arises from the medium microstructure Dominant noise source in media

17 Enhanced MRM Image

18 Magnetization Change on the Microscopic Level M H

19 MFM Images at Various Reversal Stages Happ = Oe Happ = 1220 Oe Happ = 1350 Oe Happ = 1550 Oe Happ = 6400 Oe

20 MFM Images of Positive and Negative Saturation

21 Medium Noise Experiment 1 MR readback signal 0 zoom in downtrack position (µm)

22 Determinism of Medium Noise MR readback signal positive saturation negative saturation downtrack position (µm)

23 Simulated Medium

24 Magnetic Transitions

25 Superparamagnetism Two types of materials: Those that have a net magnetic moment at each lattice site and those that don t Ferromagnetic material s moments stick together (exchange) Temperature can jumble up the moments (paramagnetism) Small volumes can spontaneously, coherently change (superparamagnetism)

26 Time Dependence of Magnetization (b) dn 1 2 N (t)e dt 1 E 1 kt

27 Time Dependence of Magnetization Single Activation Energy Activation Energy Distribution f(h ) k f(h ) k E=KV 1- H H τ -1 M(t) = 2NM e NM where τ = C e r t a k r 2 H k E kt M(t) = ( ) 2M NkTp ln t r to M(t) = Slnt + const H k

28 Time Dependence of Magnetization Spin-stand MFM, VSM Magnetization Dynamic time (seconds)

29 Stability of Magnetic Recordings Short-term Experiment Normalized Amplitude frmm 3000 frmm 4550 frmm time (seconds) 300 K

30 Stability of Magnetic Recordings Normalized Amplitude Short-term Experiment 3000 frmm 355 K 341 K 330 K 300 K time (seconds) 300 K 330 K 341 K 355 K

31 Effect of Temperature on Medium Properties Magnetization (emu) 3 x K 343 K K 384 K 409 K Applied Field (Oe) Coercivity (Oer) Temperature( K) M s does not change Reversible change in H c : decreases by ~6 Oe per K

32 Presentation Outline Introduction PRML channels soft decoding channels Decoding for 2-D ISI channels introduction of 2-D ISI MMSE equalization and decoding message passing on combined LDPC and ISI graph Decoding for separable 2-D ISI channels separating 2-D ISI by equalization decoder diagrams and performances

33 Transition Response Amplitude Spinstand Captured Transition Response

34 Data Format Preamble Synchronization Marker

35 PRML System Timing & Tap Updating xn Magnetic Recording Channel Wide-Band Noise Receive Filter (low pass) nt+τ e Adaptive Filter yn ŷn Viterbi Detector xˆ n n P ( D ) = (1 D )(1 + D ), n = 1,2,3,...

36 Serial Turbo Detector I APP I Λ ( x k ) π 1 2 DEMUX Depuncture I O APP Outer I O u k O Inner O y k x L ext π 2 MUX Puncture Λ Λ ( 1 ) p k ( u ) k

37 Drive Data Experiment Rate 16/17 ideal turbo Rate 16/17 drive turbo Ideal EPR4 Drive EPR Bit Error Rate SNR [db]

38 Advanced Media

39 Science enables: 6 million-million bits/square inch!

40 2-D Intersymbol Interference x 11 x 12 x 13 x x 21 x 22 x 23 x x 31 x 32 x 33 x x 41 x 42 x 43 x GUARD BAND r 1 h = w(i,j) i, j = xi, j +.5xi 1, j + 0.5xi, j xi 1, j 1 r 00 r 10 r 20 r 30 r 01 r 11 r 12 r 13 r 14 r 21 r 22 r 23 r 24 r 31 r 02 r 03 r 04 r 05 r 32 r 33 r 34 r 15 r 25 r 35 r 040 r 41 r 42 r 43 r 44 r 45 r 50 r 51 r 52 r 53 r 54 r w i, j

41 MMSE Equalization Combination of equalization and decoding for 2-D ISI Equalizer designed subject to peak power constraint a(i,j) a LDPC x(i,j) x Channel r(i,j) MMSE Encoder ISI Equalizer x ( i, j) LDPC Decoder a ( i, j) w(i,j) Channel

42 Iterative MMSE Equalization Soft information passed from LDPC decoder to equalizer Scheduling: MMSE-LDPC iterations a(i,j) a x(i,j) x r(i,j) MMSE LDPC Encoder Channel ISI Equalizer x ( i, j) LDPC Decoder a ( i, j) w(i,j) Extrinsic Information Channel

43 Performance Performance of MMSE Equalization and Decoding 0 Bit-Error Rate in log ISI-free ItrWiener 1-20 ItrWiener 1-10 ItrWiener 1-5 ItrWiener 1-1 Wiener SNR (db)

44 Full-graph Message Passing Message passing on the 3-level graph of the LDPC code and channel ISI Messages passed are probabilities Algorithm computes a-posteriori probabilities of the codeword bits given the observed data

45 LDPC Bipartite Graph Check Nodes Variable Nodes (x)

46 Full-graph x(i,j) x(i,j+1) x(i,j+2) From Check Nodes x(i+1,j) r(i,j) r(i+1,j) x(i+1,j+1) r(i,j+1) r(i+1,j+1) x(i+1,j+2) x(i+2,j) x(i+2,j+1) x(i+2,j+2)

47 Performance Performance of Iterative Decoding Schemes 0 Bit-Error Rate in log ISI-free ItrWiener_ Fullgraph_10 Wiener SNR (db)

48 Full-graph analysis Length 4 cycles present which degrade performance of message passing algorithm x(i,j) x(i,j+1) x(i,j+2) From Check Nodes x(i+1,j) r(i,j) r(i+1,j) x(i+1,j+1) r(i,j+1) r(i+1,j+1) x(i+1,j+2) x(i+2,j) x(i+2,j+1) x(i+2,j+2)

49 Ordered Subsets Taken from imaging applications data sets grouped into subsets to speed up computations Eliminate loops in the channel ISI graph

50 Grouped ISI Graph

51 Performance Performance of Iterative Decoding Schemes 0 Bit-Error Rate in log ISI-free Ordered Subsets ItrWiener 1-20 Fullgraph Wiener SNR (db)

52 Consider Separating the ISI Down-track separable from cross-track Linear combination

53 Separating 2-D ISI Advantages of separating equalization shortening ISI and reducing detector complexity separating 2-D ISI and reducing detector complexity 2-D ISI Channel w(i,j) r(i, j) Separating Equalization Vertical ISI y(i, j) Horizontal ISI r(i, j) w(i, j)

54 A Separable 2-D ISI Separable channel response 1 h = = ( 1 0.5) x(i, j) Vertical ISI y(i, j) Horizontal ISI r(i, j) Channel Detector x ( i, j) Separable Channel Response w(i,j)

55 Serial Turbo Codes Rate 1/2 Systematic Encoder Rate 1/1 Non-Systematic Encoder

56 Separable 2-D ISI x 21 x 22 x 23 x x 11 x 12 x 13 x x 21 x 22 x 23 x x 31 x 32 x 33 x x 41 x 42 x 43 x

57 Detection Performance -1 Bit-Error-Rate In log ZF_Horizontal_MAP Vertical_Horizontal_MAP MMSE_Equalization SNR (db)

58 Iterative Decoder Diagram I Row-by-Row Detector r(i, j) Equalization MAP Detector LDPC Decoder Hard Decision Extrinsic Information Conventional One-Dimensional Iterative Decoder

59 Iterative Decoder Diagram II Passing Transition Probability r(i, j) Vertical Decoder Horizontal Detector LDPC Decoder Hard Decision Extrinsic Information Conventional Iterative Detector

60 Decoding Performance Bit-Error-Rate In log Performance of Iterative Decoding Diagram I and II SNR (db) ISI-free Diagram I_Iter1 Diagram I_Iter2 Diagram I_Iter3 Diagram II_Iter1 Diagram II_Iter2 Diagram II_Iter5

61 Iterative Decoder Diagram III Z L ( y i, j Vertical MAP Detector ) L ( y i, j Horizontal MAP Detector ) L ( x i, j ) LDPC Decoder L LDPC ( x i, j ) Dˆ

62 Decoding Performance Bit-Error_Rate in log Performance of Iterative Decoding Diagram III Diagram III_Iter1_SubIter2 Diagram III_Iter2_SubIter2 Diagram III_Iter3_SubIter2 Diagram III_Iter4_SubIter2 Diagram III_Iter10_SubIter2 ISI_free SNR (db)

63 Performance Comparison 0-1 ISI-free Diagram III_Iter10_SubIter2 Diagram II_Iter5 Diagram I_ZF_Equa_Iter3 Diagram I_M M SE_Equa_Iter10 Bit-Error-Rate In log SNR (db)

64 Conclusions and Discussion MMSE equalization and decoding good performance with iterative equalization low complexity FIR implementation Message passing algorithms full-graph algorithm performance deteriorated due to short cycles ordered subsets message passing gives best performance for general 2-D ISI complexity proportional to code block-length Separable ISI decoding best performance for separable 2-D ISI low complexity... approximate channel response by separable response