2D Coding andIterative Detection Schemes

J. A. O’Sullivan, N. Singla, Y. Wu, and R. S. Indeck

Washington UniversityMagnetics and Information Science Center

Nanoimprinting and Switching of Patterned Media

A Washington University –Rowan University

Collaboration

ss

Enabling Technology: Disk Drives

Magnetic disk storage areal density vs. year of IBM product introduction

(From D. A. Thompson)

~10,000,000x increase in 45 years!

Conflicting Demands on Media

• Decrease volume to increase storage density

• Maintain volume for thermal stability

Medium noise is less in a medium with smaller grains

intended location

actual location

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

Motivation

Need medium which can sustain smaller, stable magnetic regions1. Continuous film with discrete ‘grains’; echange ds-coupled;

make grains smaller; create bits from 1000 grains2. Discrete film; glue (via exchange) structure within region; 1 bit

per region2a. Smooth film, ion beam medification, create discrete regions, mag.

w/in region exchange coupled

Want a manufacturable process!

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

Challenges with thePatterning of Media

• Fine features• Large area coverage• Complicated, non-rectangular structures• High substrate throughput

. . . conventional processing inadequate

Imprint Lithography

Nanoimprint Lithographyfor patterning recording media

bilayerresist

metal

(d)

(e)

(f)residual polymer

imprinter

substrate(a)

(b)

(c)

Nanoimprintingfor patterning recording media

Room-TemperatureNanoimprint Lithography

• A hyperbranched perfluorinated polymer (HBFP) is the RT imprint resist

• The low glass transition temperature (Tg=54°C) allows RT resist displacement

• Have demonstrated fine features (<20 nm) of imprinting using Alumina imprinter

Ion Beam Modification

Terris: IBM

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

Nanoimprinting

6 million-million

bits/square inch!

Medium Microstructure and Noise Each microscopic region has uniaxial

anisotropyRandomness arises from the medium microstructure Dominant noise source in media

Enhanced MRM Image

H

M

Magnetization Change on theMicroscopic Level

MFM Images at Various Reversal Stages

Happ = -6400 Oe Happ = 1220 Oe Happ = 1350 Oe Happ = 1550 Oe Happ = 6400 Oe

MFM Images of Positive and Negative Saturation

Medium Noise Experiment

downtrack position (µm)

0 10 20 30 40 50

MR

read

back

sig

nal

-1

0

1

zoom in

Determinism of Medium Noise

downtrack position (µm)

0 2 4 6 8 10

MR

read

back

sig

nal

positive saturationnegative saturation

Simulated Medium

Magnetic Transitions

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, coherentlychange (superparamagnetism)

Time Dependence of Magnetization

dN1 2dt

N1(t)e

E1kT→ ∝

−∆

(b)

Time Dependence of Magnetization

M(t) NM e NM where = C er

t

r-1

EkT= −

−2 τ τ

∆

Single Activation Energy Activation Energy Distribution

( )M(t) 2M NkTp lnttro

= −⎛⎝⎜

⎞⎠⎟

M(t) Slnt + const=

∆E = KV 1-HH

a

k

⎛⎝⎜

⎞⎠⎟

2

f(H )k

Hk

f(H )k

Hk

Time Dependence of Magnetization

Spin-standMFM, VSM

Dynamic

10-13 10-9-10-8 10-4 1

time (seconds)

Mag

netiz

atio

n

time (seconds)

10-1 100 101

Nor

mal

ized

Am

plitu

de

0.94

0.95

0.96

0.97

0.98

0.99

1.00

1.01

1500 frmm3000 frmm4550 frmm

300 K

Short-term Experiment

Stability of Magnetic Recordings

300 K

330 K

341 K

355 K

time (seconds)

10-1 100 101

Nor

mal

ized

Am

plitu

de

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

300 K

341 K330 K

355 K

3000 frmm

Short-term Experiment

Stability of Magnetic Recordings

Temperature( K)

280 300 320 340 360 380 400 420

Coe

rciv

ity (O

er)

1000

1500

2000

2500

Effect of Temperature on Medium Properties

• Ms does not change• Reversible change in Hc : decreases by ~6 Oe per K

-4000 -2000 0 2000 4000-3

-2

-1

0

1

2

3x 10

-3

Applied Field (Oe)

Mag

netiz

atio

n (e

mu)

295 K343 K364 K384 K409 K

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

Transition Response

0 20 40 60 80 100 120 140 160 180 200-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Am

plitu

de

Spinstand Captured Transition Response

Data Format

0 1 0 0 0 2 0 0 0 3 0 0 0 4 0 0 0 5 0 0 0 6 0 0 0 7 0 0 0 8 0 0 0 9 0 0 01 8 0

1 9 0

2 0 0

2 1 0

2 2 0

2 3 0

2 4 0

2 5 0

2 6 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 01 9 0

2 0 0

2 1 0

2 2 0

2 3 0

2 4 0

2 5 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0 4 0 01 8 0

1 9 0

2 0 0

2 1 0

2 2 0

2 3 0

2 4 0

2 5 0

Preamble Synchronization Marker

PRML System

ReceiveFilter

(low pass)Adaptive

FilterViterbi

DetectorMagneticRecordingChannel

Timing &Tap Updating

Wide-BandNoise

nT+τe

ny nxnx ny

,....3,2,1 ,)1)(1()( =+−= nDDDP n

Serial Turbo Detector

DEMUX

Depuncture

APP

Outer

2π

xext

L

( )1

kpΛ

( )k

uΛ

−

1

2

−πAPP

Inner

⊕( )

kxΛ

−

kyMUX

Puncture⊕

I

OI

O

I

I

O

O

ku

Drive Data Experiment

5 6 7 8 9 10 1110-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

SNR [dB]

Bit

Erro

r Rat

e

Rate 16/17 ideal turboRate 16/17 drive turboIdeal EPR4 Drive EPR4

Advanced Media

Science enables:

6 million-million bits/square inch!

2-D Intersymbol Interference

x11 x12

x22x21

x13

x23

x14

x24

x34x33x32x31

x41 x42 x43 x44

-1 -1 -1 -1-1

-1

-1

-1 -1 -1 -1-1-1

-1-1-1-1-1

-1-1

r11 r12

r22r21

r13

r23

r14

r24

r34r33r32r31

r41 r42 r43 r44

r02 r03 r04 r05

r15

r01

r25

r52 r53 r54 r55

r45

r35

r00

r10

r20

r30

r040

r51r50

⎟⎟⎠

⎞⎜⎜⎝

⎛=

25.05.05.01

h ⊕

w(i,j)

jijijijijiji wxxxxr ,1,11,,1,, 25.05.05.0 ++++= −−−−

GUARD BAND

MMSE Equalization

• Combination of equalization and decoding for 2-D ISI

• Equalizer designed subject to peak power constraint

a xLDPCEncoder

a(i,j) x(i,j) r(i,j) MMSEEqualizer

LDPCDecoder

ChannelISI

w(i,j)

),( jia∧

),( jix∧

Channel

Iterative MMSE Equalization

• Soft information passed from LDPC decoder to equalizer

• Scheduling: MMSE-LDPC iterations

a xLDPCEncoder

a(i,j) x(i,j) r(i,j) MMSEEqualizer

LDPCDecoder

ChannelISI

w(i,j) Extrinsic Information

),( jia∧

),( jix∧

Channel

PerformancePerformance of MMSE Equalization and Decoding

-6

-5

-4

-3

-2

-1

0

1 1.5 2 2.5 3 3.5 4 4.5

SNR (dB)

Bit-

Erro

r R

ate

in lo

g10

ISI-free

ItrWiener 1-20

ItrWiener 1-10

ItrWiener 1-5

ItrWiener 1-1

Wiener

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

LDPC Bipartite Graph

Check Nodes

Variable Nodes (x)

Full-graph

x(i+2,j)

x(i+1,j)

x(i,j)

x(i+2,j+1)

x(i+1,j+1)

x(i,j+1)

x(i+2,j+2)

x(i+1,j+2)

x(i,j+2)

r(i+1,j+1)

r(i,j+1)r(i,j)

r(i+1,j)

FromCheckNodes

Performance

Performance of Iterative Decoding Schemes

-6

-5

-4

-3

-2

-1

0

1 1.5 2 2.5 3 3.5 4 4.5

SNR (dB)

Bit-

Erro

r R

ate

in lo

g10

ISI-freeItrWiener_10 1-20Fullgraph_10Wiener

Full-graph analysis

• Length 4 cycles present which degrade performance of message passing algorithm

x(i+2,j) x(i+2,j+1)

x(i+1,j) x(i+1,j+1)

x(i,j) x(i,j+1)

x(i+2,j+2)

x(i+1,j+2)

x(i,j+2)

r(i+1,j+1)

r(i,j+1)r(i,j)

r(i+1,j)

FromCheckNodes

Ordered Subsets

• Taken from imaging applications – data sets grouped into subsets to speed up computations

• Eliminate loops in the channel ISI graph

Grouped ISI Graph

Performance

Performance of Iterative Decoding Schemes

-6

-5

-4

-3

-2

-1

0

1 1.5 2 2.5 3 3.5 4 4.5

SNR (dB)

Bit-

Erro

r R

ate

in lo

g10

ISI-freeOrdered SubsetsItrWiener 1-20FullgraphWiener

Consider Separating the ISI

Down-track separable from cross-track

Linear combination

Separating 2-D ISI

•Advantages of separating equalization•shortening ISI and reducing detector complexity•separating 2-D ISI and reducing detector complexity

w(i, j)

2-D ISIChannel

r(i, j)

w(i,j)

Vertical ISI Horizontal ISI

r(i, j)y(i, j)

Separating Equalization

Separable channel response

A Separable 2-D ISI

( )5.015.0

125.05.05.01

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛=h

x(i, j)Vertical ISI Horizontal ISI Channel

Detector

r(i, j)

w(i,j)

y(i, j)

Separable Channel Response

),( jix∧

Serial Turbo Codes

Rate 1/2 Systematic Encoder Rate 1/1 Non-Systematic Encoder

Separable 2-D ISI

x11 x12

x22x21

x13

x23

x14

x24

x34x33x32x31

x41 x42 x43 x44

-1 -1 -1 -1-1

-1

-1

-1 -1 -1 -1-1-1

-1-1-1-1-1

-1-1

x21 x22 x23 x24

Detection Performance

-5

-4

-3

-2

-1

5 6 7 8 9 10 11 12SNR (dB)

Bit-

Erro

r-R

ate

In lo

g10

ZF_Horizontal_MAP

Vertical_Horizontal_MAP

MMSE_Equalization

Iterative Decoder Diagram I

Equalization MAPDetector

LDPCDecoder

r(i, j)

Row-by-Row Detector

Conventional One-Dimensional Iterative Decoder

Extrinsic Information

Hard Decision

Iterative Decoder Diagram II

VerticalDecoder

HorizontalDetector

LDPCDecoder

r(i, j)

Passing TransitionProbability

Conventional Iterative Detector

Extrinsic Information

Hard Decision

Decoding Performance

Performance of Iterative Decoding Diagram I and II

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5 6SNR (dB)

Bit-

Erro

r-Rat

e In

log1

0

ISI-free

Diagram I_Iter1

Diagram I_Iter2

Diagram I_Iter3

Diagram II_Iter1

Diagram II_Iter2

Diagram II_Iter5

Iterative Decoder Diagram III

VerticalMAP Detector

HorizontalMAP Detector

LDPCDecoder

Z

⊕

⊕

⊕

⊕-

-

-

-+

+

+

+

D

)( , jixL−

)( , jiyL−

)( ,|

jiyL

)( , jiLDPC xL

Decoding Performance

Performance of Iterative Decoding Diagram III

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5SNR (dB)

Bit-

Erro

r_R

ate

in lo

g10

Diagram III_Iter1_SubIter2

Diagram III_Iter2_SubIter2

Diagram III_Iter3_SubIter2

Diagram III_Iter4_SubIter2

Diagram III_Iter10_SubIter2

ISI_free

Performance Comparison

-6

-5

-4

-3

-2

-1

0

0 1 2 3 4 5 6

SNR (dB)

Bit-

Erro

r-R

ate

In lo

g10

ISI-freeDiagram III_Iter10_SubIter2Diagram II_Iter5Diagram I_ZF_Equa_Iter3Diagram I_M M SE_Equa_Iter10

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