slide 3UH, Manoa, December 2009

Disk drive

magnetic surface

track

magnify

slide 4UH, Manoa, December 2009

Magnetic recording channel

magnetization pattern on a track

media noise

media noise

Readback waveform

• Sample readback waveform• discrete time channel

• yk = xk - xk-1 + nk

• output: yk (real)

• noise: nk Gaussian, white, variance 2

slide 5UH, Manoa, December 2009

Prior results: 1-D channel

-10 -5 0 5 100

0.2

0.4

0.6

0.8

1

SNR [dB]

Cap

acit

y [b

its/

chan

nel

-use

]

water-filling

upper bound (Holsinger 1964)

upper bound

(Shamai et al. 1991)

lower bound

(Shamai et al. 1991

lower bound

(Shamai-Verdu 1992)

slide 6UH, Manoa, December 2009

New results: 1-D channel

-10 -5 0 5 100

0.2

0.4

0.6

0.8

1

SNR [dB]

Cap

acit

y [b

its/

chan

nel

-use

]

upper and lower bound almost

coincide

lower bound

(Kavcic 2001, Vontobel, Kavcic

2008)

upper bound

(Yang, Kavcic, Tatikonda 2005)

slide 7UH, Manoa, December 2009

LDPC codes: code/channel graph

C C C

V VV V

C

V V

c1 c4c3c2

s1 s3 s4 s6s5s2

T TTTT T

z1 z3 z4 z6z5z2

q0 q2 q3 q5q4q1 q6

slide 8UH, Manoa, December 2009

Noise tolerance thresholds

• Channel: 1-D

• Regular Gallager codes with variable node degree = 3

slide 9UH, Manoa, December 2009

Simulation results r = 0.5

slide 10UH, Manoa, December 2009

General 2-D Granular Media Model

• Granular medium: 2DMR (10Tb/sq in)

channel input

bits are written on grains

scan reading

channel output

granular medium

slide 11UH, Manoa, December 2009

Ordered statistics decoding on channels with memory

• Linear block codes (Reed-Solomon) are still in data storage standards (CDs, DVDs)

• Powerful codes, but difficult to decode on channels with memory

• We are developing ordered statistics techniques (pioneered by Fossorier and Lin) for channels with memory

slide 12UH, Manoa, December 2009

Summary

• Storage channels are channels with memory

• Research in– Channel modeling– Detection/estimation– Timing recovery– Information theory– Coding/Decoding