1. Dec 2009 UH, Manoa, December 2009 Signal Processing and Coding for Data Storage Alek Kavcic University of Hawaii Graduate students and post-docs Kan Li Fabian Lim Ninoslav Marina Xiujie Huang Xiaojun Yuan

2. slide 2 UH, Manoa, December 2009 Basics of disk drive technology

3. slide 3 UH, Manoa, December 2009 Disk drive magnetic surface track magnify

4. slide 4 UH, Manoa, December 2009 Magnetic recording channel magnetization pattern on a track media noise Readback waveform Sample readback waveform discrete time channel y k = x k - x k -1 + n k output: y k (real) noise: n k Gaussian, white, variance  2

5. slide 5 UH, Manoa, December 2009 Prior results: 1-D channel -10-50510 0 0.2 0.4 0.6 0.8 1 SNR [dB] Capacity [bits/channel-use] water-filling upper bound (Holsinger 1964) upper bound (Shamai et al. 1991) lower bound (Shamai et al. 1991 lower bound (Shamai-Verdu 1992)

6. slide 6 UH, Manoa, December 2009 New results: 1-D channel -10-50510 0 0.2 0.4 0.6 0.8 1 SNR [dB] Capacity [bits/channel-use] upper and lower bound almost coincide lower bound (Kavcic 2001, Vontobel, Kavcic 2008) upper bound (Yang, Kavcic, Tatikonda 2005)

7. slide 7 UH, Manoa, December 2009 LDPC codes: code/channel graph CCC VVVV C VV c1c4c3c2 s1s3s4s6s5s2 TTTTTT z1z3z4z6z5z2 q0q2q3q5q4q1q6

8. slide 8 UH, Manoa, December 2009 Noise tolerance thresholds Channel: 1-D Regular Gallager codes with variable node degree = 3

9. slide 9 UH, Manoa, December 2009 Simulation results r = 0.5

10. slide 10 UH, 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

11. slide 11 UH, 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

12. slide 12 UH, Manoa, December 2009 Summary Storage channels are channels with memory Research in –Channel modeling –Detection/estimation –Timing recovery –Information theory –Coding/Decoding