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Disk drive

magnify. track. Disk drive. magnetic surface. Magnetic recording channel. magnetization pattern on a track. 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. Readback waveform. media noise.

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Disk drive

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  1. magnify track Disk drive magnetic surface

  2. Magnetic recording channel magnetization pattern on a track • Sample readback waveform • discrete time channel • yk = xk - xk-1 + nk • output: yk (real) • noise: nk Gaussian, white, variance 2 Readback waveform media noise media noise

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

  4. New results: 1-D channel 1 0.8 upper and lower bound almost coincide lower bound (Kavcic 2001, Vontobel, Kavcic 2008) upper bound (Yang, Kavcic, Tatikonda 2005) 0.6 Capacity [bits/channel-use] 0.4 0.2 0 -10 -5 0 5 10 SNR [dB]

  5. LDPC codes: code/channel graph c1 c2 c3 c4 C C C C V V V V V V s1 s2 s3 s4 s5 s6 T T T T T T q0 q1 q2 q3 q4 q5 q6 z1 z2 z3 z4 z5 z6

  6. Noise tolerance thresholds • Channel: 1-D • Regular Gallager codes with variable node degree = 3

  7. Simulation results r = 0.5

  8. General 2-D Granular Media Model • Granular medium: 2DMR (10Tb/sq in) granular medium scan reading bits are written on grains channel input channel output

  9. 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

  10. Summary • Storage channels are channels with memory • Research in • Channel modeling • Detection/estimation • Timing recovery • Information theory • Coding/Decoding

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