Signal Processing for Storage

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Signal Processing for Storage

• Borivoje Nikolic
• Department of Electrical Engineering and Computer
  Sciences
• University of California at Berkeley
• bora_at_eecs.berkeley.edu

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Marvel of Technology
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Disk Drives

• 1956 IBM engineers in San Jose introduced the
  first computer disk storage system
• The 305 RAMAC (Random Access Method of Accounting
  and Control) could store five million characters
  (five megabytes) of data on 50 disks, each 24
  inches in diameter.

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Todays Disks

• IBM Travelstar 17.1 Gb/in2
• Experimental densities 35-Gb/in2 every square
  inch of disk space could hold 4.37 GB -- nearly
  as much data as a 5.25-inch diameter DVD-ROM.
  (4.7 GB per surface) or seven CD-ROMs (each 650
  MB).
• NSIC is about to demonstrate 100Gb/in2
• Desktop/platter (3.5-inch diameter) 50 GB
• Notebook/platter (2.5-inch) gt20 GB
• Microdrive (1-inch) gt 2 GB.

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Trends in Magnetic Disk Drives

• Exponential growth in capacity is due to
• reduction of head flying height
• reduction of the gap size in the head
• reduction of the media thickness
• advanced signal processing methods
• advanced digitalintegrated circuits

Areal density of data in disk drives
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IBMs Areal Densities
http//www.storage.ibm.com/technolo/grochows/groch
o01.htm
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Datarate Trends in Disk Drives
Source ISSCC
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Flight Height
Rotation speeds 4500 15000 rpm
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Price Trends
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Magnetic Recording Fundamentals
Magnetic Disk Track Recording
Magnetization Levels
Detected signal in the Head
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Magnetic Recording Fundamentals

• Increased recording density results in
• reduced peak amplitude
• peak shift

Reduced Amplitude
Isolated Pulses
Superposed Pulses
Peak Shift
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Lorentzian Pulse
Lorentzian
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Bandlimited Channels
Spectral control (ISI
control) SNR limitation
Towards Shannon capacity

Equalization - Partial response
Channel coding - Trellis/Parity coding
Combined coding and Equalization - Iterative
coding
Going to 1Tb/in2 density will lower the SNR by
another 6dB
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Signal Equalization

• Lorenzian Pulse
• Equalization (1-D)(1D)n

1.0
0.5
PW50
User density PW50/T
(1-D)(1D)
(1-D)(1D)2
(1-D)(1D)3
2
3
1
1
1
EPR4
E2PR4
PR4
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Signal Response

• Simulated readback signal User density 1.4
  User density 3.0

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Read Channel Building Blocks
WriteSignal
WriteData
Encoder
Scrambler
Precomp
Servo
ReadSignal
VGA
CT Filter
Equalizer
Detector
ADC
ReadData
Decoder
Descrambler
Timing recovery
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Amplitude Spectra
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Equalization Targets
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Eye Diagrams
PR4
EPR4
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Maximum Likelihood Detection
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The Viterbi Detector

• Equalization Response Memory StatesPR4 1-D
  2 2 4 (2)EPR4
  (1-D)(1D)2 3 8E2PR4 (1-D)(1D)3
  4 16
• Alternative is to use DFEnot used in practice
  because of error propagation

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Error Distances

• Channel input error sequence

• Channel output error sequence

• Squared Euclidean error distance

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Error Probability

• Probability of misdetection of sequence Sk by Sk
  is a function of error distance, dK
• Performance of the PRML system is determined by
  the minimum distance error events

Error event distance spectrum
Q () - Error function
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Signal Processing Trends
Density
TURBO CODING
d0 or d1
n
E PRML, GEnPRML
EPRML
PARITY CODING
PRML
d0
(1,7)
(2,7)
PEAK DETECT
MFM
ANALOG
DIGITAL
H. Thapar
Time
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Current Implementation Approaches
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Parity-Coded Channel
Detect Error
Check Parity

Data
Correct Error
Viterbi Detector
P(D)
xk
-
Error Correlate

Delay
Maximum
nk
rk
Determine Likely Error Location
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Design Challenges

• One of the first Systems-on-a-Chip (SoC)
• gt 1Gb/s rate
• Single step vs. lookahead/parallel
• Reduced SNR, complex detection
• Integration with controller gives opportunities
  for more powerful coding and processing
• Iterative decoders (Turbo, LDPC)

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Architectural Choices

• Equalizer
• 6-10 taps, gt1Gb/s
• Choices of interleaving, pipelining, recoding,
  carry-save
• Infinite speed at the expense of power

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Architectural Choices

• Viterbi Decoder
• 16 32 state, trellis coded with prostprocessor
• Radix-2 vs. Radix-4, ACS vs. CSA
• Bit-level pipelining

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CSA Transformation
x y
x y
a
a
b
b-a
min(xa, yb)
min(x, yb-a)a
Min(A, B)
A B
Min(A, BK)
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Future Signal Processing

• SNRs will continue to decrease
• Iterative decoding
• Can we control the byte error rate?
• Complexity?
• Timing recovery at low SNRs
• Vertical recording is already back
• Multi-track recording?

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IBMs Advanced Storage Roadmap
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Holographic Storage