1 35 Years of Progress in Digital Magnetic Recording Hisashi Kobayashi François Dolivo François Dolivo Evangelos Eleftheriou Online: Disk Drives File Systems 300 Petabytes Petabyte [1,000,000,000,000,000 bytes OR 10 15 bytes] Exabyte [1,000,000,000,000,000,000 bytes OR 10 18 bytes] How Much Data is Out There? 300 Petabytes Offline: Magnetic Tape CDs 8 Exabytes 2 35 Years of Progress in Digital Magnetic Recording 5 Exabytes: All words ever spoken by human beings. Analog Data: Paper – Film Videotape 200 Exabytes http://www.sims.berkeley.edu/research/projects/how-much-info-2003/ 2 Exabytes: Total volume of information generated worldwide annually. 0.5 x 10 18 seconds: Age of Universe
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Most likely data sequence {an} is obtained from thesample sequence { xn} that minimizes
∑ (yn – xn )2
Viterbi Detection AlgorithmDirect maximum-likelihood detection requires a number of computations that increases exponentially with the length of the data sequenceRecursive minimization of the “squared distance”:
∑ (y (a a ))2
reduces the computational complexity dramatically∑ (yn – (an – an-2))2
‘1’
Time‘1’
‘0’
26 35 Years of Progress in Digital Magnetic Recording
‘1’
‘0’
1
‘0’
14
1990: PRML Becomes Reality
27 35 Years of Progress in Digital Magnetic Recording
Noise Predictive Maximum Likelihood (NPML)At high recording densities the signal-to-noise ratio is reduced dramatically
Magnetized area shrinks; less signal energy
Correlated data-dependent transition noise and head/electronics noise increase
An effective way to increase the signal-to-noise ratio and achieve near optimal performance, for given magnetic-recording components, is noise prediction
Predictorwn
Noisesample
Predicted Noise sample
wn
NPML is a noise prediction/whitening scheme combined with maximum likelihood detection
0 0 0 0
1 0 0 0
0 1 0 0
1 1 0 0
0 0 1 0
1 0 1 0
0 1 1 0
1 1 1 0
0 0 0 1
1 0 0 1
10
28 35 Years of Progress in Digital Magnetic Recording
+Noise
sample
A decrease of the noise power by 2x3 orders of magnitude error rate improvement
1 0 0 1
0 1 0 1
1 1 0 1
0 0 1 1
1 0 1 1
0 1 1 1
1 1 1 1
10
15
Post-Processor Detector/DecoderTwo-stage detection strategy for retrieving the recorded information
• A primary NPML detector produces an initial estimate of the detected data• A noise-predictive post-processor detects and corrects errors in the primary detector
Primary NPMLDetector
Post-Processor
Readback signal
Detecteddata
First-passdata Error
signal
29 35 Years of Progress in Digital Magnetic Recording
Post-processors: Reduced-complexity schemes to correct dominant error patterns at NPML detector output
Utilize the noise-predictive principle for detecting “error signals” in the presence correlative noise
“Soft-decoding” of combined modulation/parity inner coding schemes
NPML Channel Architecture
Sector data: 512 bytes
User dataDigital Communication: “Transmit from one point in space to another”Sector data: 512 bytes
User data
RSdecoder
Sector data: 512 bytes
Modulationdecoder
Transmit from one point in space to another
Digital Recording:“Record at one point in time and retrieve at another”
RSencoder
Sector data: 512 bytes
Parityencoder
Noise-predictivepost-processor
Modulationencoder
30 35 Years of Progress in Digital Magnetic Recording
NPMLdetector
Low-passfilter
PRequalizer
Whiteningfilter
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Then and Now
1 1 1 1 1 1 11 1 1 1 1 10 0 0 0 0 0 0 0Readback signal in the 70’s
1 1 1 1 1 1 11 1 1 1 1 10 0 0 0 0 0 0 0
31 35 Years of Progress in Digital Magnetic Recording
… and we can still guarantee at most 1 error in 1015 bits read back
… readback signal today!
2000: NPML is Adopted by Industry
32 35 Years of Progress in Digital Magnetic Recording
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Recording Density GainsSNR requirements for bit error-rate 10-6
21
22
23
[dB
]
60 %
5.5 dB
15
16
17
18
19
20
21
gnal
-to-N
oise
Rat
io (S
NR
)
33 35 Years of Progress in Digital Magnetic Recording
1990: Digital PRML leads to a 40-50 % increase in recording density2000: Digital NPML leads to a 50-60 % increase in recording density
1.8 2 2.2 2.4 2.6 2.8 3 3.2Normalized Linear Density (PW50/T)
13
14Sig
Information Theoretic Limits
SNR requirements for sector error-rate 10-4
25RS-MTR96/104
SN
R [d
B]
15
20
LDPC(4095/4376)
34 35 Years of Progress in Digital Magnetic Recording
Normalized Linear density 2.4 2.6 2.8 3.0 3.2 3.4 3.6
10
18
Future Prospects
/in2
Atom Surface Density Limit
AtomLevelAtomLevel105
106
107
Area
l Den
sity
, Gbi
ts
HDD products
HDD LabDemos
Nanotechnology ProbeContact Area Limit
SuperparamagneticEffect
Probe-Like
Storage
Probe-Like
Storage
StorageStorage
10-1
100
10
102
103
104
bb
EnhancedMagneticEnhancedMagnetic
35 35 Years of Progress in Digital Magnetic Recording
Signal processing and coding have been instrumental for the remarkable progress of Storage Densities over the last 35 years
They will be even more essential as we approach fundamental physical limits