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Contact: [email protected]
Neural Networks for PRML equalisation and data detection
What is Partial Response signalling ?
Some commonly used PR schemes for data storage
How can we choose a PR scheme for optical storage systems ?
Equaliser design
analogue and digital filters
optical filters
neural networks
System performance measures
Analytical measures
Full simulation
Effects of non-linearities
Contact: [email protected]
add ECC modulation encoder
laser drive electronics
optics
remove ECC
decoder equalisation & detection
optics
User data
disk
ak
r(t)
Uk
Optical read-out model
Modulation Encoder
Equaliser ML Detector
Noise
âk
ak
The Optical Recording Channel
Continuous Time Filter 1/T
Simulation
Write channel
Read channelUser data
âk
Ûk
Contact: [email protected]
t
h(t)
0 T 2T 3T-T-2T-3T
ISIISI
Typical pulse response for optical channel
3T
Inter-Symbol Interference (ISI)
Additive noise
• Pulse response spread over many bit-cells - ISI
• Read-out signal deteriorated by noise
written mark
Contact: [email protected]
The Partial Response Solution
Allows ISI to occur but in a ‘known’ way
PR also called ‘Correlative level coding’ - signal levels are correlated
PR signalling allows for spectrum shaping and pulse shaping
We can re-distribute signal power to concentrate it in certain parts of spectrum
We can match the signal spectrum to that of the channel
reduces noise enhancement
PR is a minimum bandwidth approach
can signal at the Nyquist rate
1/T in a bandwidth 1/2T (as in ideal LPF solution)
Contact: [email protected]
0 0.5 1.0 1.5 2.0 2.5
1.0
0.5
0
2NA
Spatial Frequency (m-1)
Nor
mal
ised
res
pons
e
(×106)
The optical channel transfer function
NA - numerical aperture of objective lens.
- Laser wavelength.
No null at DC - PR schemes with (1+D) factor likely to be suitable
Falls strictly to zero beyond the optical cut-off
Contact: [email protected]
1
0
0
1
2
0 1 2 3 4 5 6-1-2-3
0 1 2 3 4 5 6-1-2-3
0 1 2 3 4 5 6-1-2-3
1/2T0
G(D) g(t) G(f)
time b Frequency
0
1
2
3
1/2T0
1/2T0
PR Classes for optical recording
PR Class 1 or PR(1,1)
G(D) = 1+D
PR Class 2 or PR(1,2,1)
G(D) = (1+D)2 = 1 +2D + D2
PR(1,3,3,1)
G(D) = (1+D)3
Contact: [email protected]
Equalisation Methods - FIR filter
FIRHd(f)
CTFHc(f)
ChannelC(f)
Equaliser E(f)
TargetG(f)
InputX(f)
Adaptivefilter
CTFChannelC(f)
Inputxk
PR filter
+
ek
yk
zk
1/Tb
s(t) Decisiondevice
Predefined xkDecision directed
xk
LMS algorithm
b -K
D
b -K+1 bK-1
D
bK
sk
zk
FIR implementation
Contact: [email protected]
0
1
Nor
mal
ised
Mag
nitu
de
Channel bits
8/8
7/8
6/8
5/8
4/8
3/8
2/8
1/8
0/8
Ideal PR levels
..000111111000010011100000100011100011111100000000110000101000111100011000..
(a)
A readout signal (solid line), with a channel bit of 0.22µm, equalised to PR(1331).
X ideal PR samples
0 FIR equalised signal.
(c) Noiseless output histogram for a PR(1331) for a channel with a bit size of 0.26µm and no modulation coding. (d) The same channel with 30dB of additive noise.
FIR Equalisation -output signal
-0.5 0 0.5 1 1.50
50
100
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FIR Output levels
-0.5 0 0.5 1 1.50
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FIR Output levels-0.5 0 0.5 1 1.5
0
50
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FIR Output levels
-0.5 0 0.5 1 1.50
200
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600
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FIR Output levels
(b)
Sam
ples
(c) (d)
(a)
Sam
ples
Contact: [email protected]
w
Disc
Shadingband
Laserdiode
Photo-detector
2r
(a) (b)
(a) Shading band dimensions. (b) Shading band position in the collector path of the optical system
Optical PR Equalisation
Optical filtering/channel shaping by shading bands
Contact: [email protected]
0 0.50
0.2
0.4
0.6
0.8
Mag
nitu
de R
espo
nse
0 0.50
0.1
0.2
0.3
0.4
0.5
Mag
nitu
de R
espo
nse
0 0.50
0.1
0.2
0.3
0.4
Normalised frequency (1/Tb)
Mag
nitu
de R
espo
nse
Channel bit = 0.2µmw = 0.6rPR(12221)
Normalised frequency (1/Tb)
Channel bit = 0.25µmw = 0.5rPR(3443)
Normalised frequency (1/Tb)
Channel bit = 0.35µmw = 0.3rPR(1331)
0 0.50
0.1
0.2
0.3
0.4
0.5
Normalised frequency (1/Tb)
Mag
nitu
de R
espo
nse
0.6
PR responseOptically equalised channel
Channel bit = 0.3µmw = 0.4rPR(1221)
(a) (b)
(c) (d)
Optically equalised channel responses for channel bit sizes of 0.2µm, 0.25µm, 0.3µm and 0.35µm.
Optical PR Equalisation
Optically equalised
PR target spectrum
Contact: [email protected]
Electronic equalisation Optical equalisation
..1111110001111100000001111111100000011111001100011111.. ..1111110001111100000001111111100000011111001100011111..
0 0.2 0.4 0.60
50
100
150
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Output levels
0 0.2 0.4 0.60
100
200
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Output levels
0
0.2
0.4
0.6
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1
Nor
mal
ised
Mag
nitu
de
0 0.5 10
50
100
150
200
250
Output levels
0 0.5 10
100
200
300
400
500
600
Output levels
0
0.2
0.4
0.6
0.8
1
Nor
mal
ised
Mag
nitu
deN
um. o
f sa
mpl
es
Num
. of
sam
ples
Num
. of
sam
ples
Num
. of
sam
ples
(c) (d)
(e) (f)
(a) (b)
Channel bit, Tb Channel bit, Tb A 0.3µm channel using PR(1221). (a) Electronically and (b) Optically equalised signal using a shading band of 0.4r.
(c) Output level histogram of electronic equaliser and(d) optical equaliser for a noise free signal. (e) Output level histogram of electronic equaliser and (f) optical equaliser for a noisy signal.
Optical PR(1221)
Output levels 0,1,2,3,4,5,6,7
Contact: [email protected]
PR Equalisation using Neural Networks
We use a multi-layer perceptron (MLP) type of neural network as a non-linear equaliser
Is a non-linear equaliser better at coping with non-linearities inherent in optical channel ?
Neural networks have been studied for many communications and some storage applications
Complexity of network depends on
number of input units
number of hidden units
… …
rt-1
rt-14
Input layer
Hidden layer
(7 hidden units)
Linear output unit
Weighted connection
Neuron
w0
w1
w2
wn
x
Transfer function
linear
bias
ŷt
Input signal (r ) Output signal (ŷ)
Desired signal (target)
rt
rt-2
)( jijij brwa
wij
… …
rt-1
rt-14
Input layer
Hidden layer
(7 hidden units)
Linear output unit
Weighted connection
Neuron
w0
w1
w2
wn
x
Transfer function
linear
bias
ŷt
Input signal (r ) Output signal (ŷ)
Desired signal (target)
rt
rt-2
)( jijij brwa
wij
Contact: [email protected]
PRML performance measures - Full simulation
RLL generator
Optical read-out model
DetectorFIR
Read-back signal generator
Delay
Error counter
Noisegenerator
CTF ADC
ak
âk
MediaR(d,k)Tb
velocitySNRNoise source
LPF typeOrderFcBoost
Bit numberRange
Tap weights TargetMemory length
Signal processing
Signalgeneration
BER
Full computer simulation of the PRML channel.
Equal
Contact: [email protected]
20 25 30 35-10
-8
-6
-4
-2
0
SNR (dB)
log 1
0(B
ER
)
20 25 30 35-20
-15
-10
-5
0
SNR (dB)
log 1
0(B
ER
)20 25 30 35
-20
-15
-10
-5
0
SNR (dB)
log 1
0(B
ER
)
20 25 30 35-30
-25
-20
-15
-10
-5
0
SNR (dB)
log 1
0(B
ER
)
Tb = 0.35µm
PR(1331) FIRPR(1331) 0.3r SB
Tb = 0.3µm
PR(1221) FIRPR(1221) 0.4r SB
Tb = 0.25µm
PR(3443) FIRPR(3443) 0.5r SB
Tb = 0.2µm
PR(12221) FIRPR(12221) 0.6r SB
(a) (b)
(c) (d)
Channel simulation results using 77% media, 11% shot, 11%electronic, 1% laser noise for channel bit sizes of :
(a) 0.35µm
(b) 0.3µm
(c) 0.25µm
(d) 0.2µm.
Some results - phase change disk - Optical equaliser
Contact: [email protected]
Optical parametersWavelength, 650nmNumerical aperture, NA 0.6Illumination GaussianMedia DVDROMUser bit 0.266mModulation code 1/2RLL(2,10)Noise 50% Media
50% Electronic20MHz Bandwith
20 22.5 25 27.5 30-5.5
-4.5
-3.5
-2.5
-1.5
-0.5
CNR(dB)
log
10
(BE
R)
Threshold detectorPR2332 Linear FIR + ViterbiPR2332 Non-linear filter + ViterbiPR3443 Linear FIR + ViterbiPR3443 Non-linear filter + Viterbi
Equaliser details
15 tap FIR
MLP - 15 inputs, 7 hidden layers
Channel bit 0.133m
Some results - DVDROM disk - MLP equaliser
Contact: [email protected]
Ultra-high density DVDROM - MLP equaliser
Equaliser details
15 tap FIR
MLP - 15 inputs, 10 hidden layers
20 22.5 25 27.5 30-2.6
-2.4
-2.2
-2
-1.8
-1.6
-1.4
-1.2
-1
-0.8
CNR(dB)
log
10
(BE
R)
PR1111 linear filterPR1111 non-lin filterPR11111 linear filterPR11111 non-lin filterPR111111 linear filterPR111111 non-lin filter
Channel bit 0.0952 m Smallest bit size on disk 0.285 m
Smallest resolvable bit 0.27 m (DVD format 0.4 m min bit size)
Contact: [email protected]
Replace Viterbi detector with a neural network ?
Noise
Modulationencoder
Opticalreadoutmodelat
ContinuousTimeFilter at
Detector+^1/T
rt
Noise
Modulationencoder
Opticalreadoutmodelat
ContinuousTimeFilter at
Detector+^1/T
rt
… …
rt-1
rt-14
Input layer
Hidden layer
(10 hidden units)
Logistic output unit
Weighted connection
ŷt
Input signal (r ) Output signal (ŷ)Desired signal (target)
rt
rt-2
wij
… …
rt-1
rt-14
Input layer
Hidden layer
(10 hidden units)
Logistic output unit
Weighted connection
ŷt
Input signal (r ) Output signal (ŷ)Desired signal (target)
rt
rt-2
wij
…
rt-1
rt-14
Inputs Logistic output unit
ŷt
rt
rt-2
wij
…
rt-1
rt-14
Inputs Logistic output unit
ŷt
rt
rt-2
wij GLM
MLP
DVD-ROM: Channel bit size 0.133m; RLL(2,10) PR(2332)
20 22.5 25 27.5 30-5
-4
-3
-2
-1
0
CNR(dB)
log
10
(BE
R)
Linear detectorNon-linear detectorThreshold detector
Contact: [email protected]
GeneralDetector
rt
If detect “00 yt 11”
If detect “11 yt 00”
Expert detector for
pattern 11yt00
Expert detector for
pattern 00yt11
yt^
GeneralDetector
rt
If detect “00 yt 11”
If detect “11 yt 00”
Expert detector for
pattern 11yt00
Expert detector for
pattern 00yt11
yt^
0 0 yt 1 0
All MLPs are trained with 3 post detection inputs.
General MLP detector: no. of inputs = 7; no. of hidden units = 5.
Experts detectors: no. of inputs = 9; no. of hidden units = 7.
1 1 yt 0 0 The majority of errors are produced in these two patterns:
20 22.5 25 27.5 30-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
SNR
log1
0(B
ER
)
Non-linear detector
Expert detectors
20 22.5 25 27.5 30-4.5
-4
-3.5
-3
-2.5
-2
-1.5
-1
SNR
log1
0(B
ER
)
Non-linear detector
Expert detectors
Expert detectors showed significant advantage over a general non-linear detector.
Improving the neural network detector
