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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]
The Optical Recording Channel
User
data
laser drive
electronics
modulation
encoder ak
add ECC
Uk
optics
Write channel
disk
Ûk
User
data
remove
ECC
âk
decoder
equalisation
& detection
ak
Optical
read-out
model
optics
Read channel
Simulation
Noise
Modulation
Encoder
r(t)
Continuous
Time Filter
Equaliser
1/T
Contact: [email protected]
ML
Detector
âk
Typical pulse response for optical channel
h(t)
• Pulse response spread over many bit-cells - ISI
• Read-out signal deteriorated by noise
t
-3T
-2T
ISI
-T
0
T
2T
ISI
3T
Inter-Symbol
Interference (ISI)
written mark
Additive noise
3T
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]
Normalised response
The optical channel transfer function
1.0
NA - numerical aperture of
objective lens.
 - Laser wavelength.
0.5
2 NA

0
0
0.5
1.0
1.5
2.0
2.5 (×106)
Spatial Frequency (m-1)
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]
PR Classes
for optical
recordingG(f)
G(D)
g(t)
1
PR Class 1 or PR(1,1)
0
G(D) = 1+D
-3 -2 -1 0 1 2
3
4 5
6
-3 -2 -1 0 1 2
3
4 5 6
-3 -2 -1 0 1 2
3
4 5 6
0
1/2T
2
PR Class 2 or PR(1,2,1)
1
G(D) = (1+D)2 = 1 +2D + D2
0
PR(1,3,3,1)
G(D) = (1+D)3
0
1/2T
3
2
1
0
0
timeb
Contact: [email protected]
Frequency
1/2T
Which PR scheme to choose - DVD-ROM example
DVD-ROM example
1
0
0
0.1

Optical parameters
Wavelength, 
Numerical aperture, NA
Illumination
Media
User bit
Modulation code
Noise
650nm
0.6
Gaussian
DVDROM
0.266m
1/2RLL(2,10)
50% Media
50% Electronic
20MHz Bandwith

Optical variables for Step Response
(reflectance)
Channel
Transfer Function
Wavelength of illumination: PR(2332)
650nm
PR(3443)
NA of Objective Lens
0.6
PR(12221)
Illumination characteristics PR(23332)
Gaussian
PR(34443)
Illumination characteristics (radial)
I = 0.64118Io
Illumination characteristics (tangential) I = 0.99005Io
Reflectance of bit
0.8
Reflectance of track
0.8
Bit Width
0.3999um
End shape of bit
circular
Um per element
0.0095215um

Channel parameters:
CTF:
Digital Filter
Equiriple
15 Taps linear FIR using
the pseudo inverse method
to calculate the taps.
Non-linear FIR using
MLP: no. of inputs 15, no.
of hidden units 7, weight
0.2
0.3
0.4
0.5
decay.
Contact: [email protected]
Frequency (1/Tb)
Detector
Viterbi
Equalisation Methods - FIR filter
Equaliser E(f)
Input
X(f)
Input
xk
Channel
C(f)
s(t)
Channel
C(f)
Adaptive
filter
CTF
1/Tb
CTF
Hc(f)
zk
FIR
Hd(f)
Target
G(f)
Decision
device
ek
LMS algorithm
+
yk
PR filter
Decision directed
xk
Predefined xk
sk
D
D
FIR implementation
b-K
b-K+1
bK-1
bK

zk
Contact: [email protected]
FIR Equalisation -output signal
..000111111000010011100000100011100011111100000000110000101000111100011000..
8/8
200
A readout signal (solid
line), with a channel
(a)
(b)
bit of 0.22µm, equalised to PR(1331).
800
7/8
6/8
Samples
600
5/8
4/8
400
3/8
2/8
200
Ideal PR levels
Normalised Magnitude
(a)
1
150
X ideal PR samples
100
0 FIR equalised signal.
50
1/8
0/80
0
-0.5
Channel bits
0
0.5
1
FIR Output levels
250
Samples
0
-0.5
0
0.5
1
FIR Output levels
1.5
200
(c)
200
(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.
1.5
(d)
150
150
100
100
50
50
0
-0.5
0
0.5
1
FIR Output levels
Contact: [email protected]
1.5
0
-0.5
0
0.5
1
FIR Output levels
1.5
Optical PR Equalisation
Laser
diode
(a)
(b)
2r
Photo
-detector
Optical filtering/channel
shaping by shading bands
Shading
band
w
Discband position in the collector path of the optical system
(a) Shading band dimensions. (b) Shading
Wavelength, 
650nm
Numerical aperture, NA
0.6
Illumination
Gaussian
Collector aperture radius
r
Shading band
Vertical, obscuring
Media
Phase-change
Contact: [email protected]
PR response
Optical
PRequalised
Equalisation
Optically
channel
0.5
Channel bit = 0.2µm
w = 0.6r
PR(12221)
0.3
Magnitude Response
Magnitude Response
0.4
0.2
0.1
0
Normalised frequency (1/Tb)
Optically equalised
channel responses for
channel bit sizes of
0.2µm, 0.25µm, 0.3µm
and 0.35µm.
0.3
0.2
0
0.5
0.6
(b)
0
Normalised frequency (1/Tb)
0.5
Optically
equalised
Channel bit = 0.3µm
w = 0.4r
PR(1221)
0.4
0.3
0.2
(c)
0.1
Magnitude Response
0.8
0.5
Magnitude Response
0.4
0.1
(a)
0
Channel bit = 0.25µm
w = 0.5r
PR(3443)
0
0
Normalised frequency (1/Tb)
0.5
Channel bit = 0.35µm
w = 0.3r
PR(1331)
0.6
PR target
spectrum
0.4
0.2
0
(d)
0
Normalised frequency (1/Tb)
Contact: [email protected]
0.5
Optical equalisation
Electronic equalisation
1
..1111110001111100000001111111100000011111001100011111..
1
(a)
Normalised Magnitude
Normalised Magnitude
..1111110001111100000001111111100000011111001100011111..
0.8
0.6
0.4
0.2
0
(b)
0.8
0.6
Optical PR(1221)
0.4
0.2
0
Channel bit, Tb
400
(c)
(d)
Num. of samples
Num. of samples
500
A 0.3µm channel using PR(1221).
(a) Electronically and
(b) Optically equalised
signal using a shading band of 0.4r.
Channel bit, Tb
600
400
300
200
300
200
100
100
0
0
0.5
Output levels
0
1
0.6
(f)
Num. of samples
Num. of samples
(e)
150
100
50
0
0.2
0.4
Output levels
200
250
200
0
150
100
0.5
Output levels
1
Output levels 0,1,2,3,4,5,6,7
50
0
0
(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.
0
0.2
0.4
Output levels
0.6
Contact: [email protected]
PR Equalisation using Neural Networks
Input
layer
Hidden layer
Linear
output
unit
(7 hidden units)
Complexity of network depends on
number of input units
rt
number of hidden units
rt-1
ŷt
rt-2
…
…
wij
rt-14
Weighted
connection
Neuron
bias
w0
w1
w2
wn
Transfer function

x
a j   ( w ji ri  b j )
linear
Output signal (ŷ )
Input signal (r )
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
Desired signal (target)
We use a multi-layer perceptron
(MLP) type of neural network as a
non-linear equaliser
Contact: [email protected]
PRML performance measures - Full simulation
Optical
read-out model
RLL
generator
Delay
Media
R(d,k)
Tb
velocity
SNR
Noise source
Read-back signal
generator
Noise
generator
Signal
generation
ak
Error
counter
BER
âk
CTF
ADC
Equal
FIR
Detector
Signal processing
LPF type
Order
Fc
Boost
Bit number
Range
Tap weights
Target
Memory length
Full computer simulation of the PRML channel.
Contact: [email protected]
Some results - phase change disk - Optical equaliser
0
0
(a)
-5
(b)
-5
-20
PR(1331) FIR
PR(1331) 0.3r SB
-25
-30
20
25
30
SNR (dB)
-20
20
35
0
Tb = 0.3µm
PR(1221) FIR
PR(1221) 0.4r SB
25
30
SNR (dB)
(c)
(d)
-2
log10(BER)
-5
-10
-15
-20
20
35
0
(b) 0.3µm
(d) 0.2µm.
-10
-15
(a) 0.35µm
(c) 0.25µm
log10(BER)
Tb = 0.35µm
-15
log10(BER)
Channel simulation results
using 77% media, 11% shot,
11%electronic, 1% laser
noise for channel bit sizes
of :
log10(BER)
-10
Tb = 0.25µm
PR(3443) FIR
PR(3443) 0.5r SB
25
30
SNR (dB)
35
-4
-6
Tb = 0.2µm
-8
PR(12221) FIR
PR(12221) 0.6r SB
-10
20
Contact: [email protected]
25
30
SNR (dB)
35
Some results - DVDROM disk - MLP equaliser
-0.5
-1.5
log10(BER)
Equaliser details
-2.5
15 tap FIR
MLP - 15 inputs, 7 hidden layers
-3.5
-4.5
-5.5
20
Channel bit 0.133m
Threshold detector
PR2332 Linear FIR + Viterbi
PR2332 Non-linear filter + Viterbi
PR3443 Linear FIR + Viterbi
PR3443 Non-linear filter + Viterbi
22.5
25
CNR(dB)
27.5
 Optical parameters
30
Wavelength,
Numerical aperture, NA
Illumination
Media
User bit
Modulation code
Noise
Contact: [email protected]
650nm
0.6
Gaussian
DVDROM
0.266m
1/2RLL(2,10)
50% Media
50% Electronic
20MHzBandwith
Ultra-high density DVDROM - MLP equaliser
-0.8
PR1111 linear filter
PR1111 non-lin filter
PR11111 linear filter
PR11111 non-lin filter
PR111111 linear filter
PR111111 non-lin filter
-1
-1.2
Equaliser details
-1.4
log10(BER)
15 tap FIR
-1.6
MLP - 15 inputs, 10 hidden
layers
-1.8
-2
-2.2
-2.4
-2.6
20
22.5
25
CNR(dB)
Channel bit 0.0952 m
27.5
30
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
Modulation
encoder
Optical
readout
model
at
+
Continuous
Time
Filter
Detector
^
at
1/T
DVD-ROM: Channel bit size 0.133m;
RLL(2,10) PR(2332)
Hidden layer
Input
layer
rt
Logistic
(10 hidden units) output unit
0
Linear detector
Non-linear detector
Threshold detector
rt
rt-1
-1
ŷt
rt-2
…
wij
rt-14
log10(BER)
…
MLP
Weighted
connection
-2
-3
Output signal (ŷ )
Desired signal (target)
Input signal (r )
Inputs
Logistic
output unit
-4
rt
rt-1
ŷt
rt-2
…
wij
-5
20
22.5
GLM
25
CNR(dB)
rt-14
Contact: [email protected]
27.5
30
Improving the neural network detector
 The majority of errors are produced in these two patterns:  1 1 yt 0 0  0 0 yt 1 0
 All MLPs are trained
with 3 post detection
inputs.
Expert
detector for
pattern 11yt 00
If detect
“11 yt 00”
rt
 General MLP detector:
no. of inputs = 7; no. of
hidden units = 5.
^y
t
General
Detector
Expert
detector for
pattern 00yt 11
If detect
“00 yt 11”
 Experts detectors: no.
of inputs = 9; no. of
hidden units = 7.
-1
-1.5
Non-linear detector
 Expert detectors showed significant
advantage over a general non-linear
detector.
log10(BER)
-2
-2.5
-3
Expert detectors
-3.5
-4
-4.5
20
22.5
Contact: [email protected]
25
SNR
27.5
30