1. Contact: david.wright@exeter.ac.uk 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

2. Contact: david.wright@exeter.ac.uk add ECC modulation encoder laser drive electronics optics remove ECC decoder equalisation & detection optics User data disk a k r(t) U k Optical read-out model Modulation Encoder Equaliser ML Detector Noise âkâk akak The Optical Recording Channel Continuous Time Filter 1/T Simulation Write channel Read channel User data âkâk ÛkÛk

3. Contact: david.wright@exeter.ac.uk t h(t) 0T2T3T-T-2T-3T ISI 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

4. Contact: david.wright@exeter.ac.uk 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)

5. Contact: david.wright@exeter.ac.uk 00.51.01.52.02.5 1.0 0.5 0 Spatial Frequency (m -1 ) Normalised response (×10 6 ) 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

6. Contact: david.wright@exeter.ac.uk 1 0 0 1 2 0123456-2-3 0123456-2-3 0123456-2-3 1/2T0 G(D)g(t)G(f) time b Frequency 0 1 2 3 1/2T0 0 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 + D 2 PR(1,3,3,1) G(D) = (1+D) 3

7. Contact: david.wright@exeter.ac.uk Which PR scheme to choose - DVD-ROM example DVD-ROM example

8. Contact: david.wright@exeter.ac.uk Equalisation Methods - FIR filter LMS algorithm zkzk FIR implementation

9. Contact: david.wright@exeter.ac.uk 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

10. Contact: david.wright@exeter.ac.uk (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

11. Contact: david.wright@exeter.ac.uk 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

12. Contact: david.wright@exeter.ac.uk 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

13. Contact: david.wright@exeter.ac.uk 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

14. Contact: david.wright@exeter.ac.uk PRML performance measures - Full simulation Full computer simulation of the PRML channel. Equal

15. Contact: david.wright@exeter.ac.uk 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

16. Contact: david.wright@exeter.ac.uk Equaliser details 15 tap FIR MLP - 15 inputs, 7 hidden layers Channel bit 0.133  m Some results - DVDROM disk - MLP equaliser

17. Contact: david.wright@exeter.ac.uk Ultra-high density DVDROM - MLP equaliser Equaliser details 15 tap FIR MLP - 15 inputs, 10 hidden layers 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)

18. Contact: david.wright@exeter.ac.uk Replace Viterbi detector with a neural network ? GLM MLP DVD-ROM: Channel bit size 0.133  m; RLL(2,10) PR(2332)

19. Contact: david.wright@exeter.ac.uk  0 0 y t 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 y t 0 0  The majority of errors are produced in these two patterns:  Expert detectors showed significant advantage over a general non-linear detector. Improving the neural network detector