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Neural Networks for PRML equalisation and data detection

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

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Neural Networks for PRML equalisation and data detection

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  1. 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. The Optical Recording Channel laser drive electronics User data modulation encoder add ECC optics Write channel U a k k disk Ûk r(t) âk User data equalisation & detection remove ECC Read channel decoder optics Simulation Noise ak Optical read-out model Continuous Time Filter Modulation Encoder ML Detector Equaliser âk 1/T

  3. h(t) t -3T -2T -T 0 T 2T 3T ISI ISI Typical pulse response for optical channel • Pulse response spread over many bit-cells - ISI • Read-out signal deteriorated by noise Inter-Symbol Interference (ISI) Additive noise 3T written mark

  4. 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. 1.0 Normalised response 0.5 0 0 0.5 1.0 1.5 2.0 2.5 (×106) Spatial Frequency (m-1) 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. PR Classes for optical recording G(D) g(t) G(f) 1 PR Class 1 or PR(1,1) G(D) = 1+D 0 0 1/2T -3 -2 -1 0 1 2 3 4 5 6 2 PR Class 2 or PR(1,2,1) G(D) = (1+D)2 = 1 +2D + D2 1 0 -3 -2 -1 0 1 2 3 4 5 6 0 1/2T PR(1,3,3,1) G(D) = (1+D)3 3 2 1 0 -3 -2 -1 0 1 2 3 4 5 6 0 1/2T Frequency time b

  7. Which PR scheme to choose - DVD-ROM example DVD-ROM example

  8. Equalisation Methods - FIR filter LMS algorithm FIR implementation zk

  9. FIR Equalisation -output signal 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.

  10. Optical PR Equalisation Optical filtering/channel shaping by shading bands (a) Shading band dimensions. (b) Shading band position in the collector path of the optical system

  11. Optical PR Equalisation Optically equalised channel responses for channel bit sizes of 0.2µm, 0.25µm, 0.3µm and 0.35µm. Optically equalised PR target spectrum

  12. Optical PR(1221) 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. Output levels 0,1,2,3,4,5,6,7

  13. PR Equalisation using Neural Networks Complexity of network depends on number of input units number of hidden units Is a non-linear equaliser better at coping with non-linearities inherent in optical channel ? We use a multi-layer perceptron (MLP) type of neural network as a non-linear equaliser Neural networks have been studied for many communications and some storage applications

  14. PRML performance measures - Full simulation Equal Full computer simulation of the PRML channel.

  15. Some results - phase change disk - Optical equaliser 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.

  16. · Optical parameters l 650nm Wavelength, Numerical aperture, NA 0.6 Illumination Gaussian Media DVDROM m User bit 0.266 m Modulation code 1/2RLL(2,10) Noise 50% Media 50% Electronic 20MHz Bandwith Some results - DVDROM disk - MLP equaliser Equaliser details 15 tap FIR MLP - 15 inputs, 7 hidden layers Channel bit 0.133m

  17. 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. Replace Viterbi detector with a neural network ? DVD-ROM: Channel bit size 0.133m; RLL(2,10) PR(2332) MLP GLM

  19. Improving the neural network detector • 1 1 yt 0 0 • 0 0 yt 1 0 • The majority of errors are produced in these two patterns: • 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. • Expert detectors showed significant advantage over a general non-linear detector.

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