Correcting Errors in Optical Data Transmission Using ...

Correcting Errors in Optical Data Transmission Using Neural Networks Stephen Hunt1, Yi Sun1, Alex Shafarenko1, Rod Adams1, and Neil Davey1, Brendan Slater2, Ranjeet Bhamber2, Sonia Boscolo2, and Sergei K. Turitsyn2 1

Biological and Neural Computation Research Group, School of Computer Science University of Hertfordshire, Hatfield, Herts. AL10 9AB UK http://homepages.feis.herts.ac.uk/~nngroup/ {s.p.hunt,y.2.sun,a.shafarenko,r.g.adams,n.davey}@herts.ac.uk 2 Photonics Research Group, School of Engineering and Applied Science Aston University, Birmingham B4 7ET, UK http://www.ee.aston.ac.uk/research/prg/ {slaterbm,bhambers,s.a.boscolo,s.k.turitsyn}@aston.ac.uk

Abstract. Optical data communication systems are prone to a variety of processes that modify the transmitted signal, and contribute errors in the determination of 1s from 0s. This is a difficult, and commercially important, problem to solve. Errors must be detected and corrected at high speed, and the classifier must be very accurate; ideally it should also be tunable to the characteristics of individual communication links. We show that simple single layer neural networks may be used to address these problems, and examine how different input representations affect the accuracy of bit error correction. Our results lead us to conclude that a system based on these principles can perform at least as well as an existing non-trainable error correction system, whilst being tunable to suit the individual characteristics of different communication links. Keywords: Error correction, classification, optical communication, adaptive signal processing.

1 Introduction Fibre-optic data links are near ubiquitous in high-speed and long-distance data communications. Links of this type are subject to a combination of random processes and deterministic or quasi-deterministic effects, all of which can serve to degrade their performance [1]. Some of these arise as a result of the properties of the materials and equipment used, whilst others are a consequence of the design of the communication system and the regime under which it operates. Each installed fibre-optic link has a set of individual specific transmission impairments all its own: a characteristic signature of corruptions and distortions it applies to the transmitted signal, and an individual pattern of errors it introduces into the digital data stream. A system that can repair some of these distortions by post-processing the received signal, or that can separate line-specific distortions from non-recoverable errors, is potentially of great value. It has already been shown that overall system performance K. Diamantaras, W. Duch, L.S. Iliadis (Eds.): ICANN 2010, Part II, LNCS 6353, pp. 448–457, 2010. © Springer-Verlag Berlin Heidelberg 2010

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can be improved by employing a variety of post-processing techniques, such as tuneable dispersion compensation and electronic equalization (see [2-5] and references given in those sources). Post-processing techniques can be applied to signals in the optical domain and in the electrical domain (after conversion of the signal into an electric current). The use of electronic signal processing for amelioration of transmission impairments is attractive, and has become popular due to recent advances in high-speed electronics. A system that can be adapted to the characteristics of different data links, as proposed here, is of even greater value, as it may be tuned to give the best results for an individual link, and re-tuned as its characteristics change, which inevitably happens over time. In this ongoing project we have applied machine learning techniques to the problem of adaptive signal post-processing in optical data communication systems. To the best of our knowledge this is the first project in which such techniques have been applied to this particular problem, although neural networks have been applied to the analysis of performance in an optical channel [6]. In earlier work [7] we have demonstrated the feasibility of bit-error-rate improvement by adaptive post-processing of received electrical signals. Here we considerably extend our analysis. We use a much bigger data set, with data drawn from two different channels. We also use data in which the error rate, using energy thresholding, is much higher than before. This gives our classifier a more challenging task, with more errors to identify.

2 Background Optical data communications rely on the modulation of a visible-light or infra-red carrier wave to transmit a digital data stream over a fibre-optic link. There are a number of different schemes for modulating a carrier wave, but in this work we assume the simplest form of Amplitude Shift Keying, in which a 1 is represented by the light source being on, and a 0 is represented by the light source being off [1] (unsurprisingly this is known as On Off Keying). At the receiving end the light is converted into an analogue electrical signal by a photodiode, typically after some filtering. In order to correctly reproduce the digital signal that is sent along the link the received signal is compared with a decision threshold, allowing discrimination between logical 1s and 0s. There are several ways that this can be done: for example the output current may be examined at an optimized sample point within the time slot for transmitting a single bit, or the current may be integrated over some time interval and this value may be used for comparison purposes. The precise method employed depends on the design of the receiver. Here we assume that the classification is performed using current integrated over the entire time taken to transmit a single bit. Note that the approach we propose and describe here is generic and can be adapted to any receiver design. To minimize the bit-error-rate, we propose a method that permits the receiver to be adjusted to cope with the specific transmission impairments for a given link. This is achieved by applying learning algorithms based on the analysis of sampled currents within bit time slots and adaptive correction of the decisions taking into account accumulated information gained from analysis of the signal waveforms.

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3 Description of the Data The data used in these experiments is derived from a simulation of a multiplexed optical communications link carrying data bits on five parallel channels. On Off Keying is used to encode the bits for transmission, and the data values are a series of floating point numbers, each representing the amplitude of the signal received at a specific point in time. In this work we use data from two of the five channels, which we refer to as Channel 1 and Channel 2. Each channel has its own characteristics and here we do not mix the two data sets. Each data set consists of a sequence of samples representing 114,681 transmitted bits. It is worth noting that Channel 2 is not segmented in a manner that aligns well with the original bit boundaries, and hence may be harder to decode (see Figure 5). Each bit in the original signal is represented by a waveform, captured as a sequence of 32 floating point numbers: the signal amplitude at each of 32 equally spaced sample points during a single bit time slot. The waveform representing a sequence of 5 consecutive bits is shown in Figure 1. As already explained, a bit may be classified according the cumulative amplitude of the light wave. For each of the simulated light pulses in our data we know the original bit that it represents. Therefore the data consists of 32-ary vectors each with a corresponding binary label.

Fig. 1. An example of the intensity pattern for a stream of 5 bits - 0 1 0 0 1

Figure 2 gives an example of a bit that is misclassified. The middle bit of the sequence is a 0 but is identified from its cumulative amplitude (henceforth referred to as its energy) as a 1. This is due to the presence of two 1's on either side and to jitter. It would be difficult for any classifier to rectify this error. However there are other cases that can be readily identified by the human eye, and so may be amenable to automatic identification. Figure 3 illustrates an example where a misclassification occurs, even though the bit pattern seems obvious to the human observer. The central bit is misclassified as a zero based on its energy.

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Fig. 2. An example of a difficult error to identify. The middle bit is meant to be a 0, but jitter has rendered it very hard to see.

Fig. 3. The peak amplitude of the central bit is low, and it is classified as a zero from its energy. To the human eye it is ‘obvious’ that it should be classified as a 1

3.1 Representation of the Data The raw data may be pre-processed in a number of different ways before presenting it to the classifier. A single bit may be represented as a 32-ary vector (referred to here as the Waveform-1 representation), or as a single cumulative amplitude value (the sum of the 32 values, referred to as the Energy-1 representation). In order to improve classification accuracy we may also want to use information that may be present in adjacent bits. We thus create windowed input representations, in which values representing 3 contiguous bits are concatenated together, with the target output being the label of the central bit. The simplest approach (referred to as Waveform-3) is to use a 96-ary vector made up of the raw values for three consecutive bits. An alternative (referred to here as Energy-3) is to construct a vector comprising 3 consecutive

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S. Hunt et al. Table 1. The different data representations employed

Name

Arity

Description

Energy-1

1

The energy of the target bit

Energy-3

3

The energy of the target bit and one bit either side

Waveform-1

32

The waveform of the target bit

Waveform-3

96

The waveform of the target bit and the waveforms of the bits on either side

E-W-E

34

The waveform of the target bit together with the energy of the bit on either side

energy values. The third such representation we have used (referred to as E-W-E) employs a 34-ary vector, made up of the 32-ary vector of the bit being classified and the energy values of the bits either side of it in the data stream. Table 1 gives a summary of all the different data sets. 3.2 Setting the Threshold In order to find an optimum energy threshold for each channel we conduct a simple search for the value that produces the lowest bit error rate across the whole data stream for that channel. Due to the aforementioned misalignment in Channel 2 its error rate is much higher than that of Channel 1, with around a quarter of the bits being misclassified from their energy. In order to facilitate an analysis of the data we use the optimal threshold to divide it into two disjoint subsets: those bits that are correctly classified by comparing their Energy-1 value with the optimum threshold for the channel in question, and those that are mis-classified. We call these two subsets the easy and hard bits. 3.3 Visualization Using Principal Component Analysis (PCA) As each data point is a 32-ary vector of floating-point numbers it must be projected onto a lower dimensional space for visualization purposes. We use PCA to produce a linear projection onto a 2 dimensional space that preserves as much of the variance in the data as possible. Figure 4 shows this projection for the Channel 2 data set. In this projection there is a roughly linear separation between the patterns classified as 0 and as 1. This is an expected consequence of using a threshold. The separation is not an exact straight line because the thresholding takes place in a different data space to the data in the projection. The distribution of the hard cases is interesting. In the left hand side of the projection (which contains the easy zeroes) the hard ones occupy a distinct area – on the lower side and near the boundary, whereas the hard zeroes occupy the higher area on the other side of the boundary. A substantial proportion of the hard bits are spatially separable from the easy bits with which they are being confused, suggesting that a trainable classifier may be of use.

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Fig. 4. Projection of the Channel 2 data into a 2-D space based on PCA. The upper plot shows just the easy bits and the lower plot shows the data for all bits.

4 Classifier Used The classifiers employed in an optical data communications system need to be very fast under normal operating conditions. Simplicity is therefore a virtue. The main classifier we use in this work is a simple single layer neural network (SLN), comprising a single artificial neuron with a weighted input for each feature in the data vector. The SLN’s weight vector can therefore be thought of as a vector in the input space, and the decision boundary for the classifier is a hyperplane in the input space that is normal to the weight vector. Training the SLN is an iterative process of modifying the

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position of the decision boundary by modifying the weight vector, in an attempt to find the best solution to the problem of classifying input vectors into 1s and 0s. This is a simple, convex optimization problem. For the purposes of this work we use an SLN implemented using the NetLab toolbox for MatLab [8]. However, in an optical telecommunications system the classifier will have to function with great speed, and therefore will need to be implemented in hardware (probably using analogue devices); simplicity is therefore a virtue.

5 Experiments As the two channels have different characteristics they are treated separately. For each channel the bit stream is divided into a training set and a test set. As is normally the case it is sensible to validate the selection of the test set by choosing different training/test sets and then to report the mean accuracy across the different test sets. To this end we perform 10-fold cross-validation of the test set selection. We segment the data into 10 test sets. In the first data set (Channel 1) each distinct segment has 10,831 easy cases and 637 hard ones. We therefore construct 10 different training set / test set pairs. Hence each training set includes 103,212 cases and each test set has 11,468 cases in total. In each case an SLN is trained on the training set and then tested on the corresponding test set. For the Energy-1 data set we do not perform cross validation, but simply set the threshold that gives the best result over the whole data set, which can be done deterministically (see Figure 1), this represents the baseline performance. 5.1 Results for Channel 1 The results reported here are therefore (with the exception of Energy-1) evaluations on averages over the 10 different test sets. The main results are given in Table 2. Table 2. The results for Channel 1

Datasets Energy-1 Energy-3 Waveform-1 Waveform-3 E-W-E

Mean Accuracy ± Standard Deviation (%) 94.45 97.37 ± 0.13 98.30 ± 0.12 98.97 ± 0.13 98.36 ± 0.11

Error Rate (%) 5.05 2.63 1.70 1.03 1.64

These results are in accord with our earlier results on smaller data sets. We observe: • The addition of the energy of the adjacent bit either side of the target bit (Energy-3) almost halves the baseline error rate. • Waveform-3 gives best performance, reducing the original error rate by nearly four fifths. • The more information the classifier is given (the arity of the data) the better is the performance. This suggests that all the information used here is useful.

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5.2 Results for Channel 2 The results for Channel 2 are interesting. The main results are given in Table 3. Table 3. The results for Channel 2

Datasets Energy-1 Energy-3 Waveform-1 Waveform-3 E-W-E

Mean Accuracy ± Standard Deviation (%) 74.30 87.00 ± 0.24 98.15 ± 0.08 98.85 ± 0.12 98.24 ± 0.09

Error Rate (%) 25.70 13.00 1.85 1.15 1.76

These results here are more dramatic. We observe: • The addition of the energy of the bit either side of the target bit (Energy-3) again almost halves the error rate. • Waveform-3 again gives best performance, significantly reducing the original error rate. In fact the performance is returned to one that is similar to Channel 1, even though this is a much noisier channel. • The more information the classifier is given the better is the performance. • The neural network manages to overcome the alignment problem by using a weighted sum of the inputs rather than just a straightforward sum, as used by the thresholder.

Fig. 5. Examples of bits correctly classified by both neural network and the thresholder (blue), by the Neural network but not the thresholder (red) and by neither (green)

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To give a visualization of what is happening Figure 5 shows some instances of the 5 bit sequence 10100, where the middle bit is being classified. This is data from Channel 2 and the misalignment of the waveform is evident – it is shifted to the left by about half a bit width. In blue there are 50 instances of bits correctly classified by both the thresholder and the neural network, 5 instances, in red, where the thresholder is incorrect but the neural network is able to classify it correctly and in green 5 instances that neither classifier could correct. The neural network has learnt the shape of a wave representing a one and is able to use this to correct the red bits.

6 Discussion Fast and accurate signal post-processing in optical data communications systems is a challenging problem with commercial relevance. The challenge from a computational standpoint to provide a classifier that is sufficiently accurate to reduce bit error rates and fast enough to operate in real time. As a consequence we have restricted our investigation to an SLN employing input representations that are simple to obtain from a ‘raw’ sampled data stream. On the large data sets analyzed here we have shown we can reduce the error rate by about 80% on a channel where the original error rate was about 5%. But on the channel where misalignment caused the baseline error rate to be 25% we could eliminate almost all of these errors and return the error rate to just over 1%. A further benefit of the method proposed here is that the weight vector of an SLN is trainable, so an individual classifier can be tuned to fit the characteristics of a specific fibre-optic link, and a new weight vector can be found each time the characteristics of the link change sufficiently that the bit error rate rises above an acceptable level. This may be achieved by re-tuning an adjustable classifier in place, or simply by replacing an existing classifier with a new one that performs better.

References [1] Senior, J.H.: Optical Fiber Communications: Principles and Practice, 3rd edn. Pearson Education Limited, London (2009) [2] Bulow, H.: Electronic equalization of transmission impairments. In: Optical Fiber Communication Conference and Exhibit, OFC 2002, pp. 24–25 (2002) [3] Haunstein, H.F., Urbansky, R.: Application of Electronic Equalization and Error Correction in Lightwave Systems. In: 30th European Conference on Optical Communications (ECOC), Stockholm, Sweden (2004) [4] Rosenkranz, W., Xia, C.: Electrical equalization for advanced optical communication systems. AEU - International Journal of Electronics and Communications 61, 153–157 (2007) [5] Watts, P.M., Mikhailov, V., Savory, S., Bayvel, P., Glick, M., Lobel, M., Christensen, B., Kirkpatrick, P., Song, S., Killey, R.I.: Performance of single-mode fiber links using electronic feed-forward and decision feedback equalizers. Photonics Technology Letters, IEEE 17, 2206–2208 (2005)

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[6] Wu, X., Jargon, J.A., Skoog, R.A., Paraschis, L., Willner, A.E.: Applications of Artificial Neural Networks in Optical Performance Monitoring. J. Lightwave Technol. 27, 3580– 3589 (2009) [7] Hunt, S.P., Sun, Y., Shafarenko, A., Adams, R.G., Davey, N., Slater, B., Bhamber, R., Boscolo, S., Turitsyn, S.K.: Adaptive Electrical Signal Post-processing with Varying Representations in Optical Communication Systems. In: Proceedings of the 11th International Conference on Engineering Applications of Neural Networks (EANN 2009), pp. 235–245 (2009) [8] Nabney, I.T.: Netlab: Algorithms for Pattern Recognition. Springer, London (2002)