Information-theory analysis of skewed coding for suppression of pattern-dependent errors in digital communications

We present information-theory analysis of the tradeoff between bit-error rate improvement and the data-rate loss using skewed channel coding to suppress pattern-dependent errors in digital communications. Without loss of generality, we apply developed general theory to the particular example of a high-speed fiber communication system with a strong patterning effect. © 2007 IEEE.

Information theory analysis of regenerative channels

In this paper we summarize our recently proposed work on the information theory analysis of regenerative channels. We discuss how the design and the transfer function properties of the regenerator affect the noise statistics and enable Shannon capacities higher than that of the corresponding linear channels (in the absence of regeneration).

The application of artificial neural networks to the interpretation and classification of freshwater benthic invertebrate communities

This thesis presents a thorough and principled investigation into the application of artificial neural networks to the biological monitoring of freshwater. It contains original ideas on the classification and interpretation of benthic macroinvertebrates, and aims to demonstrate their superiority over the biotic systems currently used in the UK to report river water quality. The conceptual basis of a new biological classification system is described, and a full review and analysis of a number of river data sets is presented. The biological classification is compared to the common biotic systems using data from the Upper Trent catchment. This data contained 292 expertly classified invertebrate samples identified to mixed taxonomic levels. The neural network experimental work concentrates on the classification of the invertebrate samples into biological class, where only a subset of the sample is used to form the classification. Other experimentation is conducted into the identification of novel input samples, the classification of samples from different biotopes and the use of prior information in the neural network models. The biological classification is shown to provide an intuitive interpretation of a graphical representation, generated without reference to the class labels, of the Upper Trent data. The selection of key indicator taxa is considered using three different approaches; one novel, one from information theory and one from classical statistical methods. Good indicators of quality class based on these analyses are found to be in good agreement with those chosen by a domain expert. The change in information associated with different levels of identification and enumeration of taxa is quantified. The feasibility of using neural network classifiers and predictors to develop numeric criteria for the biological assessment of sediment contamination in the Great Lakes is also investigated.

Statistical mechanics of low-density parity-check codes

We review recent theoretical progress on the statistical mechanics of error correcting codes, focusing on low-density parity-check (LDPC) codes in general, and on Gallager and MacKay-Neal codes in particular. By exploiting the relation between LDPC codes and Ising spin systems with multispin interactions, one can carry out a statistical mechanics based analysis that determines the practical and theoretical limitations of various code constructions, corresponding to dynamical and thermodynamical transitions, respectively, as well as the behaviour of error-exponents averaged over the corresponding code ensemble as a function of channel noise. We also contrast the results obtained using methods of statistical mechanics with those derived in the information theory literature, and show how these methods can be generalized to include other channel types and related communication problems.

Statistical mechanics of broadcast channels using low-density parity-check codes

We investigate the use of Gallager's low-density parity-check (LDPC) codes in a degraded broadcast channel, one of the fundamental models in network information theory. Combining linear codes is a standard technique in practical network communication schemes and is known to provide better performance than simple time sharing methods when algebraic codes are used. The statistical physics based analysis shows that the practical performance of the suggested method, achieved by employing the belief propagation algorithm, is superior to that of LDPC based time sharing codes while the best performance, when received transmissions are optimally decoded, is bounded by the time sharing limit.

Analysis of magnetoencephaoographic data as a nonlinear dynamical system

This thesis presents the results from an investigation into the merits of analysing Magnetoencephalographic (MEG) data in the context of dynamical systems theory. MEG is the study of both the methods for the measurement of minute magnetic flux variations at the scalp, resulting from neuro-electric activity in the neocortex, as well as the techniques required to process and extract useful information from these measurements. As a result of its unique mode of action - by directly measuring neuronal activity via the resulting magnetic field fluctuations - MEG possesses a number of useful qualities which could potentially make it a powerful addition to any brain researcher's arsenal. Unfortunately, MEG research has so far failed to fulfil its early promise, being hindered in its progress by a variety of factors. Conventionally, the analysis of MEG has been dominated by the search for activity in certain spectral bands - the so-called alpha, delta, beta, etc that are commonly referred to in both academic and lay publications. Other efforts have centred upon generating optimal fits of "equivalent current dipoles" that best explain the observed field distribution. Many of these approaches carry the implicit assumption that the dynamics which result in the observed time series are linear. This is despite a variety of reasons which suggest that nonlinearity might be present in MEG recordings. By using methods that allow for nonlinear dynamics, the research described in this thesis avoids these restrictive linearity assumptions. A crucial concept underpinning this project is the belief that MEG recordings are mere observations of the evolution of the true underlying state, which is unobservable and is assumed to reflect some abstract brain cognitive state. Further, we maintain that it is unreasonable to expect these processes to be adequately described in the traditional way: as a linear sum of a large number of frequency generators. One of the main objectives of this thesis will be to prove that much more effective and powerful analysis of MEG can be achieved if one were to assume the presence of both linear and nonlinear characteristics from the outset. Our position is that the combined action of a relatively small number of these generators, coupled with external and dynamic noise sources, is more than sufficient to account for the complexity observed in the MEG recordings. Another problem that has plagued MEG researchers is the extremely low signal to noise ratios that are obtained. As the magnetic flux variations resulting from actual cortical processes can be extremely minute, the measuring devices used in MEG are, necessarily, extremely sensitive. The unfortunate side-effect of this is that even commonplace phenomena such as the earth's geomagnetic field can easily swamp signals of interest. This problem is commonly addressed by averaging over a large number of recordings. However, this has a number of notable drawbacks. In particular, it is difficult to synchronise high frequency activity which might be of interest, and often these signals will be cancelled out by the averaging process. Other problems that have been encountered are high costs and low portability of state-of-the- art multichannel machines. The result of this is that the use of MEG has, hitherto, been restricted to large institutions which are able to afford the high costs associated with the procurement and maintenance of these machines. In this project, we seek to address these issues by working almost exclusively with single channel, unaveraged MEG data. We demonstrate the applicability of a variety of methods originating from the fields of signal processing, dynamical systems, information theory and neural networks, to the analysis of MEG data. It is noteworthy that while modern signal processing tools such as independent component analysis, topographic maps and latent variable modelling have enjoyed extensive success in a variety of research areas from financial time series modelling to the analysis of sun spot activity, their use in MEG analysis has thus far been extremely limited. It is hoped that this work will help to remedy this oversight.

Brain ictal state characterisation through multimodal information integration

This Thesis addresses the problem of automated false-positive free detection of epileptic events by the fusion of information extracted from simultaneously recorded electro-encephalographic (EEG) and the electrocardiographic (ECG) time-series. The approach relies on a biomedical case for the coupling of the Brain and Heart systems through the central autonomic network during temporal lobe epileptic events: neurovegetative manifestations associated with temporal lobe epileptic events consist of alterations to the cardiac rhythm. From a neurophysiological perspective, epileptic episodes are characterised by a loss of complexity of the state of the brain. The description of arrhythmias, from a probabilistic perspective, observed during temporal lobe epileptic events and the description of the complexity of the state of the brain, from an information theory perspective, are integrated in a fusion-of-information framework towards temporal lobe epileptic seizure detection. The main contributions of the Thesis include the introduction of a biomedical case for the coupling of the Brain and Heart systems during temporal lobe epileptic seizures, partially reported in the clinical literature; the investigation of measures for the characterisation of ictal events from the EEG time series towards their integration in a fusion-of-knowledge framework; the probabilistic description of arrhythmias observed during temporal lobe epileptic events towards their integration in a fusion-of-knowledge framework; and the investigation of the different levels of the fusion-of-information architecture at which to perform the combination of information extracted from the EEG and ECG time-series. The performance of the method designed in the Thesis for the false-positive free automated detection of epileptic events achieved a false-positives rate of zero on the dataset of long-term recordings used in the Thesis.

Informational institutions in the agrifood sector:meta-information and meta-governance of environmental sustainability

In the agrifood sector, the explosive increase in information about environmental sustainability, often in uncoordinated information systems, has created a new form of ignorance ('meta-ignorance') that diminishes the effectiveness of information on decision-makers. Flows of information are governed by informal and formal social arrangements that we can collectively call Informational Institutions. In this paper, we have reviewed the recent literature on such institutions. From the perspectives of information theory and new institutional economics, current informational institutions are increasing the information entropy of communications concerning environmental sustainability and stakeholders' transaction costs of using relevant information. In our view this reduces the effectiveness of informational governance. Future research on informational governance should explicitly address these aspects.

Tighter decoding reliability bound for Gallager's error-correcting code

Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.

Statistical mechanics of typical set decoding

The performance of "typical set (pairs) decoding" for ensembles of Gallager's linear code is investigated using statistical physics. In this decoding method, errors occur, either when the information transmission is corrupted by atypical noise, or when multiple typical sequences satisfy the parity check equation as provided by the received corrupted codeword. We show that the average error rate for the second type of error over a given code ensemble can be accurately evaluated using the replica method, including the sensitivity to message length. Our approach generally improves the existing analysis known in the information theory community, which was recently reintroduced in IEEE Trans. Inf. Theory 45, 399 (1999), and is believed to be the most accurate to date. © 2002 The American Physical Society.

Weight vs magnetization enumerator for Gallager codes

We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (¸M), rather than on the weight enumerator (¸W) presented recently in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Critical noise levels for LDPC decoding

We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator , rather than on the weight enumerator employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Low density parity check codes: a statistical physics perspective

The modem digital communication systems are made transmission reliable by employing error correction technique for the redundancies. Codes in the low-density parity-check work along the principles of Hamming code, and the parity-check matrix is very sparse, and multiple errors can be corrected. The sparseness of the matrix allows for the decoding process to be carried out by probability propagation methods similar to those employed in Turbo codes. The relation between spin systems in statistical physics and digital error correcting codes is based on the existence of a simple isomorphism between the additive Boolean group and the multiplicative binary group. Shannon proved general results on the natural limits of compression and error-correction by setting up the framework known as information theory. Error-correction codes are based on mapping the original space of words onto a higher dimensional space in such a way that the typical distance between encoded words increases.

CDMA multiuser detection, neural networks, and statistical mechanics

A novel approach, based on statistical mechanics, to analyze typical performance of optimum code-division multiple-access (CDMA) multiuser detectors is reviewed. A `black-box' view ot the basic CDMA channel is introduced, based on which the CDMA multiuser detection problem is regarded as a `learning-from-examples' problem of the `binary linear perceptron' in the neural network literature. Adopting Bayes framework, analysis of the performance of the optimum CDMA multiuser detectors is reduced to evaluation of the average of the cumulant generating function of a relevant posterior distribution. The evaluation of the average cumulant generating function is done, based on formal analogy with a similar calculation appearing in the spin glass theory in statistical mechanics, by making use of the replica method, a method developed in the spin glass theory.

Magnetization enumerator for LDPC codes - a statistical physics approach

We propose a method based on the magnetization enumerator to determine the critical noise level for Gallager type low density parity check error correcting codes (LDPC). Our method provides an appealingly simple interpretation to the relation between different decoding schemes, and provides more optimistic critical noise levels than those reported in the information theory literature.