Statistical mechanics of mutual information maximization

An unsupervised learning procedure based on maximizing the mutual information between the outputs of two networks receiving different but statistically dependent inputs is analyzed (Becker S. and Hinton G., Nature, 355 (1992) 161). By exploiting a formal analogy to supervised learning in parity machines, the theory of zero-temperature Gibbs learning for the unsupervised procedure is presented for the case that the networks are perceptrons and for the case of fully connected committees.

Error-correcting code on a cactus:A solvable model

An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica-symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.

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.

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.

Evaluating zero error noise thresholds by replica method for Gallager code ensembles

The replica method, developed in statistical physics, is employed in conjunction with Gallager's methodology to accurately evaluate zero error noise thresholds for Gallager code ensembles. Our approach generally provides more optimistic evaluations than those reported in the information theory literature for sparse matrices; the difference vanishes as the parity check matrix becomes dense.

A statistical-mechanical analysis of coded CDMA with regular LDPC codes

We analyze, using the replica method of statistical mechanics, the theoretical performance of coded code-division multiple-access (CDMA) systems in which regular low-density parity-check (LDPC) codes are used for channel coding.

Statistical mechanics analysis of LDPC coding in MIMO Gaussian channels

Using analytical methods of statistical mechanics, we analyse the typical behaviour of a multiple-input multiple-output (MIMO) Gaussian channel with binary inputs under low-density parity-check (LDPC) network coding and joint decoding. The saddle point equations for the replica symmetric solution are found in particular realizations of this channel, including a small and large number of transmitters and receivers. In particular, we examine the cases of a single transmitter, a single receiver and symmetric and asymmetric interference. Both dynamical and thermodynamical transitions from the ferromagnetic solution of perfect decoding to a non-ferromagnetic solution are identified for the cases considered, marking the practical and theoretical limits of the system under the current coding scheme. Numerical results are provided, showing the typical level of improvement/deterioration achieved with respect to the single transmitter/receiver result, for the various cases. © 2007 IOP Publishing Ltd.

Post-Bretton Woods evidence on PPP under different exchange rate regimes

This article investigates the behaviour of exchange rates across different regimes for a post-Bretton Woods period. The exchange rate regime classification is based on the classification of Frankel et al. (2004) who condensed the 10 categories of exchange rate regimes reported by the International Monetary Fund (IMF) into three categories. Panel unitroot tests and panel cointegration are used to examine the Purchasing Power Parity (PPP) hypothesis. The latter test is used to check for both the weak and strong forms of PPP. The panel unit-root tests show no evidence of PPP and suggest there is no difference in the behaviour of exchange rates across different regimes. However, failure to detect PPP across any of the regimes could be due to structural breaks. This assumption is reinforced by the results of cointegration tests, which suggest that there exists at least a weak form of PPP for the different regimes. The evidence for strong PPP decreases as the exchange rate regime moves away from a flexible exchange rate regime.

Typical behavior of relays in communication channels

The typical behavior of the relay-without-delay channel under low-density parity-check coding and its multiple-unit generalization, termed the relay array, is studied using methods of statistical mechanics. A demodulate-and- forward strategy is analytically solved using the replica symmetric ansatz which is exact in the system studied at Nishimori's temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of a small and a large number of relay units. © 2007 The American Physical Society.

A mean field theory of coded CDMA systems

We present a mean field theory of code-division multiple access (CDMA) systems with error-control coding. On the basis of the relation between the free energy and mutual information, we obtain an analytical expression of the maximum spectral efficiency of the coded CDMA system, from which a mean field description of the coded CDMA system is provided in terms of a bank of scalar Gaussian channels whose variances in general vary at different code symbol positions. Regular low-density parity-check (LDPC)-coded CDMA systems are also discussed as an example of the coded CDMA systems.

Organizational weaknesses of the Greek Manufacturing industry: a case study of footwear

This thesis is concerned with those factors influencing the present performance of Greek manufacturing industry and the ways in which improvements could be realized after Greece joins European Communities..Detailed examination is made of the Greek footwear industry and its problems as the country emerges from a semi developed state to a position approaching parity with Western European countries. Particular attention is paid to the technology employed, capital deployment, industrial structure and managerial performance. In order to illustrate the path of development of the Greek footwear industry a comparison is undertaken with the British footwear industry which has a longer history and has employed larger scale methods since the 19th century. This comparison illustrates the opportunities and pitfalls likely to face the Greek industry in coming years. One section of the thesis is also concerned with trading relationships between the U.K. and Greece and identifies the market opportunities available to Greek industrialists. A detailed analysis is undertaken of the available secondary sources of information particularly official statistical data relating to production, capital expenditure, imports and exports, employment and consumption. Use is also made of various surveys of trade and production in footwear undertaken by trade associations and other bodies. The field research study has been largely directed towards practicing managers in companies of various size and is concerned with exposing standards of management and of relating efficiency to organization structure. The thesis is also concerned with the many wide issues affecting the development of manufacturing industry in Greece including the influence of social structure and social institutions, the values of modern Greek society and the complex organizational problems which Greece needs to overcome in order to take its place amongst the more established states of Europe.

GABA-mediated changes in inter-hemispheric beta frequency activity in early-stage Parkinson's disease

In Parkinson's disease (PD), elevated beta (15-35Hz) power in subcortical motor networks is widely believed to promote aspects of PD symptomatology, moreover, a reduction in beta power and coherence accompanies symptomatic improvement following effective treatment with l-DOPA. Previous studies have reported symptomatic improvements that correlate with changes in cortical network activity following GABAA receptor modulation. In this study we have used whole-head magnetoencephalography to characterize neuronal network activity, at rest and during visually cued finger abductions, in unilaterally symptomatic PD and age-matched control participants. Recordings were then repeated following administration of sub-sedative doses of the hypnotic drug zolpidem (0.05mg/kg), which binds to the benzodiazepine site of the GABAA receptor. A beamforming based 'virtual electrode' approach was used to reconstruct oscillatory power in the primary motor cortex (M1), contralateral and ipsilateral to symptom presentation in PD patients or dominant hand in control participants. In PD patients, contralateral M1 showed significantly greater beta power than ipsilateral M1. Following zolpidem administration contralateral beta power was significantly reduced while ipsilateral beta power was significantly increased resulting in a hemispheric power ratio that approached parity. Furthermore, there was highly significant correlation between hemispheric beta power ratio and Unified Parkinson's Disease Rating Scale (UPDRS). The changes in contralateral and ipsilateral beta power were reflected in pre-movement beta desynchronization and the late post-movement beta rebound. However, the absolute level of movement-related beta desynchronization was not altered. These results show that low-dose zolpidem not only reduces contralateral beta but also increases ipsilateral beta, while rebalancing the dynamic range of M1 network oscillations between the two hemispheres. These changes appear to underlie the symptomatic improvements afforded by low-dose zolpidem.

Amplification schemes and multi-channel DBP for unrepeatered transmission

The performance of unrepeatered transmission of a seven Nyquist-spaced 10 GBd PDM-16QAM superchannel using full signal band coherent detection and multi-channel digital back propagation (MC-DBP) to mitigate nonlinear effects is analysed. For the first time in unrepeatered transmission, the performance of two amplification systems is investigated and directly compared in terms of achievable information rates (AIRs): 1) erbium-doped fibre amplifier (EDFA) and 2) second-order bidirectional Raman pumped amplification. The experiment is performed over different span lengths, demonstrating that, for an AIR of 6.8 bit/s/Hz, the Raman system enables an increase of 93 km (36 %) in span length. Further, at these distances, MC-DBP gives an improvement in AIR of 1 bit/s/Hz (to 7.8 bit/s/Hz) for both amplification schemes. The theoretical AIR gains for Raman and MC-DBP are shown to be preserved when considering low-density parity-check codes. Additionally, MC-DBP algorithms for both amplification schemes are compared in terms of performance and computational complexity. It is shown that to achieve the maximum MC-DBP gain, the Raman system requires approximately four times the computational complexity due to the distributed impact of fibre nonlinearity.