Statistical physics of error-correcting codes

In this thesis we use statistical physics techniques to study the typical performance of four families of error-correcting codes based on very sparse linear transformations: Sourlas codes, Gallager codes, MacKay-Neal codes and Kanter-Saad codes. We map the decoding problem onto an Ising spin system with many-spins interactions. We then employ the replica method to calculate averages over the quenched disorder represented by the code constructions, the arbitrary messages and the random noise vectors. We find, as the noise level increases, a phase transition between successful decoding and failure phases. This phase transition coincides with upper bounds derived in the information theory literature in most of the cases. We connect the practical decoding algorithm known as probability propagation with the task of finding local minima of the related Bethe free-energy. We show that the practical decoding thresholds correspond to noise levels where suboptimal minima of the free-energy emerge. Simulations of practical decoding scenarios using probability propagation agree with theoretical predictions of the replica symmetric theory. The typical performance predicted by the thermodynamic phase transitions is shown to be attainable in computation times that grow exponentially with the system size. We use the insights obtained to design a method to calculate the performance and optimise parameters of the high performance codes proposed by Kanter and Saad.

Work stressors, strains and hospital unit performance

Hospital employees who work in an environment with zero tolerance to error, face several stressors that may result in psychological, physiological, and behavioural strains, and subsequently, in suboptimal performance. This thesis includes two studies which investigate the stressor-to-strain-to-performance relationships in hospitals. The first study is a cross-sectional, multi-group investigation based on secondary data from 65,142 respondents in 172 acute/specialist UK NHS trusts. This model proposes that senior management leadership predicts social support and job design which, in turn, moderate stressors-to-strains across team structure. The results confirm the model's robustness. Regression analysis provides support for main effects and minimal support for moderation hypotheses. Therefore, based on its conclusions and inherent limitations, study one lays the framework for study two. The second study is a cross-sectional, multilevel investigation of the strain-reducing effects of social environment on externally-rated unit-level performance based on primary data from 1,137 employees in 136 units, in a hospital in Malta. The term "social environment" refers to the prediction of the moderator variables, which is to say, social support and decision latitude/control, by transformational leadership and team climate across hospital units. This study demonstrates that transformational leadership is positively associated with social support, whereas team climate is positively associated with both moderators. At the same time, it identifies a number of moderating effects which social support and decision latitude/control, both separately and together, had on specific stressor-to-strain relationships. The results show significant mediated stressor-to-strain-to-performance relationships. Furthermore, at the higher level, unit-level performance is positively associated with shared unit-level team climate and with unit-level vision, the latter being one of the five sub-dimension of transformational leadership. At the same time, performance is also positively related to both transformational leadership and team climate when the two constructs are tested together. Few studies have linked the buffering effects of the social environment in occupational stress with performance. Therefore, this research strives to make a significant contribution to the occupational stress and performance literature with a focus on hospital practice. Indeed, the study highlights the wide-ranging and far-reaching implications that these findings provide for theory, management, and practice.

The electron optical limits of performance of single-polepiece magnetic electron lenses

The thesis is concerned with the electron properties of single-polepiece magnetic electron lenses especially under conditions of extreme polepiece saturation. The electron optical properties are first analysed under conditions of high polepiece permeability. From this analysis, a general idea can be obtained of the important parameters that affect ultimate lens performance. In addition, useful information is obtained concerning the design of improved lenses operating under conditions of extreme polepiece saturation, for example at flux densities of the order of 10 Tesla. It is shown that in a single-polepiece lens , the position and shape of the lens exciting coil plays an important role. In particular, the maximum permissible current density in the windings,rather than the properties of the iron, can set a limit to lens performance. This factor was therefore investigated in some detail. The axial field distribution of a single-polepiece lens, unlike that of a conventional lens, is highly asymmetrical. There are therefore two possible physical arrangements of the lens with respect to the incoming electron beam. In general these two orientations will result in different aberration coefficients. This feature has also been investigated in some detail. Single-pole piece lenses are thus considerably more complicated electron- optically than conventional double polepiece lenses. In particular, the absence of the usual second polepiece causes most of the axial magnetic flux density distribution to lie outside the body of the lens. This can have many advantages in electron microscopy but it creates problems in calculating the magnetic field distribution. In particular, presently available computer programs are liable to be considerably in error when applied to such structures. It was therefore necessary to find independent ways of checking the field calculations. Furthermore, if the polepiece is allowed to saturate, much more calculation is involved since the field distribution becomes a non-linear function of the lens excitation. In searching for optimum lens designs, care was therefore taken to ensure that the coil was placed in the optimum position. If this condition is satisfied there seems to be no theoretical limit to the maximum flux density that can be attained at the polepiece tip. However , under iron saturation condition, some broadening of the axial field distribution will take place, thereby changing the lens aberrations . Extensive calculations were therefore made to find the minimum spherical and chromatic aberration coefficients . The focal properties of such lens designs are presented and compared with the best conventional double-polepiece lenses presently available.

High-performance liquid chromatography and pharmacokinetics of some antibiotics

The principles of High Performance Liquid Chromatography (HPLC) and pharmacokinetics were applied to the use of several clinically-important drugs at the East Birmingham Hospital. Amongst these was gentamicin, which was investigated over a two-year period by a multi-disciplinary team. It was found that there was considerable intra- and inter-patient variation that had not previously been reported and the causes and consequences of such variation were considered. A detailed evaluation of available pharmacokinetic techniques was undertaken and 1- and 2-compartment models were optimised with regard to sampling procedures, analytical error and model-error. The implications for control of therapy are discussed and an improved sampling regime is proposed for routine usage. Similar techniques were applied to trimethoprim, assayed by HPLC, in patients with normal renal function and investigations were also commenced into the penetration of drug into peritoneal dialysate. Novel assay techniques were also developed for a range of drugs including 4-aminopyridine, chloramphenicol, metronidazole and a series of penicillins and cephalosporins. Stability studies on cysteamine, reaction-rate studies on creatinine-picrate and structure-activity relationships in HPLC of aminopyridines are also reported.

Evaluating and improving the performance of video content distribution in lossy networks

The contributions in this research are split in to three distinct, but related, areas. The focus of the work is based on improving the efficiency of video content distribution in the networks that are liable to packet loss, such as the Internet. Initially, the benefits and limitations of content distribution using Forward Error Correction (FEC) in conjunction with the Transmission Control Protocol (TCP) is presented. Since added FEC can be used to reduce the number of retransmissions, the requirement for TCP to deal with any losses is greatly reduced. When real-time applications are needed, delay must be kept to a minimum, and retransmissions not desirable. A balance, therefore, between additional bandwidth and delays due to retransmissions must be struck. This is followed by the proposal of a hybrid transport, specifically for H.264 encoded video, as a compromise between the delay-prone TCP and the loss-prone UDP. It is argued that the playback quality at the receiver often need not be 100% perfect, providing a certain level is assured. Reliable TCP is used to transmit and guarantee delivery of the most important packets. The delay associated with the proposal is measured, and the potential for use as an alternative to the conventional methods of transporting video by either TCP or UDP alone is demonstrated. Finally, a new objective measurement is investigated for assessing the playback quality of video transported using TCP. A new metric is defined to characterise the quality of playback in terms of its continuity. Using packet traces generated from real TCP connections in a lossy environment, simulating the playback of a video is possible, whilst monitoring buffer behaviour to calculate pause intensity values. Subjective tests are conducted to verify the effectiveness of the metric introduced and show that the results of objective and subjective scores made are closely correlated.

Performance analysis of 20 Gbit/s RZ-DPSK non-slope matched transoceanic submarine links

This paper studies the performance of a typical non-slope matched transoceanic submarine link using 20Gb/s channel rate and RZ-DPSK modulation with different duty cycles. Through comparison with direct error counting, we have also demonstrated the limitations of the available numerical approaches to the BER estimation for return-to-zero differential phase-shift keying (RZ-DPSK). The numerical results have been confirmed by experiments, and indicate that 20 Gb/s RZ-DPSK transmission is a feasible technique for the upgrade of existing submarine links.

Executive remuneration, financial performance and corporate governance in UK and Spanish listed firms

This study examines the relationship between executive directors’ remuneration and the financial performance and corporate governance arrangements of the UK and Spanish listed firms. These countries’ corporate governance framework has been shaped by differences in legal origin, culture and backgrounds. For example, the UK legal arrangements can be defined as to be constituted in common-law, whereas for Spanish firms, the legal arrangement is based on civil law. We estimate both static and dynamic regression models to test our hypotheses and we estimate our regression using Ordinary Least Squares (OLS) and the Generalised Method of Moments (GMM). Estimated results for both countries show that directors’ remuneration levels are positively related with measures of firm value and financial performance. This means that remuneration levels do not lead to a point whereby firm value is reduced due to excessive remuneration. These results hold for our long-run estimates. That is, estimates based on panel cointegration and panel error correction. Measures of corporate governance also impacts on the level of executive pay. Our results have important implications for existing corporate governance arrangements and how the interests of stakeholders are protected. For example, long-run results suggest that directors’ remuneration adjusts in a way to capture variation in financial performance

Performance analysis of 20 Gb/s RZ-DPSK non-slope matched transoceanic submarine links

Direct computation of the bit-error rate (BER) and laboratory experiments are used to assess the performance of a non-slope matched transoceanic submarine transmission link operating at 20Gb/s channel rate and employing return-to-zero differential-phase shift keying (RZ-DPSK) signal modulation. Using this system as an example, we compare the accuracies of the existing theoretical approaches to the BER estimation for the RZ-DPSK format.

Performance analysis of 20 Gbit/s RZ-DPSK non-slope matched transoceanic submarine links

This paper studies the performance of a typical non-slope matched transoceanic submarine link using 20Gb/s channel rate and RZ-DPSK modulation with different duty cycles. Through comparison with direct error counting, we have also demonstrated the limitations of the available numerical approaches to the BER estimation for return-to-zero differential phase-shift keying (RZ-DPSK). The numerical results have been confirmed by experiments, and indicate that 20 Gb/s RZ-DPSK transmission is a feasible technique for the upgrade of existing submarine links.

Bit-error probability for direct detection of optical RZ signal degraded by ASE noise and timing jitter

We analyze theoretically the interplay between optical return-to-zero signal degradation due to timing jitter and additive amplified-spontaneous-emission noise. The impact of these two factors on the performance of a square-law direct detection receiver is also investigated. We derive an analytical expression for the bit-error probability and quantitatively determine the conditions when the contributions of the effects of timing jitter and additive noise to the bit error rate can be treated separately. The analysis of patterning effects is also presented. © 2007 IEEE.

Comparison of bit error rate estimation methods for QPSK CO-OFDM transmission

In this letter, we experimentally study the statistical properties of a received QPSK modulated signal and compare various bit error rate (BER) estimation methods for coherent optical orthogonal frequency division multiplexing transmission. We show that the statistical BER estimation method based on the probability density function of the received QPSK symbols offers the most accurate estimate of the system performance.

Analysis and representation of statistical performance of JPEG2000 encoded image over wireless channels

JPEG2000 is a new coming image standard. In this paper we analyze the performance of error resilience tools in JPEG2000, and present an analytical model to estimate the quality of JPEG2000 encoded image transmitted over wireless channels. The effectiveness of the analytical model is validated by simulation results. Furthermore, analytical model is utilized by the base station to design efficient unequally error protection schemes for JPEG2000 transmission. In the design, a utility function is denned to make a tradeoff between the image quality and the cost for transmitting the image over wireless channel. © 2002 IEEE.

Analytical BER performance in differential n-PSK coherent transmission system influenced by equalization enhanced phase noise

Long-haul high speed optical transmission systems are significantly distorted by the interplay between the electronic chromatic dispersion (CD) equalization and the local oscillator (LO) laser phase noise, which leads to an effect of equalization enhanced phase noise (EEPN). The EEPN degrades the performance of optical communication systems severely with the increment of fiber dispersion, LO laser linewidth, symbol rate, and modulation format. In this paper, we present an analytical model for evaluating the performance of bit-error-rate (BER) versus signal-to-noise ratio (SNR) in the n-level phase shift keying (n-PSK) coherent transmission system employing differential carrier phase estimation (CPE), where the influence of EEPN is considered. Theoretical results based on this model have been investigated for the differential quadrature phase shift keying (DQPSK), the differential 8-PSK (D8PSK), and the differential 16-PSK (D16PSK) coherent transmission systems. The influence of EEPN on the BER performance in term of the fiber dispersion, the LO phase noise, the symbol rate, and the modulation format are analyzed in detail. The BER behaviors based on this analytical model achieve a good agreement with previously reported BER floors influenced by EEPN. Further simulations have also been carried out in the differential CPE considering EEPN. The results indicate that this analytical model can give an accurate prediction for the DQPSK system, and a leading-order approximation for the D8PSK and the D16PSK systems.

Performance of the Bayesian online algorithm for the perceptron

In this letter, we derive continuum equations for the generalization error of the Bayesian online algorithm (BOnA) for the one-layer perceptron with a spherical covariance matrix using the Rosenblatt potential and show, by numerical calculations, that the asymptotic performance of the algorithm is the same as the one for the optimal algorithm found by means of variational methods with the added advantage that the BOnA does not use any inaccessible information during learning. © 2007 IEEE.

Optical quality and visual performance with customised soft contact lenses for keratoconus

Purpose: This study investigated how aberration-controlling, customised soft contact lenses corrected higher-order ocular aberrations and visual performance in keratoconic patients compared to other forms of refractive correction (spectacles and rigid gas-permeable lenses). Methods: Twenty-two patients (16 rigid gas-permeable contact lens wearers and six spectacle wearers) were fitted with standard toric soft lenses and customised lenses (designed to correct 3rd-order coma aberrations). In the rigid gas-permeable lens-wearing patients, ocular aberrations were measured without lenses, with the patient's habitual lenses and with the study lenses (Hartmann-Shack aberrometry). In the spectacle-wearing patients, ocular aberrations were measured both with and without the study lenses. LogMAR visual acuity (high-contrast and low-contrast) was evaluated with the patient wearing their habitual correction (of either spectacles or rigid gas-permeable contact lenses) and with the study lenses. Results: In the contact lens wearers, the habitual rigid gas-permeable lenses and customised lenses provided significant reductions in 3rd-order coma root-mean-square (RMS) error, 3rd-order RMS and higher-order RMS error (p ≤ 0.004). In the spectacle wearers, the standard toric lenses and customised lenses significantly reduced 3rd-order RMS and higher-order RMS errors (p ≤ 0.005). The spectacle wearers showed no significant differences in visual performance measured between their habitual spectacles and the study lenses. However, in the contact lens wearers, the habitual rigid gas-permeable lenses and standard toric lenses provided significantly better high-contrast acuities compared to the customised lenses (p ≤ 0.006). Conclusions: The customised lenses provided substantial reductions in ocular aberrations in these keratoconic patients; however, the poor visual performances achieved with these lenses are most likely to be due to small, on-eye lens decentrations. © 2014 The College of Optometrists.