Finite-connectivity spin-glass phase diagrams and low-density parity check codes

We obtain phase diagrams of regular and irregular finite-connectivity spin glasses. Contact is first established between properties of the phase diagram and the performance of low-density parity check (LDPC) codes within the replica symmetric (RS) ansatz. We then study the location of the dynamical and critical transition points of these systems within the one step replica symmetry breaking theory (RSB), extending similar calculations that have been performed in the past for the Bethe spin-glass problem. We observe that the location of the dynamical transition line does change within the RSB theory, in comparison with the results obtained in the RS case. For LDPC decoding of messages transmitted over the binary erasure channel we find, at zero temperature and rate R=14, an RS critical transition point at pc 0.67 while the critical RSB transition point is located at pc 0.7450±0.0050, to be compared with the corresponding Shannon bound 1-R. For the binary symmetric channel we show that the low temperature reentrant behavior of the dynamical transition line, observed within the RS ansatz, changes its location when the RSB ansatz is employed; the dynamical transition point occurs at higher values of the channel noise. Possible practical implications to improve the performance of the state-of-the-art error correcting codes are discussed. © 2006 The American Physical Society.

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.

Recovery of multiple amplitude levels from a DQPSK NRZ signal using a single Mach-Zehnder Interferometer

In this research the recovery of a DQPSK signal will be demonstrated using a single Mach-Zehnder Interferometer (MZI). By changing the phase delay in one of the arms it will be shown that different delays will produce different output levels. It will also be shown that with a certain level of phase shift the DQPSK signal can be converted into four different equally spaced optical power levels. With each decoded level representing one of the four possible bit permutations. By using this additional phase shift in one of the arms the number of MZIs required for decoding can be reduced from two to one.

A sensory-linguistic approach to normal and impaired reading development

In this chapter we outline a sensory-linguistic approach to the, study of reading skill development. We call this a sensory-linguistic approach because the focus of interest is on the relationship between basic sensory processing skills and the ability to extract efficiently the orthographic and phonological information available in text during reading. Our review discusses how basic sensory processing deficits are associated with developmental dyslexia, and how these impairments may degrade word-decoding skills. We then review studies that demonstrate a more direct relationship between sensitivity to particular types of auditory and visual stimuli and the normal development of literacy skills. Specifically, we suggest that the phonological and orthographic skills engaged while reading are constrained by the ability to detect and discriminate dynamic stimuli in the auditory and visual systems respectively.

Sparsely spread CDMA - A statistical mechanics-based analysis

Sparse code division multiple access (CDMA), a variation on the standard CDMA method in which the spreading (signature) matrix contains only a relatively small number of nonzero elements, is presented and analysed using methods of statistical physics. The analysis provides results on the performance of maximum likelihood decoding for sparse spreading codes in the large system limit. We present results for both cases of regular and irregular spreading matrices for the binary additive white Gaussian noise channel (BIAWGN) with a comparison to the canonical (dense) random spreading code. © 2007 IOP Publishing Ltd.

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.

Dyslexia - towards diagnosis : the implications of corical laterality for children's reading difficulties

Dyslexia as a concept is defined and reviewed in a context of psychological, neurological and educational processes. In the present investigation these processes are recognised but emphasis is placed on dyslexia as a phenomenon of a written language system. The type of script system involved in the phenomenon is that of an alphabetic code representing phonological elements of language In script form related to meaning. The nature of this system is viewed In the light of current linguistic and psycholinguistic studies. These studies based as they are on an analysis of underlying written language structures provide a framework for examining the arbitrary and rule-governed system which a young child is expected to acquire. There appear to be fundamental implications for reading, spelling and writing processes; for example an alphabetic system requires recognition of consistent script-phonetic relationships, 'mediated word identification' and in particular uni-directional sensory and motor modes of perceiving. These are critical maturational factors in the young learner. The skills needed by the child for decoding and encoding such a phonemic script are described in a psychological and neuropsychological framework. Evidence for individual differences in these skills is noted and the category of the dyslexic-type learner emerges. Incidence is related to the probabilities of individual differences in lateralisation of brain function not favouring the acquisition of our script system In some cases. Dyslexia is therefore regarded as a primary difficulty consequent upon the incompatibility between:the written language system itself and the intrinsic, developmental skills of an individual's perceptual/motor system. It is recognised that secondary stresses e.g. socio-cultural deprivation, low intellectual potential or emotional trauma can further inhibit the learning process. Symptomology of a dyslexic syndrome is described.. The symptomology is seen by the writer to constitute a clinical entity. a specific category of learning difficulty for which predictive and diagnostic procedure could be devised for classroom use. Consequently an index of relevant test items has been compiled, based upon key clinical experiences and theoretical writings. This instrument knovn as the Aston Index is presented and discussed. The early stages of validation are reported and the proposed longtitudinal studies are described. The aim is to give teachers in the classroom the power and understanding to plan more effectively the earliest stages of teaching and learning; in particular to provide the means of matching the nature of the skill to be acquired with the underlying developmental patterns of each individual learner.

Typical case behaviour of spin systems in random graph and composite ensembles

This thesis includes analysis of disordered spin ensembles corresponding to Exact Cover, a multi-access channel problem, and composite models combining sparse and dense interactions. The satisfiability problem in Exact Cover is addressed using a statistical analysis of a simple branch and bound algorithm. The algorithm can be formulated in the large system limit as a branching process, for which critical properties can be analysed. Far from the critical point a set of differential equations may be used to model the process, and these are solved by numerical integration and exact bounding methods. The multi-access channel problem is formulated as an equilibrium statistical physics problem for the case of bit transmission on a channel with power control and synchronisation. A sparse code division multiple access method is considered and the optimal detection properties are examined in typical case by use of the replica method, and compared to detection performance achieved by interactive decoding methods. These codes are found to have phenomena closely resembling the well-understood dense codes. The composite model is introduced as an abstraction of canonical sparse and dense disordered spin models. The model includes couplings due to both dense and sparse topologies simultaneously. The new type of codes are shown to outperform sparse and dense codes in some regimes both in optimal performance, and in performance achieved by iterative detection methods in finite systems.

Near-ML detection for MDL-impaired few-mode fiber transmission

Few-mode fiber transmission systems are typically impaired by mode-dependent loss (MDL). In an MDL-impaired link, maximum-likelihood (ML) detection yields a significant advantage in system performance compared to linear equalizers, such as zero-forcing and minimum-mean square error equalizers. However, the computational effort of the ML detection increases exponentially with the number of modes and the cardinality of the constellation. We present two methods that allow for near-ML performance without being afflicted with the enormous computational complexity of ML detection: improved reduced-search ML detection and sphere decoding. Both algorithms are tested regarding their performance and computational complexity in simulations of three and six spatial modes with QPSK and 16QAM constellations.

Mitigation of pattern sensitivity in full-field electronic dispersion compensation

We investigate the pattern-dependent decoding failures in full-field electronic dispersion compensation (EDC) by offline processing of experimental signals, and find that the performance of such an EDC receiver may be degraded by an isolated "1" bit surrounded by long strings of consecutive "0s". By reducing the probability of occurrence of this kind of isolated "1" and using a novel adaptive threshold decoding method, we greatly improve the compensation performance to achieve 10-Gb/s on-off keyed signal transmission over 496-km field-installed single-mode fiber without optical dispersion compensation.

Separating the influences of prereading skills on early word and nonword reading

The essential first step for a beginning reader is to learn to match printed forms to phonological representations. For a new word, this is an effortful process where each grapheme must be translated individually (serial decoding). The role of phonological awareness in developing a decoding strategy is well known. We examined whether beginner readers recruit different skills depending on the nature of the words being read (familiar words vs. nonwords). Print knowledge, phoneme and rhyme awareness, rapid automatized naming (RAN), phonological short term memory (STM), nonverbal reasoning, vocabulary, auditory skills and visual attention were measured in 392 pre-readers aged 4 to 5 years. Word and nonword reading were measured 9 months later. We used structural equation modeling to examine the skills-reading relationship and modeled correlations between our two reading outcomes and among all pre-reading skills. We found that a broad range of skills were associated with reading outcomes: early print knowledge, phonological STM, phoneme awareness and RAN. Whereas all these skills were directly predictive of nonword reading, early print knowledge was the only direct predictor of word reading. Our findings suggest that beginner readers draw most heavily on their existing print knowledge to read familiar words.

Employing DDBPSK in optical burst switched systems to enhance throughput

We demonstrate that doubly differential decoding can demodulate phase shift keyed data much faster after the switching event of a tunable laser than usual mth power single differential decoding. This technique can significantly improve throughput of optical burst switched networks.

Dual-polarization multi-band optical OFDM transmission and transceiver limitations for up to 500 Gb/s uncompensated long-haul links

A number of critical issues for dual-polarization single- and multi-band optical orthogonal-frequency division multiplexing (DPSB/ MB-OFDM) signals are analyzed in dispersion compensation fiber (DCF)-free long-haul links. For the first time, different DP crosstalk removal techniques are compared, the maximum transmission-reach is investigated, and the impact of subcarrier number and high-level modulation formats are explored thoroughly. It is shown, for a bit-error-rate (BER) of 10-3, 2000 km of quaternary phase-shift keying (QPSK) DP-MBOFDM transmission is feasible. At high launched optical powers (LOP), maximum-likelihood decoding can extend the LOP of 40 Gb/s QPSK DPSB- OFDM at 2000 km by 1.5 dB compared to zero-forcing. For a 100 Gb/s DP-MB-OFDM system, a high number of subcarriers contribute to improved BER but at the cost of digital signal processing computational complexity, whilst by adapting the cyclic prefix length the BER can be improved for a low number of subcarriers. In addition, when 16-quadrature amplitude modulation (16QAM) is employed the digital-toanalogue/ analogue-to-digital converter (DAC/ADC) bandwidth is relaxed with a degraded BER; while the 'circular' 8QAM is slightly superior to its 'rectangular' form. Finally, the transmission of wavelength-division multiplexing DP-MB-OFDM and single-carrier DP-QPSK is experimentally compared for up to 500 Gb/s showing great potential and similar performance at 1000 km DCF-free G.652 line. © 2014 Optical Society of America.

A hierarchy of phase transitions in optimal neuronal coding:from binary to M-ary discrete optimal codes

We have investigated how optimal coding for neural systems changes with the time available for decoding. Optimization was in terms of maximizing information transmission. We have estimated the parameters for Poisson neurons that optimize Shannon transinformation with the assumption of rate coding. We observed a hierarchy of phase transitions from binary coding, for small decoding times, toward discrete (M-ary) coding with two, three and more quantization levels for larger decoding times. We postulate that the presence of subpopulations with specific neural characteristics could be a signiture of an optimal population coding scheme and we use the mammalian auditory system as an example.

Cerebellar morphology in developmental dyslexia

Recent evidence has suggested cerebellar anomalies in developmental dyslexia. Therefore, we investigated cerebellar morphology in subjects with documented reading disabilities. We obtained T1-weighted magnetic resonance images in the coronal and sagittal planes from 11 males with prior histories of developmental dyslexia, and nine similarly-aged male controls. Proton magnetic resonance spectra (TE=136 ms, TR=2.4 s) were obtained bilaterally in the cerebellum. Phonological decoding skill was measured using non-word reading. Handedness was assessed using both the Annett questionnaire of hand preference and Annett’s peg moving task. Cerebellar symmetry was observed in the dyslexics but there was significant asymmetry (right grey matter>left grey matter) in controls. The interpretation of these results depended whether a motor- or questionnaire-based method was used to determine handedness. The degree of cerebellar symmetry was correlated with the severity of dyslexics’ phonological decoding deficit. Those with more symmetric cerebella made more errors on a nonsense word reading measure of phonological decoding ability. Left cerebellar metabolite ratios were shown to correlate significantly with the degree of cerebellar asymmetry (P<0.05) in controls. This relationship was absent in developmental dyslexics. Cerebellar morphology reflects the higher degree of symmetry found previously in the temporal and parietal cortex of dyslexics. The relationship of cerebellar asymmetry to phonological decoding ability and handedness, together with our previous finding of altered metabolite ratios in the cerebellum of dyslexics, lead us to suggest that there are alterations in the neurological organisation of the cerebellum which relate to phonological decoding skills, in addition to motor skills and handedness.