Gröbner basis techniques for certain problems in coding and systems theory

There is much common ground between the areas of coding theory and systems theory. Fitzpatrick has shown that a Göbner basis approach leads to efficient algorithms in the decoding of Reed-Solomon codes and in scalar interpolation and partial realization. This thesis simultaneously generalizes and simplifies that approach and presents applications to discrete-time modeling, multivariable interpolation and list decoding. Gröbner basis theory has come into its own in the context of software and algorithm development. By generalizing the concept of polynomial degree, term orders are provided for multivariable polynomial rings and free modules over polynomial rings. The orders are not, in general, unique and this adds, in no small way, to the power and flexibility of the technique. As well as being generating sets for ideals or modules, Gröbner bases always contain a element which is minimal with respect tot the corresponding term order. Central to this thesis is a general algorithm, valid for any term order, that produces a Gröbner basis for the solution module (or ideal) of elements satisfying a sequence of generalized congruences. These congruences, based on shifts and homomorphisms, are applicable to a wide variety of problems, including key equations and interpolations. At the core of the algorithm is an incremental step. Iterating this step lends a recursive/iterative character to the algorithm. As a consequence, not all of the input to the algorithm need be available from the start and different "paths" can be taken to reach the final solution. The existence of a suitable chain of modules satisfying the criteria of the incremental step is a prerequisite for applying the algorithm.

Adaptive partition and hybrid method in fractal video compression

Fractal image compression is a relatively recent image compression method, which is simple to use and often leads to a high compression ratio. These advantages make it suitable for the situation of a single encoding and many decoding, as required in video on demand, archive compression, etc. There are two fundamental fractal compression methods, namely, the cube-based and the frame-based methods, being commonly studied. However, there are advantages and disadvantages in both methods. This paper gives an extension of the fundamental compression methods based on the concept of adaptive partition. Experimental results show that the algorithms based on adaptive partition may obtain a much higher compression ratio compared to algorithms based on fixed partition while maintaining the quality of decompressed images.

Mutual information performance of differential MPSK detection over time-varying channels

This paper provides mutual information performance analysis of multiple-symbol differential WSK (M-phase shift keying) over time-correlated, time-varying flat-fading communication channels. A state space approach is used to model time correlation of time varying channel phase. This approach captures the dynamics of time correlated, time-varying channels and enables exploitation of the forward-backward algorithm for mutual information performance analysis. It is shown that the differential decoding implicitly uses a sequence of innovations of the channel process time correlation and this sequence is essentially uncorrelated. It enables utilization of multiple-symbol differential detection, as a form of block-by-block maximum likelihood sequence detection for capacity achieving mutual information performance. It is shown that multiple-symbol differential ML detection of BPSK and QPSK practically achieves the channel information capacity with observation times only on the order of a few symbol intervals

On information rates of time-varying fading channels modeled as finite-state Markov channels

We study information rates of time-varying flat-fading channels (FFC) modeled as finite-state Markov channels (FSMC). FSMCs have two main applications for FFCs: modeling channel error bursts and decoding at the receiver. Our main finding in the first application is that receiver observation noise can more adversely affect higher-order FSMCs than lower-order FSMCs, resulting in lower capacities. This is despite the fact that the underlying higher-order FFC and its corresponding FSMC are more predictable. Numerical analysis shows that at low to medium SNR conditions (SNR lsim 12 dB) and at medium to fast normalized fading rates (0.01 lsim fDT lsim 0.10), FSMC information rates are non-increasing functions of memory order. We conclude that BERs obtained by low-order FSMC modeling can provide optimistic results. To explain the capacity behavior, we present a methodology that enables analytical comparison of FSMC capacities with different memory orders. We establish sufficient conditions that predict higher/lower capacity of a reduced-order FSMC, compared to its original high-order FSMC counterpart. Finally, we investigate the achievable information rates in FSMC-based receivers for FFCs. We observe that high-order FSMC modeling at the receiver side results in a negligible information rate increase for normalized fading rates fDT lsim 0.01.

Achieving Space and Time Diversity by Using Lattice Constellation Based Joint Alamouti Coding

In this letter, we propose a simple space-time code to simultaneously achieve both the space and time diversities over time dispersive channels by using two-dimensional lattice constellations and Alamouti codes. The proposed scheme still reserves full space diversity and double-real-symbols joint maximum likelihood decoding which has the similar computation complexity as the Alamouti code.

Pharmacology of transient receptor potential melastatin channels in the vasculature.

Mammalian transient receptor potential melastatin (TRPM) non-selective cation channels, the largest TRP subfamily, are widely expressed in excitable and non-excitable cells where they perform diverse functions ranging from detection of cold, taste, osmolarity, redox state and pH to control of Mg(2+) homeostasis and cell proliferation or death. Recently, TRPM gene expression has been identified in vascular smooth muscles with dominance of the TRPM8 channel. There has been in parallel considerable progress in decoding the functional roles of several TRPMs in the vasculature. This research on native cells is aided by the knowledge of the activation mechanisms and pharmacological properties of heterologously expressed TRPM subtypes. This paper summarizes the present state of knowledge of vascular TRPM channels and outlines several anticipated directions of future research in this area.

Real-valued fixed-complexity sphere decoder for high dimensional QAM-MIMO systems

The development of high performance, low computational complexity detection algorithms is a key challenge for real-time Multiple-Input Multiple-Output (MIMO) communication system design. The Fixed-Complexity Sphere Decoder (FSD) algorithm is one of the most promising approaches, enabling quasi-ML decoding accuracy and high performance implementation due to its deterministic, highly parallel structure. However, it suffers from exponential growth in computational complexity as the number of MIMO transmit antennas increases, critically limiting its scalability to larger MIMO system topologies. In this paper, we present a solution to this problem by applying a novel cutting protocol to the decoding tree of a real-valued FSD algorithm. The new Real-valued Fixed-Complexity Sphere Decoder (RFSD) algorithm derived achieves similar quasi-ML decoding performance as FSD, but with an average 70% reduction in computational complexity, as we demonstrate from both theoretical and implementation perspectives for Quadrature Amplitude Modulation (QAM)-MIMO systems.

Turbo-MIMO for wireless communications

This article reviews an important class of MIMO wireless communications, known collectively as turbo-MIMO systems. A distinctive property of turbo-MIMO wireless communication systems is that they can attain a channel capacity close to the Shannon limit and do so in a computationally manageable manner. The article focuses attention on a subclass of turbo-MIMO systems that use space-time coding based on bit-interleaved coded modulation. Different computationally manageable decoding (detection) strategies are briefly discussed. The article also includes computer experiments that are intended to improve the understanding of specific issues involved in the design of turbo-MIMO systems.

The effects of a volunteer mentoring programme on reading outcomes among eight- to nine-year-old children: A follow up randomized controlled trial

This article presents the findings of a randomized controlled trial evaluation of the effects of a revised version of the volunteer mentoring programme, Time to Read. Participating children received two 30-minute mentoring sessions per week from volunteer mentors who carried out paired reading activities with the children. The current trial involved 512 children aged eight to nine years from 50 primary schools. The programme was found to be effective in improving decoding skills (d=+.15), reading rate (d=+.22) and reading fluency (d=+.14) and there was some evidence of a positive effect in relation to the children’s aspirations for the future (d=+.11). However, no evidence was found of the programme having an effect on reading comprehension or reading confidence and enjoyment of reading. The article concludes by suggesting that mentoring programmes using non-specialist volunteers can be effective in improving foundational reading skills but would appear to be less effective in terms of improving higher-order skills such as comprehension. The article also suggests that such programmes are likely to be most effective if concentrating on core reading activities rather than attempting to address reading outcomes indirectly through improving children’s confidence or wider enjoyment of reading.

A Low Complexity Real-time MIMO-Preprocessing For Fixed Complexity Sphere Decoder

Modern Multiple-Input Multiple-Output (MIMO) communication systems place huge demands on embedded processing resources in terms of throughput, latency and resource utilization. State-of-the-art MIMO detector algorithms, such as Fixed-Complexity Sphere Decoding (FSD), rely on efficient channel preprocessing involving numerous calculations of the pseudo-inverse of the channel matrix by QR Decomposition (QRD) and ordering. These highly complicated operations can quickly become the critical prerequisite for real-time MIMO detection, exaggerated as the number of antennas in a MIMO detector increases. This paper describes a sorted QR decomposition (SQRD) algorithm extended for FSD, which significantly reduces the complexity and latency
of this preprocessing step and increases the throughput of MIMO detection. It merges the calculations of the QRD and ordering operations to avoid multiple iterations of QRD. Specifically, it shows that SQRD reduces the computational complexity by over 60-70% when compared to conventional
MIMO preprocessing algorithms. In 4x4 to 7x7 MIMO cases, the approach suffers merely 0.16-0.2 dB reduction in Bit Error Rate (BER) performance.

Joint complex diversity coding and channel coding over space, time and frequency

This study provides a general diversity analysis for joint complex diversity coding (CDC) and channel coding-based space-time-frequency codeing is provided. The mapping designs from channel coding to CDC are crucial for efficient exploitation of the diversity potential. This study provides and proves a sufficient condition of full diversity construction with joint three-dimensional CDC and channel coding, bit-interleaved coded complex diversity coding and symbol-interleaved coded complex diversity coding. Both non-iterative and iterative detections of joint channel code and CDC transmission are investigated. The proposed minimum mean-square error-based iterative soft decoding achieves the performance of the soft sphere decoding with reduced complexity.

Tree-Based Adaptive Spatial Detection for Adaptive Modulated MIMO Systems

Adaptive Multiple-Input Multiple-Output (MIMO) systems achieve a much higher information rate than conventional fixed schemes due to their ability to adapt their configurations according to the wireless communications environment. However, current adaptive MIMO detection schemes exhibit either low performance (and hence low spectral efficiency) or huge computational
complexity. In particular, whilst deterministic Sphere Decoder (SD) detection schemes are well established for static MIMO systems, exhibiting deterministic parallel structure, low computational complexity and quasi-ML detection performance, there are no corresponding adaptive schemes. This paper solves
this problem, describing a hybrid tree based adaptive modulation detection scheme. Fixed Complexity Sphere Decoding (FSD) and Real-Values FSD (RFSD) are modified and combined into a hybrid scheme exploited at low and medium SNR to provide the highest possible information rate with quasi-ML Bit Error
Rate (BER) performance, while Reduced Complexity RFSD, BChase and Decision Feedback (DFE) schemes are exploited in the high SNR regions. This algorithm provides the facility to balance the detection complexity with BER performance with compatible information rate in dynamic, adaptive MIMO communications
environments.

A Kernel Interleaved Scheduling Method for Streaming Applications on Soft-core Vector Processors

Massively parallel networks of highly efficient, high performance Single Instruction Multiple Data (SIMD) processors have been shown to enable FPGA-based implementation of real-time signal processing applications with performance and
cost comparable to dedicated hardware architectures. This is achieved by exploiting simple datapath units with deep processing pipelines. However, these architectures are highly susceptible to pipeline bubbles resulting from data and control hazards; the only way to mitigate against these is manual interleaving of
application tasks on each datapath, since no suitable automated interleaving approach exists. In this paper we describe a new automated integrated mapping/scheduling approach to map algorithm tasks to processors and a new low-complexity list scheduling technique to generate the interleaved schedules. When applied to a spatial Fixed-Complexity Sphere Decoding (FSD) detector
for next-generation Multiple-Input Multiple-Output (MIMO) systems, the resulting schedules achieve real-time performance for IEEE 802.11n systems on a network of 16-way SIMD processors on FPGA, enable better performance/complexity balance than current approaches and produce results comparable to handcrafted implementations.

Robust Multimodal Person Identification With Limited Training Data

This paper presents a novel method of audio-visual feature-level fusion for person identification where both the speech and facial modalities may be corrupted, and there is a lack of prior knowledge about the corruption. Furthermore, we assume there are limited amount of training data for each modality (e.g., a short training speech segment and a single training facial image for each person). A new multimodal feature representation and a modified cosine similarity are introduced to combine and compare bimodal features with limited training data, as well as vastly differing data rates and feature sizes. Optimal feature selection and multicondition training are used to reduce the mismatch between training and testing, thereby making the system robust to unknown bimodal corruption. Experiments have been carried out on a bimodal dataset created from the SPIDRE speaker recognition database and AR face recognition database with variable noise corruption of speech and occlusion in the face images. The system's speaker identification performance on the SPIDRE database, and facial identification performance on the AR database, is comparable with the literature. Combining both modalities using the new method of multimodal fusion leads to significantly improved accuracy over the unimodal systems, even when both modalities have been corrupted. The new method also shows improved identification accuracy compared with the bimodal systems based on multicondition model training or missing-feature decoding alone.

Modeling continuous self-report measures of perceived emotion using generalized additive mixed models

Emotion research has long been dominated by the “standard method” of displaying posed or acted static images of facial expressions of emotion. While this method has been useful it is unable to investigate the dynamic nature of emotion expression. Although continuous self-report traces have enabled the measurement of dynamic expressions of emotion, a consensus has not been reached on the correct statistical techniques that permit inferences to be made with such measures. We propose Generalized Additive Models and Generalized Additive Mixed Models as techniques that can account for the dynamic nature of such continuous measures. These models allow us to hold constant shared components of responses that are due to perceived emotion across time, while enabling inference concerning linear differences between groups. The mixed model GAMM approach is preferred as it can account for autocorrelation in time series data and allows emotion decoding participants to be modelled as random effects. To increase confidence in linear differences we assess the methods that address interactions between categorical variables and dynamic changes over time. In addition we provide comments on the use of Generalized Additive Models to assess the effect size of shared perceived emotion and discuss sample sizes. Finally we address additional uses, the inference of feature detection, continuous variable interactions, and measurement of ambiguity.