Thesis (Ph. D.)--University of Wisconsin--Madison, 1968. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 140-143).

Thesis (M.S.)--Wisconsin. / Includes bibliographical references (leaves 42-43).

Thesis (M.S.)--Ohio University, August, 2004. / Title from PDF t.p. Includes bibliographical references (p. 84-87)

Thesis (M.S.)--Ohio University, August, 2004. / Title from PDF t.p. Includes bibliographical references (p. 69-71)

No description available.

In this thesis, novel error rate performance metrics and transmission solutions are investigated for delay limited communication systems and for co-channel interference scenarios. The following four research problems in particular were considered. The first research problem is devoted to analysis of the higher order ergodic moments of error rates for digital communication systems with time- unlimited ergodic transmissions and the statistics of the conditional error rates of digital modulations over fading channels are considered. The probability density function and the higher order moments of the conditional error rates are obtained. Non-monotonic behavior of the moments of the conditional bit error rates versus some channel model parameters is observed for a Ricean distributed channel fading amplitude at the detector input. Properties and possible applications of the second central moments are proposed. The second research problem is the non-ergodic error rate analysis and signaling design for communication systems processing a single finite length received sequence. A framework to analyze the error rate properties of non-ergodic transmissions is established. The Bayesian credible intervals are used to estimate the instantaneous bit error rate. A novel degree of ergodicity measure is introduced using the credible interval estimates to quantify the level of ergodicity of the received sequence with respect to the instantaneous bit error rate and to describe the transition of the data detector from the non-ergodic to ergodic zone of operation. The developed non-ergodic analysis is used to define adaptive forward error correction control and adaptive power control policies that can guarantee, with a given probability, the worst case instantaneous bit error rate performance of the detector in its transition fi'om the non-ergodic to ergodic zone of operation. In the third research problem, novel retransmission schemes are developed for delay-limited retransmissions. The proposed scheme relies on a reliable reverse link for the error-free feedback message delivery. Unlike the conventional automatic repeat request schemes, the proposed scheme does not require the use of cyclic redundancy check bits for error detection. In the proposed scheme, random permutations are exploited to locate the bits for retransmission in the predefined window within the packet. The retransmitted bits are combined using the maximal-ratio combining. The complexity-performance trade-offs of the proposed scheme is investigated by mathematical analysis as well as computer simulations. The bit error rate of the proposed scheme is independent of the packet length while the throughput is dependent on the packet length. Three practical techniques suitable for implementation are proposed. The performance of the proposed retransmission scheme was compared to the block repetition code corresponding to a conventional ARQ retransmission strategy. It was shown that, for the same number of retransmissions, and the same packet length, the proposed scheme always outperforms such repetition coding, and, in some scenarios, the performance improvement is found to be significant. Most of our analysis has been done for the case of AWGN channel, however, the case of a slow Rayleigh block fading channel was also investigated. The proposed scheme appears to provide the throughput and the BER reduction gains only for the medium to large SNR values. Finally, the last research problem investigates the link error rate performance with a single co-channel interference. A novel metric to assess whether the standard Gaussian approximation of a single interferer underestimates or overestimates the link bit error rate is derived. This metric is a function of the interference channel fading statistics. However, it is otherwise independent of the statistics of the desired signal. The key step in derivation of the proposed metric is to construct the standard Gaussian approximation of the interference by a non-linear transformation. A closed form expression of the metric is obtained for a Nakagami distributed interference fading amplitude. Numerical results for the case of Nakagami and lognormal distributed interference fading amplitude confirm the validity of the proposed metric. The higher moments, interval estimators and non-linear transformations were investigated to evaluate the error rate performance for different wireless communication scenarios. The synchronization channel is also used jointly with the communication link to form a transmission diversity and subsequently, to improve the error rate performance.

M.Sc. / In this study we consider the problem ofestiniating the slope in the simple linear errors-in-variables model. There are two different types of relationship that can he specified in the errors-in-variables model: one that specifies a functional linear relationship and one describing a structural linear relationship. The different relationship specifications can lead to different estimators with different properties. These two specifications are highlighted in this study. A least squares solution (to the estimation of the slope) is given. The problem of finding the maximum likelihood solution to these two specifications is addressed. It is noted that an unidentifiability problem arises in this attempt. The solution is seen to lie in making assumptions on the error variances. Interval estimation for the slope parameter is discussed. It is noted that any interval estimator of the slope whose length is always finite will have a confidence coefficient of zero. Various interval estimation methods are reviewed but emphasis is mainly on the investigation of a bootstrap procedure for estimating the confidence interval for the slope parameter β. More specifically, the Linder and Babu (1994) (bootstrap) method for the structural relationship model with known variance ratio is investigated here. The error distributions were assumed normal. A simulation study based on this paper is carried out. The results in the simulation study show that this bootstrap procedure performs well in comparison with the normal theory estimates for normally distributed data, that is, it has better coverage accuracy than the normal approximation.

South African learners perform poorly in the geometry sections of both national and international assessments. Numerous assessment reports mention multiple errors that keep re-occurring and play a big role in the learners’ poor performance. For this research, the link between the grade 9 learners Van Hiele levels of thought and the typical errors that they made were investigated. In this mixed method study, 194 grade 9 learners in two schools in Port Elizabeth, South Africa were tested using a Van Hiele based test. A test was set up containing multiple-choice and open-ended questions and was used to determine firstly, the predominant level of geometric reasoning of the learners and secondly, to determine their typical errors. Semi-structured interviews were held with six learners to gain more insight into some of the typical errors uncovered in the tests. The quantitative data revealed that the learners’ predominant levels of geometric thought were low. Furthermore, the qualitative data revealed typical error patterns concerning angles and sides, parallel lines, hierarchy of quadrilaterals and incorrect reasons in the proofs. The quantitative and qualitative data was merged to determine if the errors could be linked to the Van Hiele levels. From the findings, it was concluded that most of their typical errors could be linked to the Van Hiele levels of the learners.

No description available.

Modern data analysis requires the study of tensors, or multi-way arrays. We consider the case where the dimension d is large and the order p is fixed. For dimension reduction and for interpretability, one considers tensor decompositions, where a tensor T can be decomposed into a sum of rank one tensors. In this thesis, I will describe some recent work that illustrate why and how to use decompositions for orthogonally decomposable tensors. Our developments are motivated by statistical applications where the data dimension is large. The estimation procedures will therefore aim to be computationally tractable while providing error rates that depend optimally on the dimension. A tensor is said to be orthogonally decomposable if it can be decomposed into rank one tensors whose component vectors are orthogonal. A number of data analysis tasks can be recast as the problem of estimating the component vectors from a noisy observation of an orthogonally decomposable tensor. In our first set of results, we study this decompositionproblem and derive perturbation bounds. For any two orthogonally decomposable tensors which are ε-perturbations of one another, we derive sharp upper bounds on the distances between their component vectors. While this is motivated by the extensive literature on bounds for perturbation of singular value decomposition, our work shows fundamental differences and requires new techniques. We show that tensor perturbation bounds have no dependence on eigengap, a quantity which is inevitable for matrices. Moreover, our perturbation bounds depend on the tensor spectral norm of the noise, and we provide examples to show that this leads to optimal error rates in several high dimensional statistical learning problems. Our results imply that matricizing a tensor is sub-optimal in terms of dimension dependence. The tensor perturbation bounds derived so far are universal, in that they depend only on the spectral norm of the perturbation. In subsequent chapters, we show that one can extract further information from how a noise is generated, and thus improve over tensor perturbation bounds both statistically and computationally. We demonstrate this approach for two different problems: first, in estimating a rank one spiked tensor perturbed by independent heavy-tailed noise entries; and secondly, in performing inference from moment tensors in independent component analysis. We find that an estimator benefits immensely— both in terms of statistical accuracy and computational feasibility — from additional information about the structure of the noise. In one chapter, we consider independent noise elements, and in the next, the noise arises as a difference of sample and population fourth moments. In both cases, our estimation procedures are determined so as to avoid accumulating the errors from different sources. In a departure from the tensor perturbation bounds, we also find that the spectral norm of the error tensor does not lead to the sharpest estimation error rates in these cases. The error rates of estimating the component vectors are affected only by the noise projected in certain directions, and due to the orthogonality of the signal tensor, the projected errors do not accumulate, and can be controlled more easily.