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Multicasting in Long-Term Evolution (LTE) environments poses several challenges if it is to be reliably implemented. Neither retransmission schemes nor Forward Error Correction (FEC), the traditional error correction approaches, can be readily applied to this system of communication if bandwidth and resources are to be used efficiently. A large number of network parameters and topology variables can influence the cost of telecommunication in such a system. These need to be considered when selecting an appropriate error correction technique for a certain LTE multicast deployment. This dissertation develops a cost model to investigate the costs associated with over-the-air LTE multicasting when different error correction techniques are applied. The benefit of this simplified model is an easily implementable and fast method to evaluate the communications costs of different LTE multicast deployments with the application of error correction techniques. / MIng (Computer and Electronic Engineering), North-West University, Potchefstroom Campus, 2014

This thesis explores the impact of peer feedback on two secondary level classrooms studying English as a foreign language in Taiwan. The effectiveness of teacher-led feedback has consistently been the focus of the relevant literature but relatively fewer studies have experimentally investigated the impact of peer-led feedback on learning. This research is based on the belief that the investigation of the process of peer-led feedback, as well as the effectiveness of peer-led correction, will enhance our understanding of learners’ communicative interactions. These data will allow us the opportunity to provide suggestions for successful second/foreign language learning. This study was conducted following a mixed-methods quasi-experimental design involving a variety of data collection and analysis techniques. Observations of peer-peer dialogues taken from a Year 7 and a Year 8 class were analysed using content analysis, in order to classify the types of peer feedback provided by the Year 7 and Year 8 learners. Pre-and post-measures, including English speaking tests, questionnaires, and checklists, were examined with non-parametric statistical tests used to explore any changes in relation to the learners’ speaking development after the quasi-experiment. Key findings included frequency and distribution of seven types of peer feedback, as used by the Year 7 and Year 8 learners, and the statistical results that revealed the differences between the pre-and post-measures. Among the seven types of peer feedback (translation, confirmation, completion, explicit indication, explicit correction, explanation and recasts), explicit correction and translation were the two techniques used most frequently by the learners. Post-test results indicated an improvement in the learners’ speaking performance. The results of pre- and post-questionnaires and pre- and post-checklists showed different levels of change in the learners’ self-evaluation of their own ability to speak English, as well as their attitudes towards corrective feedback. These results allow us to gain insight into the nature of peer interaction in communicative speaking activities as well as learners’ motives behind their feedback behaviours. Additionally, the results shed light on learners’ opinions towards corrective feedback that they received or provided in peer interaction. Further, the results yield a deepened understanding of impacts of peer feedback on L2 development by examining changes in learners’ speaking performance, self-confidence in speaking English and self-evaluation of their own ability to speak English after a peer-led correction treatment. In conclusion, the study suggests that adolescent learners are willing and able to provide each other with feedback in peer interaction. The feedback that they delivered successfully helps their peers to attend to form and has positive impacts on their peers’ English- speaking performance. Moreover, the study provides explanations for learners’ preference for certain types of feedback techniques, which hopefully helps to tackle the mismatch between teachers’ intentions and learners’ expectations of corrective feedback in the L2 classrooms.

International Telemetering Conference Proceedings / October 25-28, 1993 / Riviera Hotel and Convention Center, Las Vegas, Nevada / This paper describes algorithms implemented by the Magellan High Rate Processor to recover radar data corrupted by the failure of an onboard tape recorder that dropped bits. For data with error correction coding, an algorithm was developed that decodes data in the presence of bit errors and missing bits. For the SAR data, the algorithm takes advantage of properties in SAR data to locate corrupted bits and reduce there effects on downstream processing. The algorithms rely on communication approaches, including an efficient tree search and the Viterbi algorithm to maintain the required throughput rate.

Error correction for English language learner's (ELL) writing has long been debated in the field of teaching English to learners of other languages (TESOL). Some researchers say that written corrective feedback (WCF) is beneficial, while others contest. This study takes a look at the manageability of the innovative strategy Dynamic Written Corrective Feedback (DWCF) and asks what factors influence the manageability of the strategy (including how long marking sessions take on average) and what suggestions experienced teachers of DWCF have. The strategy has shown to be highly effective in previous studies, but its manageability has recently been in question. A qualitative analysis of the manageability of DWCF was done via interviews of experienced teachers that have used DWCF and the author's experience and reflections using the strategy. The results indicate that this strategy can be manageable with some possible adaptions and while avoiding some common pitfalls.

Quantum error correction codes were introduced as a means to protect quantum information from decoherance and operational errors. Based on their approach to error control, error correcting codes can be divided into two different classes: block codes and convolutional codes. There has been significant development towards finding quantum block codes, since they were first discovered in 1995. In contrast, quantum convolutional codes remained mainly uninvestigated. In this thesis, we develop the stabilizer formalism for quantum convolutional codes. We define distance properties of these codes and give a general method for constructing encoding circuits, given a set of generators of the stabilizer of a quantum convolutional stabilizer code, is shown. The resulting encoding circuit enables online encoding of the qubits, i.e., the encoder does not have to wait for the input transmission to end before starting the encoding process. We develop the quantum analogue of the Viterbi algorithm. The quantum Viterbi algorithm (QVA) is a maximum likehood error estimation algorithm, the complexity of which grows linearly with the number of encoded qubits. A variation of the quantum Viterbi algorithm, the Windowed QVA, is also discussed. Using Windowed QVA, we can estimate the most likely error without waiting for the entire received sequence.

Quantum error correction and fault-tolerance are at the heart of any scalable quantum computation architecture. Developing a set of tools that satisfy the requirements of fault- tolerant schemes is thus of prime importance for future quantum information processing implementations. The Clifford gate set has the desired fault-tolerant properties, preventing bad propagation of errors within encoded qubits, for many quantum error correcting codes, yet does not provide full universal quantum computation. Preparation of magic states can enable universal quantum computation in conjunction with Clifford operations, however preparing magic states experimentally will be imperfect due to implementation errors. Thankfully, there exists a scheme to distill pure magic states from prepared noisy magic states using only operations from the Clifford group and measurement in the Z-basis, such a scheme is called magic state distillation [1]. This work investigates the robustness of magic state distillation to faults in state preparation and the application of the Clifford gates in the protocol. We establish that the distillation scheme is robust to perturbations in the initial state preparation and characterize the set of states in the Bloch sphere that converge to the T-type magic state in different fidelity regimes. Additionally, we show that magic state distillation is robust to low levels of gate noise and that performing the distillation scheme using noisy Clifford gates is a more efficient than using encoded fault-tolerant gates due to the large overhead in fault-tolerant quantum computing architectures.

In recent years, there are more and more researches on semi-fragile watermarking scheme which can resist JPEG compression. But, there are few researches focused on the recovery of semi-fragile watermarked image. Therefore, in this paper, we not only present a semi-fragile watermarking scheme which can resist JPEG compression but use the error correction code (Reed-Solomon Code) to recover the area being malicious manipulated. At first, we use the semi-fragile watermarking scheme proposed by Lin and Hsieh to detect the counterfeit under the JPEG compression [9]. Its main effect is to resist JPEG compression and to detect the attacked parts without the need of the original image. And then, we will introduce how we use RS code to recover the attacked parts being detected by the semi-fragile watermarking scheme. We use the scheme ¡§Interleaving¡¨ to spread the local pixels to the global area. Next, we encode to each little image block by RS code. The redundant symbols generated by RS code will be signed to be signature attached with the watermarked image. Finally, the receiver can use semi-fragile watermarking scheme to detect attacked part and use the information of the signature to decode these attacked parts. Additionally, we also discuss how to decrease the load of the signature, thus, it can not significant loading of the watermarked image.

Quantum error correction codes were introduced as a means to protect quantum information from decoherance and operational errors. Based on their approach to error control, error correcting codes can be divided into two different classes: block codes and convolutional codes. There has been significant development towards finding quantum block codes, since they were first discovered in 1995. In contrast, quantum convolutional codes remained mainly uninvestigated. In this thesis, we develop the stabilizer formalism for quantum convolutional codes. We define distance properties of these codes and give a general method for constructing encoding circuits, given a set of generators of the stabilizer of a quantum convolutional stabilizer code, is shown. The resulting encoding circuit enables online encoding of the qubits, i.e., the encoder does not have to wait for the input transmission to end before starting the encoding process. We develop the quantum analogue of the Viterbi algorithm. The quantum Viterbi algorithm (QVA) is a maximum likehood error estimation algorithm, the complexity of which grows linearly with the number of encoded qubits. A variation of the quantum Viterbi algorithm, the Windowed QVA, is also discussed. Using Windowed QVA, we can estimate the most likely error without waiting for the entire received sequence.

Quantum computing exists at the intersection of mathematics, physics, chemistry, and engineering; the main goal of quantum computing is the creation of devices and algorithms which use the properties of quantum mechanics to store, manipulate and measure information. There exist many families of algorithms, which, using non-classical logical operations, can outperform traditional, classical algorithms in terms of memory and processing requirements. In addition, quantum computing devices are fundamentally smaller than classical processors and memory elements; since the physical models governing their performance are applicable on all scales, as opposed to classical logic elements, whose underlying principles rely on the macroscopic nature of the device in question. Quantum algorithms, for the most part, are predicated on a theory of resources. It is often assumed that quantum computers can be placed in a precise fiducial state prior to computation, and that logical operations are perfect, inducing no error on the system which they affect. These assumptions greatly simplify algorithmic design, but are fundamentally unrealistic. In order to justify their use, it is necessary to develop a framework for using a large number of imperfect devices to simulate the action of a perfect device, with some acceptable probability of failure. This is the study of fault-tolerant quantum computing. In order to pursue this study effectively, it is necessary to understand the fundamental nature of generic quantum states and operations, as well as the means by which one can correct quantum errors. Additionally, it is important to attempt to minimize the use of computational resources in achieving error reduction and fault-tolerant computing. This thesis is concerned with three projects related to the use of error-prone quantum systems to transmit and manipulate information. The first of these is concerned with the use of imperfectly-prepared states in error-correction routines. Using optimal quantum error correction, we are able to deduce a method of partially protecting encoded quantum information against preparation errors prior to encoding, using no additional qubits. The second of these projects details the search for entangled states which can be used to transmit classical information over quantum channels at a rate superior to classical states. The third of these projects concerns the transcoding of data from one quantum code into another using few ancillary resources. The descriptions of these projects are preceded by a brief introduction to representations of quantum states and channels, for completeness. Three techniques of general interest are presented in appendices. The first is an introduction to, and a minor advance in the development of optimal error correction codes. The second is a more efficient means of calculating the action of a quantum channel on a given state, given that the channel acts non-trivially only on a subsystem, rather than the entire system. Finally, we include documentation on a software package developed to aid the search for quantum transcoding operations.