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Flash memories are non-volatile memory devices. The rapid development of flash technologies leads to higher storage density, but also to higher error rates. This dissertation considers this reliability problem of flash memories and investigates suitable error correction codes, e.g. BCH-codes and concatenated codes. First, the flash cells, their functionality and error characteristics are explained. Next, the mathematics of the employed algebraic code are discussed. Subsequently, generalized concatenated codes (GCC) are presented. Compared to the commonly used BCH codes, concatenated codes promise higher code rates and lower implementation complexity. This complexity reduction is achieved by dividing a long code into smaller components, which require smaller Galois-Field sizes. The algebraic decoding algorithms enable analytical determination of the block error rate. Thus, it is possible to guarantee very low residual error rates for flash memories. Besides the complexity reduction, general concatenated codes can exploit soft information. This so-called soft decoding is not practicable for long BCH-codes. In this dissertation, two soft decoding methods for GCC are presented and analyzed. These methods are based on the Chase decoding and the stack algorithm. The last method explicitly uses the generalized concatenated code structure, where the component codes are nested subcodes. This property supports the complexity reduction. Moreover, the two-dimensional structure of GCC enables the correction of error patterns with statistical dependencies. One chapter of the thesis demonstrates how the concatenated codes can be used to correct two-dimensional cluster errors. Therefore, a two-dimensional interleaver is designed with the help of Gaussian integers. This design achieves the correction of cluster errors with the best possible radius. Large parts of this works are dedicated to the question, how the decoding algorithms can be implemented in hardware. These hardware architectures, their throughput and logic size are presented for long BCH-codes and generalized concatenated codes. The results show that generalized concatenated codes are suitable for error correction in flash memories, especially for three-dimensional NAND memory systems used in industrial applications, where low residual errors must be guaranteed.
NAND flash memory is widely used for data storage due to low power consumption, high throughput, short random access latency, and high density. The storage density of the NAND flash memory devices increases from one generation to the next, albeit at the expense of storage reliability.
Our objective in this dissertation is to improve the reliability of the NAND flash memory with a low hard implementation cost. We investigate the error characteristic, i.e. the various noises of the NAND flash memory. Based on the error behavior at different life-aging stages, we develop offset calibration techniques that minimize the bit error rate (BER).
Furthermore, we introduce data compression to reduce the write amplification effect and support the error correction codes (ECC) unit. In the first scenario, the numerical results show that the data compression can reduce the wear-out by minimizing the amount of data that is written to the flash. In the ECC scenario, the compression gain is used to improve the ECC capability. Based on the first scenario, the write amplification effect can be halved for the considered target flash and data model. By combining the ECC and data compression, the NAND flash memory lifetime improves three fold compared with uncompressed data for the same data model.
In order to improve the data reliability of the NAND flash memory, we investigate different ECC schemes based on concatenated codes like product codes, half-product codes, and generalized concatenated codes (GCC). We propose a construction for high-rate GCC for hard-input decoding. ECC based on soft-input decoding can significantly improve the reliability of NAND flash memories. Therefore, we propose a low-complexity soft-input decoding algorithm for high-rate GCC.
This thesis considers bounding functions for multivariate polynomials and rational functions over boxes and simplices. It also considers the synthesis of polynomial Lyapunov functions for obtaining the stability of control systems. Bounding the range of functions is an important issue in many areas of mathematics and its applications like global optimization, computer aided geometric design, robust control etc.
Algorithms and Architectures for Cryptography and Source Coding in Non-Volatile Flash Memories
(2021)
In this work, algorithms and architectures for cryptography and source coding are developed, which are suitable for many resource-constrained embedded systems such as non-volatile flash memories. A new concept for elliptic curve cryptography is presented, which uses an arithmetic over Gaussian integers. Gaussian integers are a subset of the complex numbers with integers as real and imaginary parts. Ordinary modular arithmetic over Gaussian integers is computational expensive. To reduce the complexity, a new arithmetic based on the Montgomery reduction is presented. For the elliptic curve point multiplication, this arithmetic over Gaussian integers improves the computational efficiency, the resistance against side channel attacks, and reduces the memory requirements. Furthermore, an efficient variant of the Lempel-Ziv-Welch (LZW) algorithm for universal lossless data compression is investigated. Instead of one LZW dictionary, this algorithm applies several dictionaries to speed up the encoding process. Two dictionary partitioning techniques are introduced that improve the compression rate and reduce the memory size of this parallel dictionary LZW algorithm.
Die stetig steigende Digitalisierung von Kommunikation und Interaktion ermöglicht eine immer flexiblere und schnellere Erfassung und Ausführung von Aktivitäten in Geschäftsprozessen. Dabei ermöglichen technologische und organisatorische Treiber, wie beispielsweise Cloud Computing und Industrie 4.0, immer komplexere organisationsübergreifende Geschäftsprozesse. Die effektive und effiziente Einbindung aller beteiligten Menschen (z.B. IT-Experten, Endanwender) ist hierbei ein entscheidender Erfolgsfaktor. Nur wenn alle Prozessbeteiligten Kenntnis über die aktuellen Geschäftsprozesse besitzen, kann eine adäquate Ausführung dieser sichergestellt werden. Die notwendige Balance zwischen Flexibilität und Stabilität wird durch die traditionellen Methoden des Geschäftsprozessmanagements (GPM) nur unzureichend gewährleistet. Sowohl aktuelle Forschungen als auch anwendungsbezogene Studien stellen die unzureichende Integration aller Beteiligten, deren fehlendes Verständnis und die geringe Akzeptanz gegenüber GPM dar. Die Dissertation, welche im Rahmen des anwenderorientierten Forschungsprojekts „BPM@Cloud“ erstellt wird, befasst sich mit der Erarbeitung einer neuen Methode zum agilen Geschäftsprozessmanagement auf Basis gebrauchssprachlicher (alltagssprachlicher, fachsprachlicher) Modellierung von Geschäftsprozessen. Die Methode umfasst drei Bestandteile (Vorgehensweise, Modellierungssprache, Softwarewerkzeug), wodurch eine ganzheitliche Unterstützung bei der Umsetzung von GPM Projekten sichergestellt wird. Durch die Adaption und Erweiterung von agilen Konzepten der Softwareentwicklung wird die Vorgehensweise zum iterativen, inkrementellen und empirischen Management von Geschäftsprozessen beschrieben. Des Weiteren wird eine Modellierungssprache für Geschäftsprozesse entwickelt, welche zur intuitiven, gebrauchssprachlichen Erfassung von Geschäftsprozessen angewendet werden kann. Die Implementierung eines Software-Prototyps ermöglicht des Weiteren die direkte Aufnahme von Feedback während der Ausführung von Geschäftsprozessen. Die drei sich ergänzenden Bestandteile – Vorgehensweise, Sprache und Software-Prototyp – bilden eine neuartige Grundlage für eine verbesserte Erfassung, Anreicherung, Ausführung und Optimierung von Geschäftsprozessen.
In this thesis, a new framework has been proposed, designed and developed for creating efficient and cost effective logistics chains for long items within the building industry. The building industry handles many long items such as pipes, profiles and so on. The handling of these long items is quite complicated and difficult because they are bulky, unstable and heavy. So it is not cost effective and efficient to handle them manually. Existing planning frameworks ignore these special requirements of such goods and are not planned for handling these goods. That leads to that many additional manual handling steps are currently required to handle long items. Therefore, it is very important to develop a new framework for creating the efficient and cost-effective logistics chain for long items. To propose such a new framework, the expert interviews were conducted to gain the fully understanding about the customer requirements. The experts from all stages of the building industry supply chain were interviewed. The data collected from the expert interviews has been analysed and the meaningful findings about the customer requirements have been applied as the valuable inputs for the proposition of the new framework. To have fully knowledge about current practices, all existing planning frameworks have been analysed and evaluated using SWOT analysis. The strengths, weaknesses, opportunities and threats of the current planning frameworks have been comparatively analysed and evaluated. The findings from SWOT analysis have been used for proposing, designing and developing the new framework. The great efforts have been made during the implementation stage. The six different key parameters for a successful implementation have been identified. They are: • Improvement Process with Employees • Control of the Improvements • Gifts/Money for the Improvements and Additional Work • KAIZEN Workshops • Motivation of the Employees for Improvements • Presentation of the Results Among these six parameters, it has been found that KAIZEN workshops is a very effective way for creating an efficient and cost-effective logistics chain for long items. It is believed that the new framework can be theoretically used for the planning of logistics that handle long items and commercial goods. This framework can also be used to plan all kinds of in-house logistics processes from the incoming goods, storage, picking, delivery combination areas and through to the outgoing goods area. The achievements of this project are as follows (1) the new framework for creating efficient and cost-effective logistics chains for long items, (2) the data collection and the data evaluation at the preliminary planning, (3) the decision for one planning variant already at the end of the structure planning, (4) the analysis and evaluation of customer requirements, (5) the consideration and implementation of the customer requirements in the new framework, (6) the creation of figures and tables as planning guideline, (7) the research and further development of Minomi with regards to long items, (8) the research on the information flow, (9) the classification of the improvements and the improvement handling at the implementation, (10) the identification of key parameters for a successful implementation of the planning framework. This framework has been evaluated both theoretically and through a case study of a logistics system planning for handling long items and commercial goods. It has been found that the new framework is theoretically sound and practically valuable. It can be applied to creating the logistics system for long items, especially for building industry.