Rewriting Schemes for Flash Memory

Flash memory is a leading storage media with excellent features such as random access and high storage density. However, it also faces significant reliability and endurance challenges. In flash memory, the charge level in the cells can be easily increased, but removing charge requires an expensive erasure operation. In this thesis we study rewriting schemes that enable the data stored in a set of cells to be rewritten by only increasing the charge level in the cells. We consider two types of modulation scheme; a convectional modulation based on the absolute levels of the cells, and a recently-proposed scheme based on the relative cell levels, called rank modulation. The contributions of this thesis to the study of rewriting schemes for rank modulation include the following: we

•propose a new method of rewriting in rank modulation, beyond the previously proposed method of “push-to-the-top”;

•study the limits of rewriting with the newly proposed method, and derive a tight upper bound of 1 bit per cell;

•extend the rank-modulation scheme to support rankings with repetitions, in order to improve the storage density;

•derive a tight upper bound of 2 bits per cell for rewriting in rank modulation with repetitions;

•construct an efficient rewriting scheme that asymptotically approaches the upper bound of 2 bit per cell.

The next part of this thesis studies rewriting schemes for a conventional absolute-levels modulation. The considered model is called “write-once memory” (WOM). We focus on WOM schemes that achieve the capacity of the model. In recent years several capacity-achieving WOM schemes were proposed, based on polar codes and randomness extractors. The contributions of this thesis to the study of WOM scheme include the following: we

•propose a new capacity-achievingWOM scheme based on sparse-graph codes, and show its attractive properties for practical implementation;

•improve the design of polarWOMschemes to remove the reliance on shared randomness and include an error-correction capability.

The last part of the thesis studies the local rank-modulation (LRM) scheme, in which a sliding window going over a sequence of real-valued variables induces a sequence of permutations. The LRM scheme is used to simulate a single conventional multi-level flash cell. The simulated cell is realized by a Gray code traversing all the relative-value states where, physically, the transition between two adjacent states in the Gray code is achieved by using a single “push-to-the-top” operation. The main results of the last part of the thesis are two constructions of Gray codes with asymptotically-optimal rate.

A working guide to the assessment, implementation and post project monitoring of fisheries habitat improvement schemes in South Cumbria

Due to changes in land use over the last century, the physical nature of many streams and rivers in the British Isles has probably changed. In some cases this change may be large for example as a result of flood defence schemes and is easily observed, whilst in other cases altered land use, farming, forestry or urbanization may have resulted in more subtle changes to river features. This working guide draws together a way of assessing habitat in any stream or river and determine sites or reaches on the assessed watercourse that may benefit from habitat improvement schemes. It will determine a method of measuring existing habitat in a broad sense, whilst referring to R and D studies currently being undertaken in this area. A method of prioritising any proposed habitat restoration work will be suggested. The limitations of fisheries improvement schemes in terms of cross functional acceptance (flood defence and conservation) will be examined along with suggested proposals for some example watercourses. The need for pre and post enhancement monitoring will be discussed as will the requirement for maintenance programs on schemes. Finally methods for determining the cost benefits of small schemes will be examined, compared to other currently used enhancement strategies. This will allow small scale revenue schemes to be used to back up pre project cost benefit analysis as required in future capital submissions.

River Wyre salmon and sea trout spawning habitat restoration / creation project. Gravel enhancement schemes.

As part of an overall desire to maintain and improve the migratory salmonid population in the River Wyre, a project was commissioned to investigate remedial action which may improve and enhance spawning success and lead to an eventual improvement in the status of adult stocks. The report, titled "River Wyre Salmon and Sea Trout Spawning Habitat Restoration/Creation Project", concluded that usable spawning gravels appeared to be in short supply in the River Wyre catchment and may be the limiting factor influencing the returning adult stock, as juvenile nursery habitat was not found to be limiting. This report looks at gravel enhancement schemes to improve River Wyre salmon and sea trout spawning habitat restoration. It examines methods for gravel enhancement schemes: mechanical cleaning and construction of gravel addition structures. Includes sites figures of sites identified for enhancement.

Convergence Properties and Fixed Points of Two General Iterative Schemes with Composed Maps in Banach Spaces with Applications to Guaranteed Global Stability

This paper investigates the boundedness and convergence properties of two general iterative processes which involve sequences of self-mappings on either complete metric or Banach spaces. The sequences of self-mappings considered in the first iterative scheme are constructed by linear combinations of a set of self-mappings, each of them being a weighted version of a certain primary self-mapping on the same space. The sequences of self-mappings of the second iterative scheme are powers of an iteration-dependent scaled version of the primary self-mapping. Some applications are also given to the important problem of global stability of a class of extended nonlinear polytopic-type parameterizations of certain dynamic systems.

A Comparison of Two Stratification Schemes Used in Sampling Canadian Atlantic Cod, Gadus morhua

Sampling is a key element in the assessment of any fish stock. It is often one of the most expensive activities of the management process; thus, improved efficiency can result in significant cost savings. In most cases a two-phase sampling strategy is employed. Two commonly used versions of such stratified random schemes were simulated using a test population based on Atlantic cod, Gadus morhua. A 1 otolith per 1 cm length frequency currently used for many flatfish and some smaller gadoids and a 3 otolith per 3 cm length frequency currently used for many of the larger gadoids. No difference was detected in the age composition or mean length at age for either scheme; however, 10 percent fewer otoliths were collected in 1 for 1 sampling than 3 for 3. There was an improvement of between 30 and 60 percent in the coefficient of variation of the estimated catch numbers at age using the 1 for 1 compared with the 3 for 3 stratified sampling. For these reasons and other operational considerations, the 1 for 1 stratified random design of sampling appears to be superior.