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.

Biomimetic accommodating intraocular lens

The crystalline lens allows the eye to focus on near and far objects. During the aging process, it loses its ability to focus and often becomes cloudy during cataract formation. At this point, traditional medical therapy replaces the lens with an artificial replacement lens. Although replacement lenses for the crystalline lens have been implanted since 1949 for cataract surgery, none of the FDA-approved lenses mimic the anatomy of the natural lens. Hence, they are not able to focus in a manner similar to the youthful lens. Instead, they function in a manner similar to the aged lens and only provide vision at a single distance or at a very limited range of focal distances. Patients with the newest implants are often obliged to use reading glasses when using near vision, or suffer from optical aberrations, halos, or glare. Therefore, there is a need to provide youthful vision after lens surgery in terms of focusing ability, accurate optical power, and sharp focus without distortion or optical aberrations.

This thesis presents an approach to restoring youthful vision after lens replacement. An intraocular lens (IOL) that can provide accurate visual acuity along with focusing ability is proposed. This IOL relies on the natural anatomy and physiology of the eye, and therefore is actuated in a manner identical to the natural lens. In addition, the lens has the capability for adjustment during or after implantation to provide high-acuity vision throughout life.

The natural anatomy and physiology of the eye is described, along with lens replacement surgery. A lens design is proposed to address the unmet need of lens-replacement patients. Specific care in the design is made for small surgical incisions, high visual acuity, adjustable acuity over years, and the ability to focus similar to the natural lens. Methods to test the IOL using human donor tissue are developed based upon prior experiments on the ex vivo natural lens. These tools are used to demonstrate efficacy of the newly developed accommodating intraocular lens.

To further demonstrate implant feasibility, materials and processes for building the lens are evaluated for biocompatibility, endurance, repeatable manufacture, and stability. The lens biomechanics are determined after developing an artificial anatomy testing setup inspired by the natural anatomy of the human focusing mechanism. Finally, based upon a mechanical and optical knowledge of the lens, several improved lens concepts are proposed and demonstrated for efficacy.