Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously

Partial MDS Codes with Local Regeneration

Partial MDS (PMDS) and sector-disk (SD) codes are classes of erasure codes that combine locality with strong erasure correction capabilities. We construct PMDS and SD codes where each local code is a bandwidth-optimal regenerating MDS code. The constructions require significantly smaller field size than the only other construction known in literature

Contemporary Coding Theory

Coding Theory naturally lies at the intersection of a large number of disciplines in pure and applied mathematics. A multitude of methods and means has been designed to construct, analyze, and decode the resulting codes for communication. This has suggested to bring together researchers in a variety of disciplines within Mathematics, Computer Science, and Electrical Engineering, in order to cross-fertilize generation of new ideas and force global advancement of the field. Areas to be covered are Network Coding, Subspace Designs, General Algebraic Coding Theory, Distributed Storage and Private Information Retrieval (PIR), as well as Code-Based Cryptography

Doctor of Philosophy

dissertationOptical methods are well-established in the fields of neuroscience, medical imaging, and diagnostics, etc. Optogenetics, for example, enables molecular specificity in optical neural stimulation and recording and has been named the "Method of the Year 2010" by Nature Methods. A novel microdevice was designed, fabricated, developed, and tested to facilitate three-dimensional (3D) deep-tissue light penetration with the capacity to accommodate spatiotemporal modulation of one or more wavelengths to advance a broad range of applications for optical neural interfaces. A 3D optrode array consisting of optically transparent "needles" can penetrate >1 mm directly into tissue, thereby creating multiple independent paths for light propagation that avoid attenuation due to tissue absorption and scattering, providing a high level of selectivity and comprehensive access to tissue not available in current interfaces. Arrays were developed based upon silicon and glass. The silicon optrode array is based upon the well-established Utah electrode array architectures and is suitable for near-infrared (NIR) applications; glass optrodes are appropriate waveguides for both visible and NIR wavelengths. Arrays were bulk-micromachined with high-aspect ratio, a process that has not been reported to be applied to glass previously. In addition to device fabrication, extensive laboratory testing was performed with various optical sources to determine loss mechanisms and emitted beam profiles in tissue across the relevant wavelength ranges, with particular focus on performance metrics for optogenetic and infrared neural stimulation applications. Optrode arrays were determined to be amenable to integration with typical neural stimulation and imaging light delivery mechanisms such as optical fibers and microscopes. Glass optrodes were able to transmit light at ~90% efficiency through depths many times greater than the tissue attenuation length, with negligible light in-coupling loss. Si optrodes were determined to be only ~40% efficient with losses mostly from high index contrast, tip backreflection, and taper radiation. The in-coupling technique and optrode geometry may be modified to produce illumination volumes appropriate for various experimental paradigms. While the focus of this work is on optical neural stimulation, optrode array devices have application in basic neuroscience research, highly selective photodynamic therapy, and deep tissue imaging for diagnostics and therapy