Simplified decoding techniques for linear block codes

Error correcting codes are combinatorial objects, designed to enable reliable transmission of digital data over noisy channels. They are ubiquitously used in communication, data storage etc. Error correction allows reconstruction of the original data from received word. The classical decoding algorithms are constrained to output just one codeword. However, in the late 50’s researchers proposed a relaxed error correction model for potentially large error rates known as list decoding. The research presented in this thesis focuses on reducing the computational effort and enhancing the efficiency of decoding algorithms for several codes from algorithmic as well as architectural standpoint. The codes in consideration are linear block codes closely related to Reed Solomon (RS) codes. A high speed low complexity algorithm and architecture are presented for encoding and decoding RS codes based on evaluation. The implementation results show that the hardware resources and the total execution time are significantly reduced as compared to the classical decoder. The evaluation based encoding and decoding schemes are modified and extended for shortened RS codes and software implementation shows substantial reduction in memory footprint at the expense of latency. Hermitian codes can be seen as concatenated RS codes and are much longer than RS codes over the same aphabet. A fast, novel and efficient VLSI architecture for Hermitian codes is proposed based on interpolation decoding. The proposed architecture is proven to have better than Kötter’s decoder for high rate codes. The thesis work also explores a method of constructing optimal codes by computing the subfield subcodes of Generalized Toric (GT) codes that is a natural extension of RS codes over several dimensions. The polynomial generators or evaluation polynomials for subfield-subcodes of GT codes are identified based on which dimension and bound for the minimum distance are computed. The algebraic structure for the polynomials evaluating to subfield is used to simplify the list decoding algorithm for BCH codes. Finally, an efficient and novel approach is proposed for exploiting powerful codes having complex decoding but simple encoding scheme (comparable to RS codes) for multihop wireless sensor network (WSN) applications.

New phosphorescence based probes and techniques for the analysis of cellular oxygen and respiration

Real time monitoring of oxygenation and respiration is on the cutting edge of bioanalysis, including studies of cell metabolism, bioenergetics, mitochondrial function and drug toxicity. This thesis presents the development and evaluation of new luminescent probes and techniques for intracellular O2 sensing and imaging. A new oxygen consumption rate (OCR) platform based on the commercial microfluidic perfusion channel μ-slides compatible with extra- and intracellular O2 sensitive probes, different cell lines and measurement conditions was developed. The design of semi-closed channels allowed cell treatments, multiplexing with other assays and two-fold higher sensitivity to compare with microtiter plate. We compared three common OCR platforms: hermetically sealed quartz cuvettes for absolute OCRs, partially sealed with mineral oil 96-WPs for relative OCRs, and open 96-WPs for local cell oxygenation. Both 96-WP platforms were calibrated against absolute OCR platform with MEF cell line, phosphorescent O2 probe MitoXpress-Intra and time-resolved fluorescence reader. Found correlations allow tracing of cell respiration over time in a high throughput format with the possibility of cell stimulation and of changing measurement conditions. A new multimodal intracellular O2 probe, based on the phosphorescent reporter dye PtTFPP, fluorescent FRET donor and two-photon antennae PFO and cationic nanoparticles RL-100 was described. This probe, called MM2, possesses high brightness, photo- and chemical stability, low toxicity, efficient cell staining and high-resolution intracellular O2 imaging with 2D and 3D cell cultures in intensity, ratiometric and lifetime-based modalities with luminescence readers and FLIM microscopes. Extended range of O2 sensitive probes was designed and studied in order to optimize their spectral characteristics and intracellular targeting, using different NPs materials, delivery vectors, ratiometric pairs and IR dyes. The presented improvements provide useful tool for high sensitive monitoring and imaging of intracellular O2 in different measurement formats with wide range of physiological applications.