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.

Reflections on the transformation of my meaning making to support the organic growth of a firm

The objective of my Portfolio is to explore the working hypothesis that the organic growth of a firm is governed by the perspectives of individuals and such perspectives are governed by their meaning-making. The Portfolio presents explorations of the transformation of my meaning making and in adopting new practices to support the organic growth of a firm. I use the work of other theorists to transition my understanding of how the world works. This transition process is an essential tool to engage with and understand the perspectives of others and develop a mental capacity to “train one’s imagination to go visiting” (Arendt, 1982; p.43). The Portfolio, therefore, is primarily located in reflective research. Using Kegan’s (1994) approach to Adult Mental Development, and Sowell’s (2007) understanding of the visions which silently shape our thoughts I organise the developments of my meaning making around three transformation pillars of change. In pillar one I seek to transform an unthinking respect for authority and break down a blind pervasiveness of thought within my reasoning process arising from an instinct for attachment and support from others whom I trust. In pillar two I seek to discontinue using autocratic leadership and learn to use the thoughts and contributions of a wider team to make improved choices about uncertain future events. In pillar three I explore the use of a more reflective thinking framework to test the accuracy of my perceptions and apply a high level of integrity in my reasoning process. The transformation of my meaning making has changed my perspectives and in turn my preferred practices to support the organic growth of a firm. I identify from practice that a transformative form of leadership is far more effective that a transactional form of leadership to stimulate the trust and teamwork required to sustain the growth a firm. Creating an environment where one feels free to share thoughts and feelings with others is an essential tool to build a team to critique the thoughts of one other. Furthermore, the entrepreneurial wisdom to grow a firm must come from a wider team, located both inside and outside the boundaries of a firm. No individual or small team has the mental capacity to provide the entrepreneurship required to drive the organic growth of a firm. I address my Portfolio to leaders in organisations who have no considered framework on the best practices required to lead a social organisation. These individuals may have no sense of what they implicitly believe drives social causation and they may have no understanding if their meaning making supports or curtails the practices required to grow a firm. They may have a very limited capacity to think in a logical manner, with the result they are using guesses from their ‘gut’ to make poor judgements in the management of a firm.

Chamber investigations of atmospheric mercury oxidation chemistry

Mercury is a potent neurotoxin even at low concentrations. The unoxidised metal has a high vapour pressure and can circulate through the atmosphere, but when oxidised can deposit and be accumulated through the food chain. This work aims to investigate the oxidation processes of atmospheric Hg0(g). The first part describes efforts to make a portable Hg sensor based on Cavity Enhanced Absorption Spectroscopy (CEAS). The detection limit achieved was 66 ngm−3 for a 10 second averaging time. The second part of this work describes experiments carried out in a temperature controlled atmospheric simulation chamber in the Desert Research Institute, Reno, Nevada, USA. The chamber was built around an existing Hg CRDS system that could measure Hg concentrations in the chamber of<100 ngm−3 at 1 Hz enabling reactions to be followed. The main oxidant studied was bromine, which was quantified with a LED based CEAS system across the chamber. Hg oxidation in the chamber was found to be mostly too slow for current models to explain. A seven reaction model was developed and tested to find which parameters were capable of explaining the deviation. The model was overdetermined and no unique solution could be found. The most likely possibility was that the first oxidation step Hg + Br →HgBr was slower than the preferred literature value by a factor of two. However, if the more uncertain data at low [Br2] was included then the only parameter that could explain the experiments was a fast, temperature independent dissociation of HgBr some hundreds of times faster than predicted thermolysis or photolysis rates. Overall this work concluded that to quantitatively understand the reaction of Hg with Br2, the intermediates HgBr and Br must be measured. This conclusion will help to guide the planning of future studies of atmospheric Hg chemistry.