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.

Compilation and analysis of integrated regional input-output tables for NUTS 2 regions in Ireland

In 1966, Roy Geary, Director of the ESRI, noted “the absence of any kind of import and export statistics for regions is a grave lacuna” and further noted that if regional analyses were to be developed then regional Input-Output Tables must be put on the “regular statistical assembly line”. Forty-five years later, the lacuna lamented by Geary still exists and remains the most significant challenge to the construction of regional Input-Output Tables in Ireland. The continued paucity of sufficient regional data to compile effective regional Supply and Use and Input-Output Tables has retarded the capacity to construct sound regional economic models and provide a robust evidence base with which to formulate and assess regional policy. This study makes a first step towards addressing this gap by presenting the first set of fully integrated, symmetric, Supply and Use and domestic Input-Output Tables compiled for the NUTS 2 regions in Ireland: The Border, Midland and Western region and the Southern & Eastern region. These tables are general purpose in nature and are consistent fully with the official national Supply & Use and Input-Output Tables, and the regional accounts. The tables are constructed using a survey-based or bottom-up approach rather than employing modelling techniques, yielding more robust and credible tables. These tables are used to present a descriptive statistical analysis of the two administrative NUTS 2 regions in Ireland, drawing particular attention to the underlying structural differences of regional trade balances and composition of Gross Value Added in those regions. By deriving regional employment multipliers, Domestic Demand Employment matrices are constructed to quantify and illustrate the supply chain impact on employment. In the final part of the study, the predictive capability of the Input-Output framework is tested over two time periods. For both periods, the static Leontief production function assumptions are relaxed to allow for labour productivity. Comparative results from this experiment are presented.