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.

An evaluation of the implications of the best interests of the child principle in the context of same-sex parenting in Ireland

Same-sex parenting is by no means a new phenomenon but the legal recognition and acceptance of gay and lesbian couples as parents is a relatively recent development in most countries. Traditionally, such recognition has been opposed on the basis of the claim that the best interests of children could not be met by gay and lesbian parents. This thesis examines the validity of this argument and it explores the true implications of the best interests principle in this context. The objective is to move away from subjective or moral conceptions of the best interests principle to an understanding which is informed by relevant sociological and psychological data and which is guided by reference to the rights contained in the UN Convention on the Rights of the Child. Using this perspective, the thesis addresses the overarching issue of whether the law should offer legal recognition and protection to gay and lesbian families and the more discrete matter of how legal protection should be provided. It is argued that the best interests principle can be used to demand that same-sex parenting arrangements should be afforded legal recognition and protection. Suggestions are also presented as to the most appropriate manner of providing for this recognition. In this regard, guidance is drawn from the English and South African experience in this area. Overall, the objective is to assess the current laws from the perspective of the best interests principle so as to ensure that the law operates in a manner which adheres to the rights and interests of children.

Recoding: reprogrammed genetic decoding with an emphasis on antizyme regulatory frameshifting

Recoding embraces mechanisms that augment the rules of standard genetic decoding. The deviations from standard decoding are often purposeful and their realisation provides diverse and flexible regulatory mechanisms. Recoding events such as programed ribosomal frameshifting are especially plentiful in viruses. In most organisms only a few cellular genes are known to employ programed ribosomal frameshifting in their expression. By far the most prominent and therefore well-studied case of cellular +1 frameshifting is in expression of antizyme mRNAs. The protein antizyme is a key regulator of polyamine levels in most eukaryotes with some exceptions such as plants. A +1 frameshifting event is required for the full length protein to be synthesized and this requirement is a conserved feature of antizyme mRNAs from yeast to mammals. The efficiency of the frameshifting event is dependent on the free polyamine levels in the cell. cis-acting elements in antizyme mRNAs such as specific RNA structures are required to stimulate the frameshifting efficiency. Here I describe a novel stimulator of antizyme +1 frameshifting in the Agaricomycotina class of Basidiomycete fungi. It is a nascent peptide that acts from within the ribosome exit tunnel to stimulate frameshifting efficiency in response to polyamines. The interactions of the nascent peptide with components of the peptidyl transferase centre and the protein exit tunnel emerge in our understanding as powerful means which the cell employs for monitoring and tuning the translational process. These interactions can modulate the rate of translation, protein cotranslational folding and localization. Some nascent peptides act in concert with small molecules such as polyamines or antibiotics to stall the ribosome. To these known nascent peptide effects we have added that of a stimulatory effect on the +1 frameshifting in antizyme mRNAs. It is becoming evident that nascent peptide involvement in regulation of translation is a much more general phenomenon than previously anticipated.

Constraint-force-based approach of modelling compliant mechanisms: principle and application

Numerous works have been conducted on modelling basic compliant elements such as wire beams, and closed-form analytical models of most basic compliant elements have been well developed. However, the modelling of complex compliant mechanisms is still a challenging work. This paper proposes a constraint-force-based (CFB) modelling approach to model compliant mechanisms with a particular emphasis on modelling complex compliant mechanisms. The proposed CFB modelling approach can be regarded as an improved free-body- diagram (FBD) based modelling approach, and can be extended to a development of the screw-theory-based design approach. A compliant mechanism can be decomposed into rigid stages and compliant modules. A compliant module can offer elastic forces due to its deformation. Such elastic forces are regarded as variable constraint forces in the CFB modelling approach. Additionally, the CFB modelling approach defines external forces applied on a compliant mechanism as constant constraint forces. If a compliant mechanism is at static equilibrium, all the rigid stages are also at static equilibrium under the influence of the variable and constant constraint forces. Therefore, the constraint force equilibrium equations for all the rigid stages can be obtained, and the analytical model of the compliant mechanism can be derived based on the constraint force equilibrium equations. The CFB modelling approach can model a compliant mechanism linearly and nonlinearly, can obtain displacements of any points of the rigid stages, and allows external forces to be exerted on any positions of the rigid stages. Compared with the FBD based modelling approach, the CFB modelling approach does not need to identify the possible deformed configuration of a complex compliant mechanism to obtain the geometric compatibility conditions and the force equilibrium equations. Additionally, the mathematical expressions in the CFB approach have an easily understood physical meaning. Using the CFB modelling approach, the variable constraint forces of three compliant modules, a wire beam, a four-beam compliant module and an eight-beam compliant module, have been derived in this paper. Based on these variable constraint forces, the linear and non-linear models of a decoupled XYZ compliant parallel mechanism are derived, and verified by FEA simulations and experimental tests.