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.

The effects of copayment policies on adherence to prescription medicines in publicly insured populations

Introduction: Copayments for prescriptions are associated with decreased adherence to medicines resulting in increased health service utilisation, morbidity and mortality. In October 2010 a 50c copayment per prescription item was introduced on the General Medical Services (GMS) scheme in Ireland, the national public health insurance programme for low-income and older people. The copayment was increased to €1.50 per prescription item in January 2013. To date, the impact of these copayments on adherence to prescription medicines on the GMS scheme has not been assessed. Given that the GMS population comprises more than 40% of the Irish population, this presents an important public health problem. The aim of this thesis was to assess the impact of two prescription copayments, 50c and €1.50, on adherence to medicines.Methods: In Chapter 2 the published literature was systematically reviewed with meta-analysis to a) develop evidence on cost-sharing for prescriptions and adherence to medicines and b) develop evidence for an alternative policy option; removal of copayments. The core research question of this thesis was addressed by a large before and after longitudinal study, with comparator group, using the national pharmacy claims database. New users of essential and less-essential medicines were included in the study with sample sizes ranging from 7,007 to 136,111 individuals in different medication groups. Segmented regression was used with generalised estimating equations to allow for correlations between repeated monthly measurements of adherence. A qualitative study involving 24 individuals was conducted to assess patient attitudes towards the 50c copayment policy. The qualitative and quantitative findings were integrated in the discussion chapter of the thesis. The vast majority of the literature on this topic area is generated in North America, therefore a test of generalisability was carried out in Chapter 5 by comparing the impact of two similar copayment interventions on adherence, one in the U.S. and one in Ireland. The method used to measure adherence in Chapters 3 and 5 was validated in Chapter 6. Results: The systematic review with meta-analysis demonstrated an 11% (95% CI 1.09 to 1.14) increased odds of non-adherence when publicly insured populations were exposed to copayments. The second systematic review found moderate but variable improvements in adherence after removal/reduction of copayments in a general population. The core paper of this thesis found that both the 50c and €1.50 copayments on the GMS scheme were associated with larger reductions in adherence to less-essential medicines than essential medicines directly after the implementation of policies. An important exception to this pattern was observed; adherence to anti-depressant medications declined by a larger extent than adherence to other essential medicines after both copayments. The cross country comparison indicated that North American evidence on cost-sharing for prescriptions is not automatically generalisable to the Irish setting. Irish patients had greater immediate decreases of -5.3% (95% CI -6.9 to -3.7) and -2.8% (95% CI -4.9 to -0.7) in adherence to anti-hypertensives and anti-hyperlipidaemic medicines, respectively, directly after the policy changes, relative to their U.S. counterparts. In the long term, however, the U.S. and Irish populations had similar behaviours. The concordance study highlighted the possibility of a measurement bias occurring for the measurement of adherence to non-steroidal anti-inflammatory drugs in Chapter 3. Conclusions: This thesis has presented two reviews of international cost-sharing policies, an assessment of the generalisability of international evidence and both qualitative and quantitative examinations of cost-sharing policies for prescription medicines on the GMS scheme in Ireland. It was found that the introduction of a 50c copayment and its subsequent increase to €1.50 on the GMS scheme had a larger impact on adherence to less-essential medicines relative to essential medicines, with the exception of anti-depressant medications. This is in line with policy objectives to reduce moral hazard and is therefore demonstrative of the value of such policies. There are however some caveats. The copayment now stands at €2.50 per prescription item. The impact of this increase in copayment has yet to be assessed which is an obvious point for future research. Careful monitoring for adverse effects in socio-economically disadvantaged groups within the GMS population is also warranted. International evidence can be applied to the Irish setting to aid in future decision making in this area, but not without placing it in the local context first. Patients accepted the introduction of the 50c charge, however did voice concerns over a rising price. The challenge for policymakers is to find the ‘optimal copayment’ – whereby moral hazard is decreased, but access to essential chronic disease medicines that provide advantages at the population level is not deterred. This evidence presented in this thesis will be utilisable for future policy-making in Ireland.