Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation

For many algebraic codes the main part of decoding can be reduced to a shift register synthesis problem. In this paper we present an approach for solving generalised shift register problems over skew polynomial rings which occur in error and erasure decoding of $\ell$-Interleaved Gabidulin codes. The algorithm is based on module minimisation and has time complexity $O(\ell \mu^2)$ where $\mu$ measures the size of the input problem.Comment: 10 pages, submitted to WCC 201

Row Reduction Applied to Decoding of Rank Metric and Subspace Codes

We show that decoding of $\ell$-Interleaved Gabidulin codes, as well as list-$\ell$ decoding of Mahdavifar--Vardy codes can be performed by row reducing skew polynomial matrices. Inspired by row reduction of \F[x] matrices, we develop a general and flexible approach of transforming matrices over skew polynomial rings into a certain reduced form. We apply this to solve generalised shift register problems over skew polynomial rings which occur in decoding $\ell$-Interleaved Gabidulin codes. We obtain an algorithm with complexity $O(\ell \mu^2)$ where $\mu$ measures the size of the input problem and is proportional to the code length $n$ in the case of decoding. Further, we show how to perform the interpolation step of list-$\ell$-decoding Mahdavifar--Vardy codes in complexity $O(\ell n^2)$, where $n$ is the number of interpolation constraints.Comment: Accepted for Designs, Codes and Cryptograph

Sub-quadratic Decoding of One-point Hermitian Codes

We present the first two sub-quadratic complexity decoding algorithms for one-point Hermitian codes. The first is based on a fast realisation of the Guruswami-Sudan algorithm by using state-of-the-art algorithms from computer algebra for polynomial-ring matrix minimisation. The second is a Power decoding algorithm: an extension of classical key equation decoding which gives a probabilistic decoding algorithm up to the Sudan radius. We show how the resulting key equations can be solved by the same methods from computer algebra, yielding similar asymptotic complexities.Comment: New version includes simulation results, improves some complexity results, as well as a number of reviewer corrections. 20 page

Video Processing Acceleration using Reconfigurable Logic and Graphics Processors

A vexing question is `which architecture will prevail as the core feature of the next state of the art video processing system?' This thesis examines the substitutive and collaborative use of the two alternatives of the reconfigurable logic and graphics processor architectures. A structured approach to executing architecture comparison is presented - this includes a proposed `Three Axes of Algorithm Characterisation' scheme and a formulation of perfor- mance drivers. The approach is an appealing platform for clearly defining the problem, assumptions and results of a comparison. In this work it is used to resolve the advanta- geous factors of the graphics processor and reconfigurable logic for video processing, and the conditions determining which one is superior. The comparison results prompt the exploration of the customisable options for the graphics processor architecture. To clearly define the architectural design space, the graphics processor is first identifed as part of a wider scope of homogeneous multi-processing element (HoMPE) architectures. A novel exploration tool is described which is suited to the investigation of the customisable op- tions of HoMPE architectures. The tool adopts a systematic exploration approach and a high-level parameterisable system model, and is used to explore pre- and post-fabrication customisable options for the graphics processor. A positive result of the exploration is the proposal of a reconfigurable engine for data access (REDA) to optimise graphics processor performance for video processing-specific memory access patterns. REDA demonstrates the viability of the use of reconfigurable logic as collaborative `glue logic' in the graphics processor architecture

Clinical trial metadata:Defining and extracting metadata on the design, conduct, results and costs of 125 randomised clinical trials funded by the National Institute for Health Research Health Technology Assessment programme

Background:  By 2011, the Health Technology Assessment (HTA) programme had published the results of over 100 trials with another 220 in progress. The aim of the project was to develop and pilot ‘metadata’ on clinical trials funded by the HTA programme.   Objectives: The aim of the project was to develop and pilot questions describing clinical trials funded by the HTA programme in terms of it meeting the needs of the NHS with scientifically robust studies. The objectives were to develop relevant classification systems and definitions for use in answering relevant questions and to assess their utility.   Data sources: Published monographs and internal HTA documents.   Review methods: A database was developed, ‘populated’ using retrospective data and used to answer questions under six prespecified themes. Questions were screened for feasibility in terms of data availability and/or ease of extraction. Answers were assessed by the authors in terms of completeness, success of the classification system used and resources required. Each question was scored to be retained, amended or dropped.    Results: One hundred and twenty-five randomised trials were included in the database from 109 monographs. Neither the International Standard Randomised Controlled Trial Number nor the term ‘randomised trial’ in the title proved a reliable way of identifying randomised trials. Only limited data were available on how the trials aimed to meet the needs of the NHS. Most trials were shown to follow their protocols but updates were often necessary as hardly any trials recruited as planned. Details were often lacking on planned statistical analyses, but we did not have access to the relevant statistical plans. Almost all the trials reported on cost-effectiveness, often in terms of both the primary outcome and quality-adjusted life-years. The cost of trials was shown to depend on the number of centres and the duration of the trial. Of the 78 questions explored, 61 were well answered, 33 fully with 28 requiring amendment were the analysis updated. The other 17 could not be answered with readily available data.   Limitations: The study was limited by being confined to 125 randomised trials by one funder.   Conclusions: Metadata on randomised controlled trials can be expanded to include aspects of design, performance, results and costs. The HTA programme should continue and extend the work reported here