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.

Trade-off between minimum number of wireless sensors and the accuracy of temperature profile in cold rooms: a model-based framework

Evaluation of temperature distribution in cold rooms is an important consideration in the design of food storage solutions. Two common approaches used in both industry and academia to address this question are the deployment of wireless sensors, and modelling with Computational Fluid Dynamics (CFD). However, for a realworld evaluation of temperature distribution in a cold room, both approaches have their limitations. For wireless sensors, it is economically unfeasible to carry out large-scale deployment (to obtain a high resolution of temperature distribution); while with CFD modelling, it is usually not accurate enough to get a reliable result. In this paper, we propose a model-based framework which combines the wireless sensors technique with CFD modelling technique together to achieve a satisfactory trade-off between minimum number of wireless sensors and the accuracy of temperature profile in cold rooms. A case study is presented to demonstrate the usability of the framework.

Novel smart modules for imaging, communications, and displays

This dissertation proposes and demonstrates novel smart modules to solve challenging problems in the areas of imaging, communications, and displays. The smartness of the modules is due to their ability to be able to adapt to changes in operating environment and application using programmable devices, specifically, electronically variable focus lenses (ECVFLs) and digital micromirror devices (DMD). The proposed modules include imagers for laser characterization and general purpose imaging which smartly adapt to changes in irradiance, optical wireless communication systems which can adapt to the number of users and to changes in link length, and a smart laser projection display that smartly adjust the pixel size to achieve a high resolution projected image at each screen distance. The first part of the dissertation starts with the proposal of using an ECVFL to create a novel multimode laser beam characterizer for coherent light. This laser beam characterizer uses the ECVFL and a DMD so that no mechanical motion of optical components along the optical axis is required. This reduces the mechanical motion overhead that traditional laser beam characterizers have, making this laser beam characterizer more accurate and reliable. The smart laser beam characterizer is able to account for irradiance fluctuations in the source. Using image processing, the important parameters that describe multimode laser beam propagation have been successfully extracted for a multi-mode laser test source. Specifically, the laser beam analysis parameters measured are the M2 parameter, w0 the minimum beam waist, and zR the Rayleigh range. Next a general purpose incoherent light imager that has a high dynamic range (>100 dB) and automatically adjusts for variations in irradiance in the scene is proposed. Then a data efficient image sensor is demonstrated. The idea of this smart image sensor is to reduce the bandwidth needed for transmitting data from the sensor by only sending the information which is required for the specific application while discarding the unnecessary data. In this case, the imager demonstrated sends only information regarding the boundaries of objects in the image so that after transmission to a remote image viewing location, these boundaries can be used to map out objects in the original image. The second part of the dissertation proposes and demonstrates smart optical communications systems using ECVFLs. This starts with the proposal and demonstration of a zero propagation loss optical wireless link using visible light with experiments covering a 1 to 4 m range. By adjusting the focal length of the ECVFLs for this directed line-of-sight link (LOS) the laser beam propagation parameters are adjusted such that the maximum amount of transmitted optical power is captured by the receiver for each link length. This power budget saving enables a longer achievable link range, a better SNR/BER, or higher power efficiency since more received power means the transmitted power can be reduced. Afterwards, a smart dual mode optical wireless link is proposed and demonstrated using a laser and LED coupled to the ECVFL to provide for the first time features of high bandwidths and wide beam coverage. This optical wireless link combines the capabilities of smart directed LOS link from the previous section with a diffuse optical wireless link, thus achieving high data rates and robustness to blocking. The proposed smart system can switch from LOS mode to Diffuse mode when blocking occurs or operate in both modes simultaneously to accommodate multiple users and operate a high speed link if one of the users requires extra bandwidth. The last part of this section presents the design of fibre optic and free-space optical switches which use ECVFLs to deflect the beams to achieve switching operation. These switching modules can be used in the proposed optical wireless indoor network. The final section of the thesis presents a novel smart laser scanning display. The ECVFL is used to create the smallest beam spot size possible for the system designed at the distance of the screen. The smart laser scanning display increases the spatial resoluti on of the display for any given distance. A basic smart display operation has been tested for red light and a 4X improvement in pixel resolution for the image has been demonstrated.