Submitted in fulfilment of the academic requirements for the Master of Science in Engineering in Electrical and Information Engineering degree in the School of Electrical and Information Engineering at the University of Witwatersrand, Johannesburg, South Africa. August 2017 / There has been a surge in the demand of high speed reliable communication infrastructure in the last few decades. Advanced technology, namely the internet has transformed the way people live and how they interact with their environment. The Internet of Things (IoT) has been a very big phenomenon and continues to transform infrastructure in the home and work place. All these developments are underpinned by the availability of cost-effective, reliable and error free communication services. A perfect and reliable communication channel through which to transmit information does not exist. Telecommunication channels are often characterised by random noise and unpredictable disturbances that distort information or result in the loss of information. The need for reliable error-free communication has resulted in advanced research work in the field of Forward Error Correction (FEC). Low density parity check (LDPC) codes, discovered by Gallager in 1963 provide excellent error correction performance which is close to the vaunted Shannon limit when used with long block codes and decoded with the sum-product algorithm (SPA). However, long block code lengths increase the decoding complexity exponentially and this problem is exacerbated by the intrinsic complexity of the SPA and its approximate derivatives. This makes it impossible for the SPA to be implemented in any practical communication device. Bit flipping LDPC decoders, whose error correction performance pales in comparison to the SPA have been devised to counter the disadvantages of the SPA. Even though, the bit flipping algorithms do not perform as well as the SPA, their exceeding low complexity makes them attractive for practical implementation in high speed communication devices. Thus, a lot of research has gone into the design and development of improved bit flipping algorithms. This research work analyses and focusses on the design of improved multi-bit flipping algorithms which converge faster than single-bit flipping algorithms. The aim of the research is to devise methods with which to obtain thresholds that can be used to determine erroneous sections of a given codeword so that they can be corrected. Two algorithms that use multi-thresholds are developed during the course of this research. The first algorithm uses multiple adaptive thresholds while the second algorithm uses multiple near optimal SNR dependant fixed thresholds to identify erroneous bits in a codeword. Both algorithms use soft information modification to further improve the decoding performance. Simulations show that the use of multiple adaptive or near optimal SNR dependant fixed thresholds improves the bit error rate (BER) and frame error rate (FER) correcting performance and also decreases the average number of iterations (ANI) required for convergence. The proposed algorithms are also investigated in terms of quantisation for practical applications in communication devices. Simulations show that the bit length of the quantizer as well as the quantization strategy (uniform or non-uniform quantization) is very important as it affects the decoding performance of the algorithms significantly. / MT2018

A dissertation submitted in fulfilment of the requirements for the degree of Master of Science in the Centre for Telecommunication Access and Services, School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg, 2016 / Reed-Solomon codes are very popular codes used in the field of forward error correction due to their correcting capabilities. Thus, a lot of research has been done dedicated to the development of decoding algorithms for this class of code. [Abbreviated Abstract. Open document to view full version]

In this project we perform data transmission across noisy channels and recover the message first by using the Golay code, and then by using the first-order Reed- Muller code. The main objective of this thesis is to determine which code among the above two is more efficient for text message transmission by applying the two codes to exactly the same data with the same channel error bit probabilities. We use the comparison of the error-correcting capability and the practical speed of the Golay code and the first-order Reed-Muller code to meet our goal. / by Olga Shukina. / Thesis (M.S.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

The main goal of video coding algorithms is to achieve high compression efficiency while maintaining quality of the compressed signal at the highest level. Human visual system is the ultimate receiver of compressed signal and final judge of its quality. This dissertation presents work towards optimal video compression algorithm that is based on the characteristics of our visual system. Modeling phenomena such as backward temporal masking and motion masking we developed algorithms that are implemented in the state-of- the-art video encoders. Result of using our algorithms is visually lossless compression with improved efficiency, as verified by standard subjective quality and psychophysical tests. Savings in bitrate compared to the High Efficiency Video Coding / H.265 reference implementation are up to 45%. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

In the first chapters we will give a short introduction to signature schemes in single and multi-user settings. We give the definition of a signature scheme and explain a group of possible attacks on them. In Chapter 6 we give a construction which derives a subliminal-free RSA public key. In the construction we use a computationally binding and unconditionally hiding commitment scheme. To establish a subliminal-free RSA modulus n, we have to construct the secret primes p and q. To prove p and q are primes we use Lehmann's primality test on the commitments. The chapter is based on the paper, "RSA signature schemes with subliminal-free public key" (Tatra Mountains Mathematical Publications 41 (2008)). In chapter 7 a one-time signature scheme using run-length encoding is presented, which in the random oracle model offers security against chosen-message attacks. For parameters of interest, the proposed scheme enables about 33% faster verification with a comparable signature size than a construction of Merkle and Winternitz. The public key size remains unchanged (1 hash value). The main cost for the faster verification is an increase in the time required for signing messages and for key generation. The chapter is based on the paper "A one-time signature using run-length encoding" (Information Processing Letters Vol. 108, Issue 4, (2008)). / by Viktoria Villanyi. / Thesis (Ph.D.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

Perceptual video coding has been a promising area during the last years. Increases in compression ratios have been reported by applying foveated video coding techniques where the region of interest (ROI) is selected by using a computational attention model. However, most of the approaches for perceptual video coding only use visual features ignoring the auditory component. In recent physiological studies, it has been demonstrated that auditory stimuli affects our visual perception. In this work, we validate some of those physiological tests using complex video sequence. We designed and developed a web-based tool for video quality measurement. After conducting different experiments, we observed that in the general reaction time to detect video artifacts was higher when video was presented with the audio information. We observed that emotional information in audio guide human attention to particular ROI. We also observed that sound frequency change spatial frequency perception in still images. / by Freddy Torres. / Thesis (M.S.C.S.)--Florida Atlantic University, 2013. / Includes bibliography. / Mode of access: World Wide Web. / System requirements: Adobe Reader.

Recently, multimedia applications and their use have grown dramatically in popularity in strong part due to mobile device adoption by the consumer market. Applications, such as video conferencing, have gained popularity. These applications and others have a strong video component that uses the mobile device’s resources. These resources include processing time, network bandwidth, memory use, and battery life. The goal is to reduce the need of these resources by reducing the complexity of the coding process. Mobile devices offer unique characteristics that can be exploited for optimizing video codecs. The combination of small display size, video resolution, and human vision factors, such as acuity, allow encoder optimizations that will not (or minimally) impact subjective quality. The focus of this dissertation is optimizing video services in mobile environments. Industry has begun migrating from H.264 video coding to a more resource intensive but compression efficient High Efficiency Video Coding (HEVC). However, there has been no proper evaluation and optimization of HEVC for mobile environments. Subjective quality evaluations were performed to assess relative quality between H.264 and HEVC. This will allow for better use of device resources and migration to new codecs where it is most useful. Complexity of HEVC is a significant barrier to adoption on mobile devices and complexity reduction methods are necessary. Optimal use of encoding options is needed to maximize quality and compression while minimizing encoding time. Methods for optimizing coding mode selection for HEVC were developed. Complexity of HEVC encoding can be further reduced by exploiting the mismatch between the resolution of the video, resolution of the mobile display, and the ability of the human eyes to acquire and process video under these conditions. The perceptual optimizations developed in this dissertation use the properties of spatial (visual acuity) and temporal information processing (motion perception) to reduce the complexity of HEVC encoding. A unique feature of the proposed methods is that they reduce encoding complexity and encoding time. The proposed HEVC encoder optimization methods reduced encoding time by 21.7% and bitrate by 13.4% with insignificant impact on subjective quality evaluations. These methods can easily be implemented today within HEVC. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

Next, we investigate several models of TRC including the discrete memoryless TRC, the Gaussian TRC and the bandlimited Gaussian TRC, and prove an outer bound on the capacity region of each of the TRC models. In particular, the outer bound on the capacity region of the bandlimited Gaussian TRC is a theoretical outer bound on the capacity region achievable by physical-layer network coding (PNC). Furthermore, we model a cellular relay network consisting of multiple users, multiple relays and multiple base stations as a collection of two-node point-to-point systems and three-node networks, where each two-node point-to-point system consists of two bandlimited Gaussian channels and each three-node network consists of a bandlimited Gaussian TRC. We obtain performance bounds of PNC on the cellular relay network by simulation and our simulation results show that the average maximum equal-rate throughput over all users under every PNC strategy investigated is generally worse than the average equal-rate throughput over all users under some routing strategy. This is possibly due to larger interference among the nodes under the PNC strategies compared with the routing strategy. / Our investigation of wireless relay networks begins by studying the two-way relay channel (TRC), in which a user and a base station exchange their messages with the help of a middle relay. We model the TRC as a three-node point-to-point relay network and propose practical symbol-level network coding schemes for the three-node network. We obtain several rate regions achievable by the network coding schemes and show that the use of symbol-level network coding rather than routing alone always enlarges the achievable rate region. Inparticular, the use of symbol-level network coding always increases the maximum equal-rate throughput. Furthermore, we model a cellular relay network consisting of multiple users, multiple relays and multiple base stations as a collection of two-node point-to-point systems and three-node point-to-point relay networks where each point-to-point channel is modeled as a bandlimited Gaussian channel. We propose several practical symbol-level network coding schemes on the network and investigate the benefit of symbol-level network coding by simulation. Our simulation results show that the use of symbol-level network coding rather than routing alone increases the average maximum equal-rate throughput over all users. / Fong, Lik Hang Silas. / Adviser: Yeung, Wai-Ho Raymond. / Source: Dissertation Abstracts International, Volume: 73-04, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 267-270). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.

by Patrick Chi-man Fung. / Thesis (M.Sc.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references (leaves 57-58). / LIST OF FIGURES / LIST OF IMAGES / LIST OF TABLES / NOTATIONS / Chapter 1 --- INTRODUCTION --- p.1 / Chapter 2 --- THEORY --- p.3 / Chapter 2.1 --- Matrix Representation of LOT --- p.3 / Chapter 2.2 --- Feasibility of LOT --- p.5 / Chapter 2.3 --- Properties of Good Feasible LOT --- p.6 / Chapter 2.4 --- An Optimal LOT --- p.7 / Chapter 2.5 --- Approximation of an Optimal LOT --- p.10 / Chapter 2.6 --- Representation of an Approximately Optimal LOT --- p.13 / Chapter 3 --- IMPLEMENTATION --- p.17 / Chapter 3.1 --- Mathematical Background --- p.17 / Chapter 3.2 --- Analysis of LOT Flowgraph --- p.17 / Chapter 3.2.1 --- The Fundamental LOT Building Block --- p.17 / Chapter 3.2.2 --- +1/-1 Butterflies --- p.19 / Chapter 3.3 --- Conclusion --- p.25 / Chapter 4 --- RESULTS --- p.27 / Chapter 4.1 --- Objective of Energy Packing --- p.27 / Chapter 4.2 --- Nature of Target Images --- p.27 / Chapter 4.3 --- Methodology of LOT Coefficient Selection --- p.28 / Chapter 4.4 --- dB RMS Error in Pixel Values --- p.29 / Chapter 4.5 --- Negative Pixel Values in Reverse LOT --- p.30 / Chapter 4.6 --- LOT Coefficient Energy Distribution --- p.30 / Chapter 4.7 --- Experimental Data --- p.32 / Chapter 5 --- DISCUSSION AND CONCLUSIONS --- p.46 / Chapter 5.1 --- RMS Error (dB) and LOT Coeffs. Drop Ratio --- p.46 / Chapter 5.1.1 --- Numeric Experimental Results --- p.46 / Chapter 5.1.2 --- Human Visual Response --- p.46 / Chapter 5.1.3 --- Conclusion --- p.49 / Chapter 5.2 --- Number of Negative Pixel Values in RLOT --- p.50 / Chapter 5.3 --- LOT Coefficient Energy Distribution --- p.51 / Chapter 5.4 --- Effect of Changing the Block Size --- p.54 / REFERENCES --- p.57 / APPENDIX / Tables of Experimental Data --- p.59

Chei Kwok-hung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves 66-73). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Typical Digital Communication Systems --- p.2 / Chapter 1.1.1 --- Source coding --- p.3 / Chapter 1.1.2 --- Channel coding --- p.5 / Chapter 1.2 --- Joint Source-Channel Coding System --- p.5 / Chapter 1.3 --- Thesis Organization --- p.7 / Chapter Chapter 2 --- Trellis Coding --- p.9 / Chapter 2.1 --- Convolutional Codes --- p.9 / Chapter 2.2 --- Trellis-Coded Modulation --- p.12 / Chapter 2.2.1 --- Set Partitioning --- p.13 / Chapter 2.3 --- Trellis-Coded Quantization --- p.14 / Chapter 2.4 --- Joint TCQ/TCM System --- p.17 / Chapter 2.4.1 --- The Combined Receiver --- p.17 / Chapter 2.4.2 --- Viterbi Decoding --- p.19 / Chapter 2.4.3 --- Sequence MAP Decoding --- p.20 / Chapter 2.4.4 --- Sliding Window Decoding --- p.21 / Chapter 2.4.5 --- Block-Based Decoding --- p.23 / Chapter Chapter 3 --- Soft Decoding Joint TCQ/TCM over AWGN Channel --- p.25 / Chapter 3.1 --- System Model --- p.26 / Chapter 3.2 --- TCQ with Optimal Soft-Decoder --- p.27 / Chapter 3.3 --- Gaussian Memoryless Source --- p.30 / Chapter 3.3.1 --- Theorem Limit --- p.31 / Chapter 3.3.2 --- Performance on PAM Constellations --- p.32 / Chapter 3.3.3 --- Performance on PSK Constellations --- p.36 / Chapter 3.4 --- Uniform Memoryless Source --- p.38 / Chapter 3.4.1 --- Theorem Limit --- p.38 / Chapter 3.4.2 --- Performance on PAM Constellations --- p.39 / Chapter 3.4.3 --- Performance on PSK Constellations --- p.40 / Chapter Chapter 4 --- Soft Decoding Joint TCQ/TCM System over Rayleigh Fading Channel --- p.42 / Chapter 4.1 --- Wireless Channel --- p.43 / Chapter 4.2 --- Rayleigh Fading Channel --- p.44 / Chapter 4.3 --- Idea Interleaving --- p.45 / Chapter 4.4 --- Receiver Structure --- p.46 / Chapter 4.5 --- Numerical Results --- p.47 / Chapter 4.5.1 --- Performance on 4-PAM Constellations --- p.48 / Chapter 4.5.2 --- Performance on 8-PAM Constellations --- p.50 / Chapter 4.5.3 --- Performance on 16-PAM Constellations --- p.52 / Chapter Chapter 5 --- Joint TCVQ/TCM System --- p.54 / Chapter 5.1 --- Trellis-Coded Vector Quantization --- p.55 / Chapter 5.1.1 --- Set Partitioning in TCVQ --- p.56 / Chapter 5.2 --- Joint TCVQ/TCM --- p.59 / Chapter 5.2.1 --- Set Partitioning and Index Assignments --- p.60 / Chapter 5.2.2 --- Gaussian-Markov Sources --- p.61 / Chapter 5.3 --- Simulation Results and Discussion --- p.62 / Chapter Chapter 6 --- Conclusion and Future Work --- p.64 / Chapter 6.1 --- Conclusion --- p.64 / Chapter 6.2 --- Future Works --- p.65 / Bibliography --- p.66 / Appendix-Publications --- p.73