A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in the Centre for Telecommunications Access and Services, School of Electrical and Information Engineering, October 2019 / In the field of forward error correction, the development of decoding algorithms with a high error correction performance and tolerable complexity has been of great interest for the reliable transmission of data through a noisy channel. The focus of the work done in this thesis is to exploit techniques used in forward error correction in the development of an iterative soft-decision decoding approach that yields a high performance in terms of error correction and a tolerable computational complexity cost when compared to existing decoding algorithms. The decoding technique developed in this research takes advantage of the systematic structure exhibited by linear block codes to implement an information set decoding approach to correct errors in the received vector outputted from the channel. The proposed decoding approach improves the iterative performance of the algorithm as the decoder is only required to detect and correct a subset of the symbols from the received vector. These symbols are referred to as the information set. The information set, which matches the length of the message, is then used decode the entire codeword. The decoding approach presented in the thesis is tested on both Reed Solomon and Low Density Parity Check codes. The implementation of the decoder varies for both the linear block codes due to the different structural properties of the codes. Reed Solomon codes have the advantage of having a row rank inverse property which enables the construction of a partial systematic structure using any set of columns in the parity check matrix. This property provides a more direct implementation for finding the information set required by the decoder based on the soft reliability information. However, the dense structure of the parity check matrix of Reed Solomon codes presents challenges in terms of error detection and correction for the proposed decoding approach. To counter this problem, a bit-level implementation of the decoding technique for Reed Solomon codes is presented in the thesis. The presentation of the parity check matrix extension technique is also proposed in the thesis. This technique involves the addition of low weight codewords from the dual code, that match the minimum distance of the code, to the parity check matrix during the decoding process. This helps add sparsity to the symbol-level implementation of the proposed decoder. This sparsity helps with the efficient exchange of the soft information during the message passing stage of the proposed decoder. Most high performance Low Density Parity Check codes proposed in literature lack a systematic structure. This presents a challenge for the proposed decoding approach in obtaining the information set. A systematic construction for a Quasi-Cyclic Low Density Parity Check code is also presented in this thesis so as to allow for the information set decoding. The proposed construction is able to match the error correction performance of a high performance Quasi-Cyclic Low Density Parity Check matrix design, while having the benefit of a low complexity construction for the encoder. In addition, this thesis also proposes a stopping condition for iterative decoding algorithms based on the information set decoding technique. This stopping condition is applied to other high performance iterative decoding algorithms for both Reed Solomon codes and Low Density Parity Check codes so as to improve the iterative performance. This improves on the overall efficiency of the decoding algorithms. / PH2020

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published_or_final_version / abstract / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

published_or_final_version / Electrical and Electronic Engineering / Master / Master of Philosophy

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International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / How to rise the reliability of the data transmission is one of the main problem faced by modern digital communication designers. This paper studies the error-correcting codes being suitable for the channel existing both the random and burst error. A new error control scheme is given. The scheme is a concatenated coding system using an interleaved Reed-Solomon code with symbols over GF (24) as the outer code and a Viterbi-decoded convolutional code as the inner code. As a result of the computer simulation, it is proved that the concatenated coding system has a output at a very low bit error rate (BER)and can correct a lot of compound error patterns. It is suitable for the serious disturb channel existing both the random and burst error. This scheme will be adopted for a remote control system.

M.Ing. / Application Layer Forward Error Correction (AL-FEC) is a relatively new concept which uses erasure codes to add reliability insurance to particular application streams on a network. This concept has become particularly popular for media streaming services. Fountain codes have shown promise as the erasure code of choice for these implementations. The Fountain code concept is a principle that has two popular instantiations, the Luby Transform (LT) code and the Raptor code. While the Raptor code is the more efficient of the two, the LT code is the focal point of our dissertation. Our main objective in this dissertation was broken up into two different primary objectives which we had to satisfy in its completion. The first of these primary objectives entailed the finding of sets of input parameters which would yield an optimal implementation of the LT code for a given set of input block sizes. The simulation work performed in this investigation was done on a wide range of input parameters for each input block size concerned. While there have been a number of other studies which have performed such parameter optimisation we have not found any that present such comprehensive results as we do. The second of the primary objectives related to the analysis of the code when applied as an AL-FEC reliability mechanism for streaming media. This simulation work was performed on simulated IP network environments using the NS2 network simulator. The codes which were applied to the network were based on the optimal parameter sets found in the first objective. We analysed the effective throughput achievable by the code in the face of various packet loss rates. With the data obtained from the simulations we then derived a constraint on the allowable bit-rate of media which uses the LT code as an AL-FEC reliability mechanism. In performing the work in this dissertation it was identified that it was required to develop the LT code related simulation tools for performing the respective investigations. This involved development of a stand-alone LT code simulator as well as an LT code AL-FEC reliability mechanism for NS2.