Thesis (Ph. D.)--West Virginia University, 2007. / Title from document title page. Document formatted into pages; contains xiv, 161 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 152-161).

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 109-114).

Thesis (Ph. D.)--University of Texas at Austin, 2006. / Vita. Includes bibliographical references.

D.Ing. / When digital information is to be transmitted over a communications channel or stored in a data recording system, it is first mapped onto a code sequence by an encoder. The code sequence has certain properties which makes it suitable for use on the channel, ie the sequence complies to the channel input restrictions. These input restrictions are often described in terms of a required power spectral density of the code sequence. In addition, the code sequence can also be chosen in such a way as to enable the receiver to correct errors which occur in the channel. The set of rules which governs the encoding process is referred to as a line code or a modulation code for the transmission or storage of data, respectively. Before a new line code or modulation code can be developed, the properties that the code sequence should have for compliance to the channel input, restrictions and possession of desired error correction capabilities have to be established. A code' construction algorithm, which is often time consuming and difficult to apply, is then used to obtain the new code. In this dissertation, new classes of sequences which comply to the input restrictions and error correction requirements of practical channels are defined, and new line codes and recording codes are developed for mapping data onto these sequences. Several theorems which show relations between' information theoretical aspects of different classes of code sequences are presented. Algorithms which can be used to transform an existing line code or modulation code into a new code for use on another channel are introduced. These algorithms are systematic and easy to apply, and precludes the necessity of applying a code construction algorithm.

M.Ing. / Certain properties of codewords after deletions or insertions of bits are investigated. This is used in the enumeration of the number of subwords or superwords after deletions or insertions. Also, new upper bounds for insertion/deletion correcting codes are derived from these properties. A decoding algorithm to correct up to two deletions per word for Helberg's s = 2 codes is proposed. By using subword and superword tables, new s = 2 codebooks with greater cardinalities than before are presented. An insertion/deletion channel model is presented which can be used in evaluating insertion/deletion correcting codes. By changing the parameters, various channel configurations can be attained. Furthermore, a new convolutional coding scheme for correcting insertion/deletion errors is introduced and an investigation of the performance is done by using the presented channel model.

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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