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Thesis (Ph. D.)--University of Wisconsin--Madison, 1966. / Typescript. Vita. Includes bibliographical references (leaves 148-150).

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M.Ing. (Electrical and Electronic Engineering) / In this thesis, spectral shaping techniques are applied to the insertion/deletion error correcting codes. Spectral shaping techniques are introduced and applied to insertion/deletion error correcting codes. The attainable rates for subcodes with spectral properties are computed and presented. The theory of comma-free codes is briefly reviewed and a new construction method is given : for comma-free insertion/deletion correcting codes. This method serves as a lower bound on the cardinality of comma-free insertion/deletion codes. The idea of a marker is introduced as an alternative method of finding word boundaries. Rules are given for governing the construction of marker code books that can differentiate between additive and insertion/deletion errors. The marker code books are then used in such: a way as not to violate the spectral properties of the abovementioned insertion/deletion correcting codes. A new class of codes is presented that has higher order spectral zeros at both DC and the Nyquist frequency. It is shown that these codes are insertion/deletion and additive error correcting. Besides this, it is shown that the abovementioned class of codes can correct two adjacent additive errors.

In some practical systems, most of the errors are of 1 → 0 type and 0 → 1 errors occur very rarely. In this thesis, first, the capacity of the asymmetric channel is derived. The capacity of the binary symmetric channel (BSC) and the Z-channel can be derived from this expression as special cases. Second, the error detecting capability of Bose-Lin codes beyond the maximum designed error detection capability are described. Third, a new class of a systematic t-unidirectional error detecting codes over Z [subscript m], m≥2 is designed. These codes can detect 2 errors using r=2 check bits and up to m[superscript (r-2)] + r-2 errors using r>2 check bits. Some upper bound on the maximum number of detectable errors when using r check bits are given. Finally, some analysis on the data throughput when using the following protocols over the m-ary Z-Channel, m≥2 are derived: (1) ARQ protocols using t-Asymmetric Error Detecting (t-AED) codes. (2) ARQ protocols using All Asymmetric Error Detecting (AAED) codes. (3) Type-I Hybrid ARQ protocols using t-Asymmetric Error Correcting and All Asymmetric Error Detecting (t-EC/AAED) codes. (4) ARQ Protocols with diversity combining using t-Asymmetric Error Correcting and All Asymmetric Error Detecting (t-EC/AAED) codes. Finally, some open research problems are described. / Graduation date: 2005

In Shannon’s seminal paper, “A Mathematical Theory of Communication”, he defined ”Channel Capacity” which predicted the ultimate performance that transmission systems can achieve and suggested that capacity is achievable by error-correcting (channel) coding. The main idea of error-correcting codes is to add redundancy to the information to be transmitted so that the receiver can explore the correlation between transmitted information and redundancy and correct or detect errors caused by channels afterward. The discovery of turbo codes and rediscovery of Low Density Parity Check codes (LDPC) have revived the research in channel coding with novel ideas and techniques on code concatenation, iterative decoding, graph-based construction and design based on density evolution. This dissertation focuses on the design aspect of graph-based channel codes such as LDPC and Irregular Repeat Accumulate (IRA) codes via density evolution, and use the technique (density evolution) to design IRA codes for scalable image/video communication and LDPC codes for distributed source coding, which can be considered as a channel coding problem. The first part of the dissertation includes design and analysis of rate-compatible IRA codes for scalable image transmission systems. This part presents the analysis with density evolution the effect of puncturing applied to IRA codes and the asymptotic analysis of the performance of the systems. In the second part of the dissertation, we consider designing source-optimized IRA codes. The idea is to take advantage of the capability of Unequal Error Protection (UEP) of IRA codes against errors because of their irregularities. In video and image transmission systems, the performance is measured by Peak Signal to Noise Ratio (PSNR). We propose an approach to design IRA codes optimized for such a criterion. In the third part of the dissertation, we investigate Slepian-Wolf coding problem using LDPC codes. The problems to be addressed include coding problem involving multiple sources and non-binary sources, and coding using multi-level codes and nonbinary codes.

Thesis (Ph. D.)--Oregon State University, 2010. / Printout. Includes bibliographical references (leaves 47-48). Also available on the World Wide Web.

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