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Department of Mathematics: Dissertations, Theses, and Student Research
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On Dyadic Parity Check Codes And Their Generalizations, Meraiah Martinez
On Dyadic Parity Check Codes And Their Generalizations, Meraiah Martinez
Department of Mathematics: Dissertations, Theses, and Student Research
In order to communicate information over a noisy channel, error-correcting codes can be used to ensure that small errors don’t prevent the transmission of a message. One family of codes that has been found to have good properties is low-density parity check (LDPC) codes. These are represented by sparse bipartite graphs and have low complexity graph-based decoding algorithms. Various graphical properties, such as the girth and stopping sets, influence when these algorithms might fail. Additionally, codes based on algebraically structured parity check matrices are desirable in applications due to their compact representations, practical implementation advantages, and tractable decoder performance analysis. …