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Design And Analysis Of Graph-Based Codes Using Algebraic Lifts And Decoding Networks, Allison Beemer

Department of Mathematics: Dissertations, Theses, and Student Research

Error-correcting codes seek to address the problem of transmitting information efficiently and reliably across noisy channels. Among the most competitive codes developed in the last 70 years are low-density parity-check (LDPC) codes, a class of codes whose structure may be represented by sparse bipartite graphs. In addition to having the potential to be capacity-approaching, LDPC codes offer the significant practical advantage of low-complexity graph-based decoding algorithms. Graphical substructures called trapping sets, absorbing sets, and stopping sets characterize failure of these algorithms at high signal-to-noise ratios. This dissertation focuses on code design for and analysis of iterative graph-based message-passing decoders. The …

Combinatorial And Algebraic Coding Techniques For Flash Memory Storage, Kathryn A. Haymaker

Department of Mathematics: Dissertations, Theses, and Student Research

Error-correcting codes are used to achieve reliable and efficient transmission when storing or sending information across a noisy channel. This thesis investigates a mathematical approach to coding techniques for storage devices such as flash memory storage, although many of the resulting codes and coding schemes can be applied in other contexts. The main contributions of this work include the design of efficient codes and decoding algorithms using discrete structures such as graphs and finite geometries, and developing a variety of strategies for adapting codes to a multi-level setting.

Information storage devices are prone to errors over time, and the frequency …