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Full-Text Articles in Other Mathematics
On Coding For Partial Erasure Channels, Carolyn Mayer
On Coding For Partial Erasure Channels, Carolyn Mayer
Department of Mathematics: Dissertations, Theses, and Student Research
Error correcting codes have been essential to the technology we use in everyday life in digital storage, wireless communication, barcodes, and much more. Different channel models are used for different types of communication (for example, if information is sent to one person or to many people) and different types of errors. Partial erasure channels were recently introduced to model applications in which some information remains after an erasure event. These remnants of information may be used to increase the chances of successful decoding. We introduce a new partial erasure channel in which partial erasures correspond to individual bit erasures in …
Design And Analysis Of Graph-Based Codes Using Algebraic Lifts And Decoding Networks, Allison Beemer
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 …