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Analysis Of Connections Between Pseudocodewords, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker
Analysis Of Connections Between Pseudocodewords, Nathan Axvig, Deanna Dreher, Katherine Morrison, Eric T. Psota, Lance C. Pérez, Judy L. Walker
Department of Mathematics: Faculty Publications
The role of pseudocodewords in causing noncodeword outputs in linear programming (LP) decoding, graph cover decoding, and iterative message-passing decoding is investigated. The three main types of pseudocodewords in the literature — linear programming pseudocodewords, graph cover pseudocodewords, and computation tree pseudocodewords — are reviewed and connections between them are explored. Some discrepancies in the literature on minimal and irreducible pseudocodewords are highlighted and clarified, and a value for the minimal degree cover necessary to realize an LP pseudocodeword is found. Additionally, some conditions for the existence of connected realizations of graph cover pseudocodewords are given. This allows for further …