Analysis of connections between pseudocodewords

Authors:
Nathan Axvig;Deanna Dreher;Katherine Morrison;Eric Psota;Lance C. Pérez;Judy L. Walker
Affiliations:
Department of Mathematics, University of Nebraska, Lincoln, NE;Department of Mathematics, University of Nebraska, Lincoln, NE;Department of Mathematics, University of Nebraska, Lincoln, NE;Department of Electrical Engineering, University of Nebraska, Lincoln, NE;Department of Electrical Engineering, University of Nebraska, Lincoln, NE;Department of Mathematics, University of Nebraska, Lincoln, NE
Venue:
IEEE Transactions on Information Theory
Year:
2009

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Abstract

The role of pseudocodewords in causing noncodeword outputs in linear programming 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 the minimal degree cover necessary to realize a pseudocodeword is found. Additionally, some conditions for the existence of connected realizations of graph cover pseudocodewords are given. This allows for further analysis of when graph cover pseudocodewords induce computation tree pseudocodewords. Finally, an example is offered that shows that existing theories on the distinction between graph cover pseudocodewords and computation tree pseudocodewords are incomplete.