Analysis of Connections between Pseudocodewords

Authors

Nathan Axvig, University of Nebraska - LincolnFollow
Deanna Dreher, University of Nebraska - Lincoln
Katherine Morrison, University of Nebraska - LincolnFollow
Eric T. Psota, University of Nebraska-LincolnFollow
Lance C. Pérez, University of Nebraska-LincolnFollow
Judy L. Walker, University of Nebraska - LincolnFollow

Document Type

Article

Date of this Version

2009

Citation

Published in IEEE Transactions on Information Theory ( Volume: 55 , Issue: 9 , Sept. 2009 )

DOI: 10.1109/TIT.2009.2025529

Comments

Copyright 2009 IEEE. Used by permission.

Abstract

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 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.