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Exploration of AWGNC and BSC Pseudocodeword Redundancy [article]

Jens Zumbragel, Mark F. Flanagan, Vitaly Skachek
2010 arXiv   pre-print
This paper provides new results on the AWGNC, BSC, and max-fractional pseudocodeword redundancies of codes. The pseudocodeword redundancies for all codes of small length (at most 9) are computed.  ...  The AWGNC, BSC, and max-fractional pseudocodeword redundancy of a code is defined as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal to the  ...  ACKNOWLEDGMENTS The authors would like to thank Nigel Boston, Christine Kelley and Pascal Vontobel for helpful discussions.  ... 
arXiv:1005.3486v1 fatcat:5syloiijh5hzpahdsmlaquqosq

Exploration of AWGNC and BSC Pseudocodeword Redundancy

Jens Zumbrägel, Mark Flanagan, Vitaly Skachek
unpublished
This paper provides new results on the AWGNC, BSC, and max-fractional pseudocodeword redundancies of codes. The pseudocodeword redundancies for all codes of small length (at most 9) are computed.  ...  The AWGNC, BSC, and max-fractional pseu-docodeword redundancy ρ(C) of a code C is defined as the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight is equal  ...  ACKNOWLEDGMENTS The authors would like to thank Nigel Boston, Christine Kelley and Pascal Vontobel for helpful discussions.  ... 
fatcat:r4tji5ke7bgale7p7srb2ap2my

Graph-Cover Decoding and Finite-Length Analysis of Message-Passing Iterative Decoding of LDPC Codes [article]

Pascal O. Vontobel, Ralf Koetter
2005 arXiv   pre-print
Therefore, we give some characterizations of this polytope and explain its relation to earlier concepts that were introduced to understand the behavior of message-passing iterative decoding for finite-length  ...  We are interested in graph-cover decoding because it is a theoretical tool that can be used to show connections between linear programming decoding and message-passing iterative decoding.  ...  A different avenue is pursued by the following lemma and its corollaries which explore the effect of girth on the fundamental polytope upon adding redundant rows to a parity-check matrix.  ... 
arXiv:cs/0512078v1 fatcat:qizbeeqchrfc7el5rzyhuxewva

Pseudocodewords, Expander Graphs, and the Algebraic Construction of Low-density Parity-check Codes

Christine Ann Kelley
2006
X 2 ε classfile conforms to the University of Notre Dame style guidelines established in Spring 2004.  ...  This way, you have total control over how you want the symbols and sub-/superscripts in titles and captions look like.  ...  G: (a) if p is a good pseudocodeword of G, then w BSC/AW GN (p) ≥ w max−frac (p) ≥ d min , and (b) if p is a bad pseudocodeword [22] of G, then w BSC/AW GN (p) ≥ w max−frac (p) ≥ s min t , where t is  ... 
doi:10.7274/jd472v2639f fatcat:2dp5ttjhx5dwtf7gjhrpyhgcxu

Analysis of Dynamic Social and Technological Networks (Dagstuhl Seminar 11452) Coding Theory (Dagstuhl Seminar 11461)

Holger Giese, Bernhard Rumpe, Bernhard Schätz, Janos Sztipanovits, Lars Elden, Andreas, Vito Latora, Cecilia Mascolo, Mirco, Joachim Rosenthal, M Shokrollahi, Judy
2011 Science and Engineering of Cyber-Physical Systems   unpublished
This motivates our interest in M@RT, and especially in continuous re-appraisal of requirements at run-time, which calls for effective and light-way methods for model representation and reasoning at run-time  ...  We recently proposed a formulation for the Requirements Problem of SAS (revisiting foundational work by Zave et. al., TOSEM'97, and a more recent one by Jureta et al., RE'08), as a dynamic problem (Qureshi  ...  The AWGNC, BSC, and max-fractional pseudocodeword redundancies of a binary linear code are defined to be the smallest number of rows in a parity-check matrix such that the corresponding minimum pseudoweight  ... 
fatcat:bwnjnbq2bjbolk52twaysozyxu