Result: Minimum Pseudoweight and Minimum Pseudocodewords of LDPC Codes

Title:
Minimum Pseudoweight and Minimum Pseudocodewords of LDPC Codes
Authors:
XIA, Shu-Tao, FU, Fang-Wei
Source:
IEEE transactions on information theory. 54(1):480-485
Publisher Information:
New York, NY: Institute of Electrical and Electronics Engineers, 2008.
Publication Year:
2008
Physical Description:
print, 30 ref
Original Material:
INIST-CNRS
Subject Terms:
Telecommunications, Télécommunications, Sciences exactes et technologie, Exact sciences and technology, Sciences appliquees, Applied sciences, Telecommunications et theorie de l'information, Telecommunications and information theory, Théorie de l'information, du signal et des communications, Information, signal and communications theory, Théorie de l'information, Information theory, Théorie du signal et des communications, Signal and communications theory, Codage, codes, Coding, codes, Borne inférieure, Lower bound, Cota inferior, Code contrôle parité, Parity check codes, Code correcteur erreur, Error correcting code, Código corrector error, Décodage maximum vraisemblance, Maximum likelihood decoding, Descodificación máxima verosimilitud, Graphe de Tanner, Tanner graph, Grafo de Tanner, Programmation linéaire, Linear programming, Programación lineal, Rapport signal bruit, Signal to noise ratio, Relación señal ruido, Fundamental cone, linear programming (LP) decoding, low-density parity-check (LDPC) codes, pseudocodewords, pseudoweight, stopping sets
Document Type:
Academic journal Article
File Description:
text
Language:
English
Author Affiliations:
Graduate School at Shenzhen of Tsinghua University, Shenzhen, Guangdong 518055, China
National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China
Chern Institute of Mathematics and the Key Laboratory of Pure Mathematics and Combinatorics, Nankai University, Tianjin 300071, China
ISSN:
0018-9448
Access URL:
http://pascal-francis.inist.fr/vibad/index.php?action=search&terms=19978139
Rights:
Copyright 2008 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Telecommunications and information theory
Accession Number:
edscal.19978139
Database:
PASCAL Archive

Further Information

In this correspondence, we study the minimum pseudoweight ana minimum pseudocodewords ot low-density parity-check (LDPC) codes under linear programming (LP) decoding. First, we show that the lower bound of Kelley, Sridhara, Xu, and Rosenthal on the pseudoweight of a nonzero pseudocodeword of an LDPC code whose Tanner graph has girth greater than 4 is tight if and only if this pseudocodeword is a real multiple of a codeword. Then, the lower bound of Kashyap and Vardy on the stopping distance of an LDPC code is proved to be also a lower bound on the pseudoweight of a nonzero pseudocodeword of an LDPC code whose Tanner graph has girth 4, and this lower bound is tight if and only if this pseudocodeword is a real multiple of a codeword. Using these results we further obtain that for some LDPC codes, there are no other minimum pseudocodewords except the real multiples of minimum weight codewords. This means that the LP decoding for these LDPC codes is asymptotically optimal in the sense that the ratio of the probabilities of decoding errors of LP decoding and maximum-likelihood decoding approaches 1 as the signal-to-noise ratio (SNR) tends to infinity. Finally, some LDPC codes are listed to illustrate these results.