Recent developments in low-density parity-check codes

Wen Ching Winnie Li, Min Lu, Chenying Wang

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q-regular bipartite graphs with large girth constructed in [8]. The LDPC codes based on these graphs have attracted much attention. We show that the first few of these graphs are Ramanujan graphs.

Original languageEnglish (US)
Title of host publicationCoding and Cryptology - Second International Workshop, IWCC 2009, Proceedings
Pages107-123
Number of pages17
DOIs
StatePublished - Sep 10 2009
Event2nd International Workshop on Coding and Cryptology, IWCC 2009 - Zhangjiajie, China
Duration: Jun 1 2009Jun 5 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5557 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Workshop on Coding and Cryptology, IWCC 2009
CountryChina
CityZhangjiajie
Period6/1/096/5/09

Fingerprint

Low-density Parity-check (LDPC) Codes
Rational functions
Ramanujan Graphs
Numerator
Girth
Denominator
Graph in graph theory
Regular Graph
Bipartite Graph
Rational function
Generating Function

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Li, W. C. W., Lu, M., & Wang, C. (2009). Recent developments in low-density parity-check codes. In Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings (pp. 107-123). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5557 LNCS). https://doi.org/10.1007/978-3-642-01877-0_11
Li, Wen Ching Winnie ; Lu, Min ; Wang, Chenying. / Recent developments in low-density parity-check codes. Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. 2009. pp. 107-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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Li, WCW, Lu, M & Wang, C 2009, Recent developments in low-density parity-check codes. in Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5557 LNCS, pp. 107-123, 2nd International Workshop on Coding and Cryptology, IWCC 2009, Zhangjiajie, China, 6/1/09. https://doi.org/10.1007/978-3-642-01877-0_11

Recent developments in low-density parity-check codes. / Li, Wen Ching Winnie; Lu, Min; Wang, Chenying.

Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. 2009. p. 107-123 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5557 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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AB - In this paper we prove two results related to low-density parity-check (LDPC) codes. The first is to show that the generating function attached to the pseudo-codewords of an LDPC code is a rational function, answering a question raised in [6]. The combinatorial information of its numerator and denominator is also discussed. The second concerns an infinite family of q-regular bipartite graphs with large girth constructed in [8]. The LDPC codes based on these graphs have attracted much attention. We show that the first few of these graphs are Ramanujan graphs.

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Li WCW, Lu M, Wang C. Recent developments in low-density parity-check codes. In Coding and Cryptology - Second International Workshop, IWCC 2009, Proceedings. 2009. p. 107-123. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-01877-0_11