Stopping sets and the girth of tanner graphs

Alon Orlitsky, R. Urbanke, K. Viswanathan, Junan Zhang

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

57 Citations (Scopus)

Abstract

Recent work has related the error probability of iterative decoding over erasure channels to the presence of stopping sets in the Tanner graph of the code used. In particular, it was shown that the smallest number of uncorrected erasures is the size of the graph's smallest stopping set. Relating stopping sets and girths, we consider the size σ(d, g) of the smallest stopping set in any bipartite graph of girth g and left degree d. For g ≥ 8 and any d, we determine σ(d, g) exactly. For larger gs we bound σ(d, g) in terms of d, showing that for fixed d, σ(d,g) grows exponentially with g. Since constructions of high-girth graphs are known, one can therefore design codes with good erasure-correction guarantees under iterative decoding.

Original languageEnglish (US)
Title of host publicationIEEE International Symposium on Information Theory - Proceedings
Pages2
Number of pages1
StatePublished - 2002
Externally publishedYes
Event2002 IEEE International Symposium on Information Theory - Lausanne, Switzerland
Duration: Jun 30 2002Jul 5 2002

Other

Other2002 IEEE International Symposium on Information Theory
CountrySwitzerland
CityLausanne
Period6/30/027/5/02

Fingerprint

Iterative decoding
Error probability

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Orlitsky, A., Urbanke, R., Viswanathan, K., & Zhang, J. (2002). Stopping sets and the girth of tanner graphs. In IEEE International Symposium on Information Theory - Proceedings (pp. 2)

Stopping sets and the girth of tanner graphs. / Orlitsky, Alon; Urbanke, R.; Viswanathan, K.; Zhang, Junan.

IEEE International Symposium on Information Theory - Proceedings. 2002. p. 2.

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

Orlitsky, A, Urbanke, R, Viswanathan, K & Zhang, J 2002, Stopping sets and the girth of tanner graphs. in IEEE International Symposium on Information Theory - Proceedings. pp. 2, 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland, 6/30/02.
Orlitsky A, Urbanke R, Viswanathan K, Zhang J. Stopping sets and the girth of tanner graphs. In IEEE International Symposium on Information Theory - Proceedings. 2002. p. 2
Orlitsky, Alon ; Urbanke, R. ; Viswanathan, K. ; Zhang, Junan. / Stopping sets and the girth of tanner graphs. IEEE International Symposium on Information Theory - Proceedings. 2002. pp. 2
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