### 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 language | English (US) |
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Title of host publication | IEEE International Symposium on Information Theory - Proceedings |

Pages | 2 |

Number of pages | 1 |

State | Published - 2002 |

Externally published | Yes |

Event | 2002 IEEE International Symposium on Information Theory - Lausanne, Switzerland Duration: Jun 30 2002 → Jul 5 2002 |

### Other

Other | 2002 IEEE International Symposium on Information Theory |
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Country | Switzerland |

City | Lausanne |

Period | 6/30/02 → 7/5/02 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IEEE International Symposium on Information Theory - Proceedings.*pp. 2, 2002 IEEE International Symposium on Information Theory, Lausanne, Switzerland, 6/30/02.

}

TY - GEN

T1 - Stopping sets and the girth of tanner graphs

AU - Orlitsky, Alon

AU - Urbanke, R.

AU - Viswanathan, K.

AU - Zhang, Junan

PY - 2002

Y1 - 2002

N2 - 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.

AB - 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.

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M3 - Conference contribution

SP - 2

BT - IEEE International Symposium on Information Theory - Proceedings

ER -