### Abstract

We analyze the performance of Low-Density-Parity-Check codes in the error-floor domain where the Signal-to-Noise-Ratio, s, is large, s ≥ 1. We describe how the instanton method of theoretical physics, recently adapted to coding theory, solves the problem of characterizing the error-floor domain in the Laplacian channel. An example of the (155,64,20) LDPC code with four iterations (each iteration consisting of two semi-steps: from bits-tochecks and from checks-to-bits) of the min-sum decoding is discussed. A generalized computational tree analysis is devised to explain the rational structure of the leading instantons. The asymptotic for the symbol Bit-Error-Rate in the error-floor domain is comprised of individual instanton contributions, each estimated as ∼ exp(-linst;L s), where the effective distances, linst;L, of the the leading instantons are 7.6,8.0 and 8.0 respectively. (The Hamming distance of the code is 20.) The analysis shows that the instantons are distinctly different from the ones found for the same coding/decoding scheme performing over the Gaussian channel. We validate instanton results against direct simulations and offer an explanation for remarkable performance of the instanton approximation not only in the extremal, s→∞, limit but also at the moderate s values of practical interest.

Original language | English (US) |
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Title of host publication | 43rd Annual Allerton Conference on Communication, Control and Computing 2005 |

Publisher | University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering |

Pages | 1795-1804 |

Number of pages | 10 |

Volume | 4 |

ISBN (Print) | 9781604234916 |

State | Published - 2005 |

Externally published | Yes |

Event | 43rd Annual Allerton Conference on Communication, Control and Computing 2005 - Monticello, United States Duration: Sep 28 2005 → Sep 30 2005 |

### Other

Other | 43rd Annual Allerton Conference on Communication, Control and Computing 2005 |
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Country | United States |

City | Monticello |

Period | 9/28/05 → 9/30/05 |

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### ASJC Scopus subject areas

- Computer Networks and Communications
- Computer Science Applications

### Cite this

*43rd Annual Allerton Conference on Communication, Control and Computing 2005*(Vol. 4, pp. 1795-1804). University of Illinois at Urbana-Champaign, Coordinated Science Laboratory and Department of Computer and Electrical Engineering.