## Abstract

Random coding of a channel with an erasure option is studied. By analyzing the large deviations behavior of the code ensemble, we obtain exact single-letter formulas for the error exponents in lieu of Forney's lower bounds. The analysis technique we use is based on an enhancement an specialization of tools for assessing the moments of certain distance enumerators. We specialize our results to the setup of the binary symmetric channel case with uniform random coding distribution and derive an explicit expression for the error exponent which, unlike Forney's bounds, does not involve optimization over two parameters. We also establish the fact that for this setup, the difference between the exact error exponent corresponding to the probability of undetected decoding error and the error exponent corresponding to the erasure event is equal to the threshold parameter. Numerical calculations indicate that for this setup, as well as for a Z-channel, Forney's bound coincides with the exact random coding exponent.

Original language | English |
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Title of host publication | 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings |

Pages | 260-264 |

Number of pages | 5 |

DOIs | |

State | Published - 2010 |

Event | 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States Duration: 13 Jun 2010 → 18 Jun 2010 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8103 |

### Conference

Conference | 2010 IEEE International Symposium on Information Theory, ISIT 2010 |
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Country/Territory | United States |

City | Austin, TX |

Period | 13/06/10 → 18/06/10 |

### Bibliographical note

Funding Information:This work has been supported by CNR, progetto finalizzato Chimica Fine II. The collaboration of G. Oliveri is also'aknowledged.