## Abstract

The problem of mismatched decoding with an additive metric q for a discrete memoryelss channel W is addressed. Two max-min multi-letter upper bounds on the mismatch capacity C_{q}(W) are derived. We further prove that if the average probability of error of a sequence of codebooks converges to zero sufficiently fast, then the rate of the code-sequence is upper bounded by the 'product-space' improvement of the random coding lower bound on the mismatched capacity, C^{(∞)}_{q} (W), introduced by Csiszár and Narayan. In particular, if q is a bounded rational metric, and the average probability of error converges to zero faster than O(1/n), then R ≤ C^{(∞)}_{q} (W). Consequently, in this case if a sequence of codes of rate R is known to achieve average probability of error which is o(1/n), then there exists a sequence of codes operating at a rate arbitrarily close to R with average probability of error which vanishes exponentially fast. We conclude by presenting a general expression for the mismatch capacity of a general channel with a general type-dependent decoding metric.

Original language | English |
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Title of host publication | Proceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 531-535 |

Number of pages | 5 |

ISBN (Electronic) | 9781467377041 |

DOIs | |

State | Published - 28 Sep 2015 |

Event | IEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong Duration: 14 Jun 2015 → 19 Jun 2015 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2015-June |

ISSN (Print) | 2157-8095 |

### Conference

Conference | IEEE International Symposium on Information Theory, ISIT 2015 |
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Country/Territory | Hong Kong |

City | Hong Kong |

Period | 14/06/15 → 19/06/15 |

### Bibliographical note

Publisher Copyright:© 2015 IEEE.