## Abstract

We revisit the multicasting approach to the analysis of converse bounds that we recently introduced, and present a refined proof technique for upper bounding the mismatch capacity of the DMC PYX with decoding metric q. To this end, we present an algorithm, which given a 2-user broadcast channel PY ZX, decoding metrics (q, p), and rate-R codebook, produces a sub-codebook of possibly lower rate R', which has the property that the intersecting event of erroneous p-decoding by the Z receiver and correct q-decoding of the Y receiver has a vanishing probability. This results in a bound on the mismatch capacity of the channel to the Y-receiver that is given in terms of the sum of an achievable rate for a Z receiver of any broadcast channel having marginal PYX plus the corresponding rate reduction R - R'. We further detect the p∗ metric which yields the tightest bound out of all the type-dependent metrics, and focusing on the case of zero rate reduction, we show that the resulting bound is at least as tight as our previous best known upper bound [1]. We conclude by presenting sufficient conditions for the tightness of our bound and equivalence classes of code composition-channel-metric triplets.

Original language | English |
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Title of host publication | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 1130-1135 |

Number of pages | 6 |

ISBN (Electronic) | 9781538682098 |

DOIs | |

State | Published - 12 Jul 2021 |

Event | 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Virtual, Melbourne, Australia Duration: 12 Jul 2021 → 20 Jul 2021 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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Volume | 2021-July |

ISSN (Print) | 2157-8095 |

### Conference

Conference | 2021 IEEE International Symposium on Information Theory, ISIT 2021 |
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Country/Territory | Australia |

City | Virtual, Melbourne |

Period | 12/07/21 → 20/07/21 |

### Bibliographical note

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