## Abstract

We introduce a new analysis technique that we use to derive a single-letter upper bound on the mismatch capacity of a stationary point-to-point memoryless channel with decoding metric q. Our bound is obtained by considering a multicast transmission over a two-user broadcast channel with decoding metrics q and ρ at the receivers, referred to as (q, ρ)-surely degraded. This channel has the property that the intersection event of the correct q-decoding of receiver 1 and the erroneous ρ-decoding of receiver 2 has zero probability for any codebook of a certain composition P . Our bound holds in the strong converse sense of exponential decay of the probability of correct decoding at rates above the bound. Several examples that demonstrate the strict improvement of our bound compared to previous results are analyzed. Further, we detect equivalence classes of isomorphic channel-metric pairs (W, q) that share the same mismatch capacity. We prove that if the class contains a matched pair, then our bound is tight and the mismatch capacity of the entire class is fully characterized and is equal to the LM rate, which is the highest rate achievable by random coding, and may be strictly lower than the Shannon (matched) capacity.

Original language | English |
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Title of host publication | 2020 IEEE Information Theory Workshop, ITW 2020 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

ISBN (Electronic) | 9781728159621 |

DOIs | |

State | Published - 11 Apr 2021 |

Event | 2020 IEEE Information Theory Workshop, ITW 2020 - Virtual, Riva del Garda, Italy Duration: 11 Apr 2021 → 15 Apr 2021 |

### Publication series

Name | 2020 IEEE Information Theory Workshop, ITW 2020 |
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### Conference

Conference | 2020 IEEE Information Theory Workshop, ITW 2020 |
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Country/Territory | Italy |

City | Virtual, Riva del Garda |

Period | 11/04/21 → 15/04/21 |

### Bibliographical note

Publisher Copyright:©2021 IEEE

### Funding

This work was supported by the Israel Science Foundation (ISF) grant no. 631/17.

Funders | Funder number |
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Israel Science Foundation | 631/17 |