## Abstract

We propose a source/channel duality in the exponential regime, where success/failure in source coding parallels error/correctness in channel coding, and a distortion constraint becomes a log-likelihood ratio (LLR) threshold. We establish this duality by first deriving exact exponents for lossy coding of a memoryless source P, at distortion D, for a general i.i.d. codebook distribution Q, for both encoding success (R < R(P, Q, D)) and failure (R > R(P, Q, D)). We then turn to maximum likelihood (ML) decoding over a memoryless channel P with an i.i.d. input Q, and show that if we substitute P = QP, Q = Q, and D = 0 under the LLR distortion measure, then the exact exponents for decoding-error (R < I(Q, P)) and strict correct-decoding (R > I(Q, P)) follow as special cases of the exponents for source encoding success/failure, respectively. Moreover, by letting the threshold D take general values, the exact random-coding exponents for erasure (D > 0) and list decoding (D < 0) under the simplified Forney decoder are obtained. Finally, we derive the exact random-coding exponent for Forney's optimum tradeoff erasure/list decoder, and show that at the erasure regime it coincides with Forney's lower bound and with the simplified decoder exponent, settling a long standing conjecture.

Original language | English |
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Title of host publication | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 3140-3144 |

Number of pages | 5 |

ISBN (Electronic) | 9781509040964 |

DOIs | |

State | Published - 9 Aug 2017 |

Externally published | Yes |

Event | 2017 IEEE International Symposium on Information Theory, ISIT 2017 - Aachen, Germany Duration: 25 Jun 2017 → 30 Jun 2017 |

### Publication series

Name | IEEE International Symposium on Information Theory - Proceedings |
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ISSN (Print) | 2157-8095 |

### Conference

Conference | 2017 IEEE International Symposium on Information Theory, ISIT 2017 |
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Country/Territory | Germany |

City | Aachen |

Period | 25/06/17 → 30/06/17 |

### Bibliographical note

Publisher Copyright:© 2017 IEEE.

### Funding

1This research was supported in part by the Israel Academy of Science, grant # 676/15.

Funders | Funder number |
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Israel Academy of Sciences and Humanities | 676/15 |

## Keywords

- Correct-decoding exponent
- Erasure/list decoding
- Random coding exponents
- Source coding exponents