## Abstract

The problem of block-coded communication where in each block the channel law belongs to one of two disjoint sets is considered. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to detect the set which contains the underlying channel. The simplified case where each of the sets is a singleton is studied first. The decoding error, false alarm, and misdetection probabilities of a given code are defined, and the optimum detection/decoding rule in a generalized Neyman-Pearson sense is derived. Sub-optimal detection/decoding rules are also introduced which are simpler to implement. Then, various achievable bounds on the error exponents are derived, including the exact single-letter characterization of the random coding exponents for the optimal detector/decoder. The random coding analysis is then extended to general sets of channels, and an asymptotically optimal detector/decoder under a worst case formulation of the error probabilities is derived, as well as its random coding exponents. The case of a pair of binary symmetric channels is discussed in detail.

Original language | English |
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Article number | 7994676 |

Pages (from-to) | 6364-6392 |

Number of pages | 29 |

Journal | IEEE Transactions on Information Theory |

Volume | 63 |

Issue number | 10 |

DOIs | |

State | Published - Oct 2017 |

Externally published | Yes |

## Keywords

- Detection complexity
- error exponents
- expurgated bounds
- false alarm
- joint detection/decoding
- misdetection
- mismatch detection
- random coding
- universal detection