Codeword or noise? Exact random coding exponents for joint detection and decoding

Nir Weinberger, Neri Merhav

Research output: Contribution to journalArticlepeer-review


We consider the problem of coded communication, where in each time frame, the transmitter is either silent or transmits a codeword from a given (randomly selected) codebook. The task of the decoder is to decide whether transmission has taken place, and if so, to decode the message. We derive the optimum detection/decoding rule in the sense of the best tradeoff among the probabilities of decoding error, false alarm, and misdetection. For this detection/decoding rule, we then derive single-letter characterizations of the exact exponential rates of these probabilities for the average code in the ensemble. It is shown that previously proposed decoders are in general strictly suboptimal.

Original languageEnglish
Article number6848789
Pages (from-to)5077-5094
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number9
StatePublished - Sep 2014
Externally publishedYes


  • Joint detection/decoding
  • error exponent
  • false alarm
  • misdetection
  • random coding
  • synchronization
  • unequal error protection


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